energies

Article A Hybrid Ant Colony and Cuckoo Search Algorithm for Route Optimization of Heating Engineering

Yang Zhang 1,2 , Huihui Zhao 2 , Yuming Cao 1,*, Qinhuo Liu 2,* , Zhanfeng Shen 2, Jian Wang 3 and Minggang Hu 1

1 North China Power Engineering Co., Ltd. of China Power Engineering Consulting Group, Beijing 100120, China; [email protected] (Y.Z.); [email protected] (M.H.) 2 State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China; [email protected] (H.Z.); [email protected] (Z.S.) 3 School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 100044, China; [email protected] * Correspondence: [email protected] (Y.C.); [email protected] (Q.L.); Tel.: +86-010-648-49840 (Q.L.)



Received: 19 September 2018; Accepted: 3 October 2018; Published: 8 October 2018


Abstract: The development of remote sensing and intelligent algorithms create an opportunity to include ad hoc technology in the heating route design area. In this paper, classification maps and heating route planning regulations are introduced to create the fitness function. Modifications of ant colony optimization and the cuckoo search algorithm, as well as a hybridization of the two algorithms, are proposed to solve the specific Zhuozhou–Fangshan heating route design. Compared to the fitness function value of the manual route (234.300), the best route selected by modified ant colony optimization (ACO) was 232.343, and the elapsed time for one solution was approximately 1.93 ms. Meanwhile, the best route selected by modified Cuckoo Search (CS) was 244.247, and the elapsed time for one solution was approximately 0.794 ms. The modified ant colony optimization algorithm can find the route with smaller fitness function value, while the modified cuckoo search algorithm can find the route overlapped to the manual selected route better. The modified cuckoo search algorithm runs more quickly but easily sticks into the premature convergence. Additionally, the best route selected by the hybrid ant colony and cuckoo search algorithm is the same as the modified ant colony optimization algorithm (232.343), but with higher efficiency and better stability.

Keywords: heating engineering; route planning; ant colony optimization; cuckoo search; hybrid intelligent algorithm

1. Introduction With the acceleration of urbanization, heating engineering has become a common municipal infrastructure in modern cities, especially in the northern part of China. Central-heating facilities can significantly amplify the scale effect and protect the environment. Because the heating route often crosses the city and the engineering is mainly carried out underground, the heat routing decision-making process becomes more complicated. The job has been based on manual design until now. The travelling salesman problem (TSP) is a kind of route optimization problem where a salesperson has to visit a list of cities exactly once and then return to the departure city, with the aim of minimizing the total travelled distance or the overall cost of the trip [1]. Regarding the heating engineering route selection problem, there are several similarities compared with the TSP. For example, the visited cities should also be passed only once, and the aim is also to find the minimum of the fitness function. However, the optimum heating route does not traverse all cities, and the specific

Energies 2018, 11, 2675; doi:10.3390/en11102675 www.mdpi.com/journal/energies Energies 2018, 11, 2675 2 of 23 start point and end point of the route are usually different; furthermore, the route must follow several regulations rather than be selected randomly. Therefore, we referenced the intelligent algorithms suitable for the TSP and devoted them to improving and proposing an effective algorithm to settle our heating engineering route selection problem. Generally, intelligent algorithms can be classified into three types [2]: evolutionary algorithms (EAs) [3,4], trajectory-based algorithms [5,6], and swarm-intelligence (SI)-based algorithms [7,8]. SI-based algorithms often inspired by nature, especially biological systems. Through mimicking a population of simple agents or boids, the noncentralized control individual act should lead to the emergence of “intelligent” global behavior. SI-based algorithms can select the optimum solution by iterations of a number of generations. At each generation, the solutions are normally constructed based on historical information gained from previous generations [9]. Examples of SI-based algorithms include ant colony optimization (ACO) [10], particle swarm optimization (PSO) [11], artificial bee colony (ABC) [12], firefly algorithm (FA) [13], cuckoo search approach(CSA) [14], and intelligent water drops (IWD) [15]. There have been several research achievements using SI-based algorithms to address the TSP. In this study, we chose ACO and CSA as our research object, as both of them are well developed, high-performance algorithms that complement each other well. ACO was developed by Dorigo in 1991 inspired by the behavior of ants seeking for food [10]. In the natural world, ants of some species (initially) wander randomly, and upon finding food return to their colony while laying down pheromone trails. The other ants are more likely to follow the trail with higher pheromones and release their own pheromones along their trails. Meanwhile, the pheromone trail evaporates over time, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, the more time the pheromones have to evaporate. That is, the pheromone between two nodes may be reinforced and evaporated simultaneously. The positive feedback eventually leads to many ants following a single path, and the optimum path is selected. ACO was originally used for discrete optimization problems, and it specializes in solving the TSP. Although ACO was proposed a relatively long time ago, it is still widely used. Various studies have developed and improved the algorithm, such as the elitist ant system [16,17], the rank-based ant system (ASrank) [18], the max–min ant system (MMAS) [19,20], and the ant colony system (ACS) [21]. All of them are based on the modification of the ACO algorithm by adjusting the parameters or changing the search strategy. Most of the extension algorithms have been tested on the TSP, which confirms the central role of this problem in ACO research. There have also been some improvements to the parameters in recent years. Yu et al. [22] proposed ACO with a new “ant-weight strategy” pheromone updating rule; based on experimental results, they found that the proposed algorithm was effective for the capacitated vehicle routing problem (CVRP), which was a generalized TSP. Tuba et al. [23] proposed a new type of ACO and implemented it for the TSP. The method was based on pheromone trail correction and can avoid search stagnation. The correction calculation was based on the properties of the best-found solution so far. Meanwhile, there are some studies devoted to hybrid ACO with other intelligent algorithms to increase efficiency. Chen and Chien presented the genetically simulated annealing ant colony system with PSO techniques for solving the TSP [24]. Deng et al. [25] proposed a novel two-stage hybrid algorithm called the GA-PSO-ACO algorithm that combined the evolutionary ideas of the genetic algorithms, PSO and ACO. Mahi [26] proposed a new hybrid method to optimize parameters using PSO. In addition, the 3-opt heuristic method was added to the proposed method to improve local solutions. Zhang coupled ACO with path relinking method to solve the TSP [27]. Kaabachi implied the decision support system to highlight the performance of ACO [28]. Wei introduced the minimum spanning tree and proposed an evolutionary ACO algorithm [29]. CSA was developed by Yang and Deb [14] in 2009 inspired by the brood parasitism behavior of cuckoos. Cuckoos lay eggs in the host’s nest by Lévy flights and carefully matches its eggs to the host’s eggs. If the host recognizes the cuckoo’s eggs in its nest, it will either throw the eggs out or simply desert its nest and make a new one elsewhere. The surviving eggs hatch and the birds grow up, and the cycle of the next generation starts. The best nest is selected after a number of generations have Energies 2018, 11, 2675 3 of 23 been produced. CSA is a relatively new algorithm that has rapidly developed since it was proposed. It is effective in solving continuous optimization problems [30,31]. However, there have also been several attempts to modify and apply the algorithm to the discrete TSP. Generally, the modification can be categorized into two classes. One is the adjustment of the parameters, and the other is hybridization with other intelligence algorithms [32]. For the first method, Uroš Mlakar et al. [33] proposed a hybrid self-adaptive CS algorithm (HSA-CS) with which the search space was explored using three exploration search strategies, i.e., random long-distance search strategy, stochastic moderate-distance search strategy and stochastic short-distance search strategy. Saelim et al. [34] proposed crossover and random replacement for generating new solutions in place of Lévy flight, and the switching parameter pa was treated as being adaptive. The proposed algorithm was used to solve seven TSPs, and outperformed the original CS. Ouaarab et al. [35] proposed the random-key cuckoo search (RKCS) algorithm for solving the TSP. RKCS can switch between the continuous and combinatorial search space, which enable cuckoo search to provide a good search mechanism with a fine balance between intensification and diversification. Additionally, Ouaarab et al. [36] improved and developed the CSA by rebuilding three types of cuckoos. The new category of the cuckoo made it possible to perform more efficiently with fewer iterations. For the second method, Abu-Srhan et al. [37] combined CS with GA to avoid the local minima problem and to benefit from the advantages of both types of algorithms. A 2-opt operation was added to the algorithm to improve the results. Teymourian et al. [38] enhanced the IWD and CS algorithms for solving the CVRP. The authors approached the CVRP with four state-of-the-art algorithms: an improved intelligent water drops (IIWD) algorithm; an advanced cuckoo search (ACS) algorithm; and two hybrid algorithms coupling these methods, called a local search hybrid algorithm (LSHA) and a post-optimization hybrid algorithm (POHA). LSHA and POHA took advantage of the merits of ACS and IIWD, and can effectively handle CVRP, where in most cases, LSHA outperformed other three algorithms in the literature. Besides, CS has been hybrided with improved shuffled frog leaping algorithm [39], global harmony search algorithm [40], simulated annealing algorithm [41], FA [42] and so on. As mentioned above, there have been various studies on ACO and CS aimed at solving the TSP. However, studies for optimizing the heating route in reality are rare. The ACO algorithm is constructive to global search, whereas the CS algorithm is capable to localized search. Therefore, a hybrid algorithm that combines the two ideas may result in a two-stage procedure that can surpass each of them individually. In this paper, we modified the ACO and CS algorithms, and proposed a hybrid ant colony and cuckoo search (HACCS) algorithm to combine the advantages of both algorithms. The HACCS was then applied to the Zhuozhou–Fangshan (ZF) heating engineering project. This study is organized as follows. Section2 introduces the study area and the study context, and the principle of heating route selection is provided as well. Data organization and management methods are supplied for subsequent applications. Section3 provides the fundamentals and improvements of ACO and CSA algorithms, as well as the hybrid HACCS algorithm. Section4 shows the operation results of the modified ACO, the modified CS and the HACCS algorithms. The results are compared with the real route that was selected manually. Finally, Section5 discusses the findings and draws the concluding remarks. Several future research directions of interest are outlined.

2. Materials and Methods

2.1. Study Area The ZF heating engineering project is important according to the 13th five-year plan for China energy development. The project is beneficial to Jing-Jin-Ji collaborative development and can significantly optimize the energy structure of Beijing. The total heating coverage of the project is approximately 35 million square meters. After the implementation of the project, the coal consumption of heating, CO2 emissions, carbon emissions, SO2 emissions, and NOx emissions can be reduced by 425,000 tons, 623,000 tons, 17 tons, 34 tons, and 102 tons per year, respectively. Thus, it plays Energies 2018, 11, 2675 4 of 23 Energies 2018, 11, x FOR PEER REVIEW 4 of 23 an importantreduced by role 425,000 in the tons, improvement 623,000 tons, of 17 the tons, regional 34 tons, urban and 102 environment tons per year, and respectively. the residents’ Thus, qualityit of life.plays an important role in the improvement of the regional urban environment and the residents’ Thequality ZF of heating life. engineering project starts from the Zhuozhou thermal power plant in Hebei provinceThe and ZF ends heating at the engineering Fangshan project boiler starts plant from in Beijing. the Zhuozhou The locations thermal ofpower the startplant pointin Hebei and the province and ends at the Fangshan boiler plant in Beijing. The locations of the start point and the end end point are shown in Figure1. From the image acquired from Google Earth, we can generally find point are shown in Figure 1. From the image acquired from Google Earth, we can generally find that that the landcover type of the study area are mainly high-grade highway (HGH), highway under the landcover type of the study area are mainly high-grade highway (HGH), highway under constructionconstruction (HUC), (HUC), vegetation, vegetation, water, water, and and buildings. buildings.

FigureFigure 1. The 1. The location location of of the the start start point point andand end po pointint of of the the ZF ZF heating heating engineering engineering project. project.

2.2. The2.2. PrincipleThe Principle of the of the Heating Heating Route Route Selection Selection In thisIn this study, study, we we focused focused on on the the route route selection selection for for the the preliminary preliminary design design phase, phase, as the as detailed the detailed route design for the construction phase required more sensitive data, such as the other pipe network route design for the construction phase required more sensitive data, such as the other pipe network distribution of the study area, which were difficult to acquire. So our primary task was to provide distribution of the study area, which were difficult to acquire. So our primary task was to provide the the general direction and critical nodes of an alternative optimum route for further refinement. general directionHeating route and critical decision-making nodes of anshould alternative follow several optimum principles. route for We further selected refinement. the regulations Heatingfrom the routedesign decision-making code for the city heating should networ followk several (CJJ 34-2010) principles. [43]. The We regulations selected the related regulations to our from the designstudy are code listed for theas follows: city heating network (CJJ 34-2010) [43]. The regulations related to our study are listed as follows: (1) Heating pipes through nonbuilt areas should be laid along the highway. (1) (2)Heating Heating pipes pipes through along nonbuiltthe urban areasroad should be be parallel laid along to the the center highway. line of the road and lay outside of the roadway. The same pipe should be laid only on one side of the street. (2) Heating pipes along the urban road should be parallel to the center line of the road and lay (3) Heating pipes across the river, railway and road should perpendicularly intersect with each outsideother. of Under the roadway. special circumstances, The same pipe the should intersec betion laid angle only between on one the side pipeline of the and street. railway or (3) Heatingsubway pipes should across not the be river, less than railway 60°; andthe inters roadection should angle perpendicularly between the pipeline intersect and with river each or other. Underroad special should circumstances, not be less thanthe 45°. intersection angle between the pipeline and railway or subway should not be less than 60◦; the intersection angle between the pipeline and river or road should There are regulations for the geological conditions: the selection of a heating pipe network is ◦ suitablenot be lessto avoid than 45unfavorable. areas (i.e., soft soil areas, earthquake fault zones, landslide danger zones, and high underground water level areas). The minimum horizontal clearance and the There are regulations for the geological conditions: the selection of a heating pipe network is suitable to avoid unfavorable areas (i.e., soft soil areas, earthquake fault zones, landslide danger zones, and high underground water level areas). The minimum horizontal clearance and the minimum vertical clearance between the heating pipe and other pipes are also indicated in the design code. Energies 2018, 11, 2675 5 of 23

In addition to regulations raised by the design code for the city heating network, the proprietor also treats cost as a significant consideration. The cost can be divided into two parts: one is related to the length of the route, and the other is related to the land use patterns. Obviously, the longer the route, the higher the cost. Regarding the land use patterns, if the construction occupies farm land or urban land or lands that have been used for other purposes, the occupancy fee and relocation fee should be considered in the total cost. Crossing water may be inevitable under some circumstances, it is a special case because shield technology may bring high cost. Generally, the cost per meter can be ranked as follows: cross water, cross building, cross vegetation, along HGH, along HUC. We treat the fitness function as the sum weight of all the pixels the route covers. The route with the minimum value of the fitness function should be the optimum route. Thus, the route selection can be transferred into a search for the minimum value of the fitness function as shown in Equation (1).

t f = ∑ (IBp × wb + IVp × wv + IWp × ww + IHGHp × whgh + IHUCp × whuc) (1) p=1 where p is the pixels the route covered. One can trace the corresponding row and column numbers of p in the binary images. IB is the building binary image where the building pixels are set to 1 while other pixels are set to 0. IV, IW, IHGH, and IHUC represent the binary images of vegetation, water, HGH, and HUC, respectively. wb, wv, ww, whgh, and whuc represent the weights of building, vegetation, water, HGH, and HUC, respectively. For example, if the location of p is a building pixel, then the IBp is 1, and IVp, IWp, IHGHp, and IHUCp are 0, so only the wb has an effect on the fitness function f. ACO and CS are introduced to solve our route optimization problem. It is crucial to transfer the specific unresolved issues to the natural phenomena proposed by the algorithms. According to the regulations mentioned above, the heating route is preferred along the road. Therefore, it is a good idea to transfer the continuous image to discrete segments by breaking the roads into a number of segments at the intersections. The two endpoints of every segment are treated as the elementary entities (nodes). For example, in the ACO algorithm, the nodes can be compared to the cities; in the CS algorithm, the nodes can be compared to the location of eggs. Thus, we can derive a distance matrix from the node distribution as shown in Equation (2).   d1,1 d1,2 ... d1,n    d2,1 d2,2 ... d2,n  D =  (i, j ∈ [1, n]) (2)  ......  dn,1 dn,2 ... dn,n where i and j are the nodes in the study area. The distance matrix has characteristics as follows:

(1) The distance of the same node equals 0, i.e., if i = j, di,j = 0;

(2) The distance from node i to node j equals the distance from node j to node i, i.e., di,j = dj,i; (3) The distance between node i and node j can be calculated by the pixel number and the weight of the pixels. The formula can be expressed as Equation (3):

 h  whgh × ∑ IHGHp (a)   p=1  c di,j = whuc × ∑ IHUCp (b) (i, j ∈ [1, n], i 6= j) (3)  p=1   sl  ∑ (IBp × wb + IVp × wv + IWp × ww) (c)  p=1

The equation illustrates the calculation method of the distance matrix. Suppose the start point is node i, and the end point is node j, where i and j belong to the same road, the distance between i Energies 2018, 11, 2675 6 of 23 and j is the sum weight of the pixels that the real curving segment covered. When the road is HGH, the distance can be calculated as (a) in Equation (3). When the road is the HUC, the distance can be calculatedEnergies as2018 (b), 11, inx FOR Equation PEER REVIEW (3). Otherwise, if i and j belong to different roads, then the6 of distance23 between i and j is the sum weight of pixels that the linear segment from i to j covered, as shown in (c) can be calculated as (a) in Equation (3). When the road is the HUC, the distance can be calculated as (b) in Equationin Equation (3). (3). Otherwise, if i and j belong to different roads, then the distance between i and j is the sum weight of pixels that the linear segment from i to j covered, as shown in (c) in Equation (3). 2.3. Data Organization and Management To2.3. executeData Organization intelligent and Management route optimization, several data sets were collected and processed. The classificationTo execute data intelligent were the route essential optimization, data for several our algorithms.data sets were We collected extracted and 5processed. classification The maps from theclassification Google Earthdata were image. the essential Figure2 data shows for our the algorithms. HGH, HUC, We vegetation, extracted 5 classification water, and maps building from binary images.the StatisticsGoogle Earth show image. that thereFigure are 2 shows 35 highways, the HGH, 10 HUC, country vegetation, roads, 128 water, building and building groups, binary 15 rivers or images. Statistics show that there are 35 highways, 10 country roads, 128 building groups, 15 rivers lakes, and the rest of the areas are regarded as vegetation. or lakes, and the rest of the areas are regarded as vegetation.

(a) Classification map of HUC (b) Classification map of HGH (c) Classification map of water

(d) Classification map of building (e) Classification map of vegetation

FigureFigure 2. 2.Classification Classification maps maps of of the the study study area. area.

AccordingAccording to theto the principle principle of heating heating route route sele selection,ction, the routes the routesalong the along HUC theor HGH HUC have or HGH priority. Furthermore, because the cost of laying the heating line along the HUC is lower than along have priority. Furthermore, because the cost of laying the heating line along the HUC is lower than the HGH, the HUC has preference. Regarding vegetation, buildings and water, the occupancy fee alongand the relocation HGH, the fee HUC may has decrease preference. successively. Regarding We as vegetation,signed weights buildings of different and classifications water, the occupancy by fee andDelphi relocation method. fee The may weights decrease of the successively.land cover types We were assigned set to 0.0477, weights 0.0953, of different0.190, 0.286, classifications and 0.381 by Delphifor method. HUC, HGH, The vegetation, weights of building the land groups, cover and types wate werer, respectively. set to 0.0477, In other 0.0953, words, 0.190, we 0.286, assigned and 0.381 for HUC,0.0477 HGH, to the vegetation,HUC pixels in building the HUC groups, binary imag ande, water, 0.0953 respectively. to the HGH pi Inxels other in the words, HGH webinary assigned 0.0477image, to the 0.190 HUC to the pixels vegetation in the pixels HUC in binary the vegetati image,on 0.0953binary image, to the 0.286 HGH to pixelsthe building in the pixels HGH in binary image,the 0.190 building to the binary vegetation image, pixelsand 0.381 in theto the vegetation water pixels binary in th image,e water 0.286binary to image. the building Therefore, pixels the in the problem of this study was converted into searching for the minimum value of the sum weight of the building binary image, and 0.381 to the water pixels in the water binary image. Therefore, the problem pixels the route covered. of this study was converted into searching for the minimum value of the sum weight of the pixels the We extracted the two endpoints or intersections of the HUC and the HGH as nodes. From routeFigure covered. 2, we found that there was no intersection in the HUC. However, there were several Weintersections extracted among the two different endpoints HGH. or intersectionsHence, we divided of the the HUC HGH and into the segments HGH as by nodes. intersections. From Figure 2, we foundThere that were there a total was of 115 no road intersection segments in (230 the nodes) HUC.. Based However, on the there weights were we several assigned intersections for the pixels, among different HGH. Hence, we divided the HGH into segments by intersections. There were a total of Energies 2018, 11, 2675 7 of 23

115 roadEnergies segments 2018, 11, x (230FOR PEER nodes). REVIEW Based on the weights we assigned for the pixels, we calculated7 of 23 the distance between every two nodes. Thus, a 230 × 230 distance matrix was obtained. The distribution weEnergies calculated 2018, 11, xthe FOR distance PEER REVIEW between every two nodes. Thus, a 230 × 230 distance matrix was obtained.7 of 23 of theThe nodes distribution in the study of the area nodes is in shown the study in Figure area is3 shown. in Figure 3. we calculated the distance between every two nodes. Thus, a 230 × 230 distance matrix was obtained. The distribution of the nodes in the study area is shown in Figure 3.

(a) Distribution of HUC nodes (b) Distribution of HGH nodes (c) Distribution of total nodes

(a) Distribution of HUCFigureFigure nodes 3. 3.The The( distributionb distribution) Distribution of the theof nodesHGH nodes nodesin in the the study study(c area.) Distribution area. of total nodes

Figure 3. The distribution of the nodes in the study area. ReferencedReferenced to [2 to,28 [2,28],], the the optimum optimum range range ofof the va variableriable (nodes) (nodes) number number should should be no be more no morethan than 75 for ACO and between 15 and 40 for CS. As it is unlikely that points far from the centre line will be 75 for ACOReferenced and between to [2,28], 15 the and optimum 40 for CS.range As of it the is va unlikelyriable (nodes) thatpoints number far should from be the no centremore than line will chosen between the start point and the end point, we eliminated points outside of the 8 km buffer be chosen75 for between ACO and the between start point15 and and40 for the CS. end As it point, is unlikely we eliminated that points pointsfar from outside the centre of line the will 8 km be buffer (Figure 4a). Meanwhile, the nodes at the intersections can be merged into one. As shown in Figure chosen between the start point and the end point, we eliminated points outside of the 8 km buffer (Figure4b,4a). the Meanwhile, 4 blue points theat the nodes intersection at the intersectionscan be merged can into be one merged red point. into Thus, one. the As number shown of in nodes Figure 4b, (Figure 4a). Meanwhile, the nodes at the intersections can be merged into one. As shown in Figure the 4 bluewas ultimately points at thedecreased intersection to 35. It can should be merged be noted into that one the redcorresponding point. Thus, distance the number matrix ofand nodes the was 4b, the 4 blue points at the intersection can be merged into one red point. Thus, the number of nodes ultimatelycovered decreased pixels of tothe 35. segments It should need be to noted be updated that the simultaneously. corresponding distance matrix and the covered was ultimately decreased to 35. It should be noted that the corresponding distance matrix and the pixels of the segments need to be updated simultaneously. covered pixels of the segments need to be updated simultaneously.

(a) Buffer of the study area (b) Merge of the intersection

(a) BufferFigure of 4. the Reduction study area of nodes by ( bbuffering) Merge and of the merging. intersection

Figure 4. Reduction of nodes by buffering and merging. 3. The Principle of theFigure Intelligent 4. Reduction Algorithms of nodes by buffering and merging. 3. The Principle of the Intelligent Algorithms 3. The3.1. Principle Modified ofAnt the Colony Intelligent Optimization Algorithms Algorithm

3.1. Modified3.1. ModifiedThe Ant ACO ColonyAnt algorithm Colony Optimization Optimization simulates Algorithmthe Algorithm optimization of ant foraging behavior. It was originally used to solve the TSP. The TSP can be described as an oriented graph with N cities (nodes) (4): The ACO algorithm simulates the optimization of ant foraging behavior. It was originally used The ACO algorithm simulates the optimization of ant foraging behavior. It was originally used to to solve the TSP. The TSP can be described asGNA an= oriented(), graph with N cities (nodes) (4): solve the TSP. The TSP can be described as an oriented graph with N cities (nodes) (4): (4) GNA= (), where N = {1, 2, 3 … n}, A = {(i, j)|i, j ∈ N}. The distance between two cities can be expressed as (dij(4))n×n , while the fitness function can be expressed asG Equation= (N, A )(5): (4) where N = {1, 2, 3 … n}, A = {(i, j)|i, j ∈ N}. The distance between two cities can be expressed as (dij)n×n, while the fitness function can be expressed as Equationn (5): where N = {1, 2, 3 ... n},A = {(i, j)|i, j ∈f N()wdd}.=+ The distance between two cities can be expressed as  iill−1 n1 (5) (d ) , while the fitness function can be expressedl=n2 as Equation (5): ij n×n f ()wdd=+  iill−1 n1 (5) l=2 n f (w) = d + d ∑ il−1il n1 (5) l=2

Energies 2018, 11, 2675 8 of 23

Energies 2018, 11, x FOR PEER REVIEW 8 of 23 where w is an arrangement of the N cities. It is worth noting that the last city coincides with the first where w is an arrangement of the N cities. It is worth noting that the last city coincides with the first city, which means that the ant should return to the start point. city, which means that the ant should return to the start point. Regarding our specific heating route optimization problem, the efficient route was only confined Regarding our specific heating route optimization problem, the efficient route was only to theconfined segments to the from segments the start from point the tostart the point end to point. the end For point. example, For example, as shown as inshown Figure in 5Figure, there 5, were 9 nodesthere in were the 9 graph, nodes supposein the graph, the suppose start point the start was point 1, and was the 1, and end the point end waspoint 6. was If the6. If routethe route one ant visitedone was ant 1visited→ 2 →was3 1→ → 42 →→ 35 →→ 46 →→ 5 →7 →6 →8 7→ → 98 →→ 91, → we 1, onlywe only updated updated the the pheromones pheromones from 1 1 to 6, i.e., τto12 ,6,τ i.e.,23, ττ3412, ,ττ2345, τ,34τ, 56τ45. , τ56.

FigureFigure 5. 5.A A sketchsketch map with with nine nine nodes. nodes.

TheThe value value of theof the fitness fitness function function for for oneone ant wa wass the the sum sum weight weight of ofthethe pixels pixels from from the start the start pointpoint to the to endthe end point. point. The The cities cities visitedvisited after after the the en endd point point were were ignored. ignored. Also, Also,taking takingFigure 5 Figure as an 5 as an example,example, the the costcost can be expressed expressed as as Equation Equation (6):(6): =++++ fant_ one sssss12 23 34 45 56 (6) fant_one = s12 + s23 + s34 + s45 + s56 (6) where sij is the cost of the segment from i to j. If i and j belong to the same road, sij is the sum weight whereof stheij is pixels the cost covered of the by segment the real curving from i toroad.j. If Otherwise,i and j belong sij refers to theto the same sum road, weightsij ofis pixels the sum in the weight of thecovered pixels linear covered segment by the from real i curvingto j. road. Otherwise, sij refers to the sum weight of pixels in the covered linearThe modified segment procedure from i to isj .shown as follows: The(1) modifiedRoute Construction procedure is shown as follows: (1) RouteBesides Construction the predefined parameters of the original ACO algorithms, we also need to initialize the start point (SP), end point (EP), nodes (N), binary image of HUC (imgC), binary image of HGH Besides(imgH), binary the predefined image of building parameters (imgB of), thebinary original image ACO of vegetation algorithms, (imgV we), binary also need image to of initialize water the start( pointimgW), (S andP), end weights point of ( EeveryP), nodes land (coverN), binary type ( imagew). Then, of HUCthe distance (imgC ),matrix binary can image be generated of HGH by (imgH ), binaryEquation image (3). of building (imgB), binary image of vegetation (imgV), binary image of water (imgW), and weightsEvery of ant every randomly land cover selects type a city (w ).and Then, stores the the distance visited cities matrix in cansequence be generated into a vector by Equation named (3). Everyvisited. antThe unvisited randomly cities selects are also a stored city and in a ve storesctor named the visited allowed. cities The ant in selects sequence the next into city a to vector k namedarrive visited. at according The unvisited to roulette cities wheels. are alsoThe storedrandom inprobability a vector namedptij () is allowed. calculated The following ant selects k the nextEquation city to(7). arrive at according to roulette wheels. The random probability pij(t) is calculated following Equation (7). τηαβ×  [()][()]ijtt ij  αβ k  τη× (a) pt()=  [ik (ttα )] [ ik β ( )] ij  ∈ [τij(t)] ×[ηij(t)] (7)  k allowedk  α β (a) k ∑ [τik0(t)] ×[ηik(t)] pij(t) =  k∈allowed (b) (7)  k  0 where i and j are the start point and the end point of the segment. (b) τ ij ()t is the intensity of the pheromone between i and j at time t. allowedk stores the yet where i and j are the start point and the end point of the segment. unvisited cities. α and β are two constants, that can be described as the weighted values of τij(t) is the intensity of the pheromoneη between i and j at time t. allowedk stores the yet unvisitedpheromone cities. andα and visibiβ arelity, two respectively. constants, thatij is canthe visibility be described of the as segment, the weighted which valuescan be expressed of pheromone as the reciprocal of the distance between i and j as shown in Equation (8):

Energies 2018, 11, 2675 9 of 23

Energiesand visibility, 2018, 11, respectively.x FOR PEER REVIEWηij is the visibility of the segment, which can be expressed as the reciprocal9 of 23 of the distance between i and j as shown in Equation (8): η = 1/d ηijij= 1/dij ij (8)(8)

k k If j belongs to allowedk, ptk () is calculated by (a) in Equation (7), else, kpt() is set to 0 as (b) If j belongs to allowedk, pijij(t) is calculated by (a) in Equation (7), else, pij(ijt) is set to 0 as (b) in inEquation Equation (7). (7). Different fromfrom thethe originaloriginal ACO ACO for for TSP, TSP, the the first first element element of theof the visited visited vector vector was was the fixedthe fixed start startpoint point for all for ants, all andants, the and random the random generation generation of the visitedof the visited vector wasvector from was the from second the point,second and point, the andvalid the points valid werepoints from were the from first the point first (startpoint point)(start point) to the to end the pointend point (not (not necessarily necessarily visited visited all theall the35points). 35 points). In the originaloriginal ACO,ACO, thethe nodes nodes can can be be connected connected randomly, randomly, with with the the only only constraint constraint being being that that the thenodes nodes cannot cannot be repeated be repeated in one in route.one route. However, Howeve in ther, in heating the heating route route optimization optimization problem, problem, the route the routeshould should also follow also follow the constraints the constraints that the that intersection the intersection angle between angle between two adjacent two segmentsadjacent shouldsegments be ◦ shouldno less thanbe no 90 less, and than there 90°, shouldand there not should be crossovers not be crossovers among the among segments. the Therefore,segments. whenTherefore, generating when generatingthe visited vector,the visited a stricter vector, node-selection a stricter strategynode-sel shouldection bestrategy conducted, should and be the conducted, pseudocode and is listed the pseudocodeas follows (Figure is listed6): as follows (Figure 6):

= for i1: Nallowed =−+−22 aXX (this last ) ( YY this last ) =−+−22 bXX (this next ) ( YY this next ) =−+−22 cXX (next last ) ( YY next last ) ()abc222+− cosθ = 2ab if cosθ < 0

discard Pnext ( X next , Y next ) end end Figure 6. PseudocodePseudocode for intersection angle constraints. where N is the number of the residual nodes still unvisited. Pnext(Xnext, Ynext) is one of the where Nallowed is the number of the residual nodes still unvisited. PXYnext(,) next next is one of the points from the allowed vector, while Pthis(Xthis, Ythis) and Plast(Xlast, Ylast) are the current point and points from the allowed vector, while P (,)XY and P (,)XY are the current point the previous point. this this this last last last and theAfter previous this procedure, point. a subset of the allowed vector was derived in which all the candidate pointsAfter conformed this procedure, to the heating a subset routing of the regulations. allowed vector Therefore, was derived the next in point which was all chosen the candidate from the pointssubset conformed instead of theto the previous heatingallowed routingvector. regulations. Inevitably, Therefore, there wasthe next a condition point was that chosen there from were the no subsetavailable instead points of forthethe previous next visited allowed node vector. before Inevitably, the ant reachedthere was the a condition end point. that If thisthere happened, were no availablethe ant was points declared for the to next be lost visite andd wasnode flagged before the to no ant longer reached participate the end point. in the If updating this happened, and fitness the antfunction was declared calculation. to be lost and was flagged to no longer participate in the updating and fitness function calculation. (2) Pheromone Updating (2) Pheromone Updating The pheromone can be initialized as a constant for all the segments, as shown in Equation (9): The pheromone can be initialized as a constant for all the segments, as shown in Equation (9): ττij ==∀C ∀i, j (9) ij Cij, (9) When all ants reach the end point, the path’s pheromone intensity should be updated, and the update is is divided divided into into two two steps: steps: one one is the is theevap evaporation,oration, and andthe theother other is the is reinforcement. the reinforcement. The formulationThe formulation is shown is shown in Equation in Equation (10): (10):

m k ττij ==− (1 − ρ)τττij + + ∆τ (10) ij(1 ) ij∑  ijij (10) = kk =1 τ k where m is the number of ants (solutions), 0 < ρ <= 1 is the evaporation rate of the pheromones,  ij is the pheromone released by the kth ant from path i to j. That is, the first part of the formula is the

Energies 2018, 11, 2675 10 of 23

k where m is the number of ants (solutions), 0 < ρ <= 1 is the evaporation rate of the pheromones, ∆τij is the pheromone released by the kth ant from path i to j. That is, the first part of the formula is the Energies 2018, 11, x FOR PEER REVIEW 10 of 23 evaporation of the pheromone, while the second part is the reinforcement of the pheromone. It is worthevaporation noting that of the the pheromone pheromone, updating while the wassecond only part focused is the onreinforcement the segments of the between pheromone. the start It is point and theworth end noting point. that the pheromone updating was only focused on the segments between the start point and the end point. (3) Iteration Stopping (3) Iteration Stopping There are two conditions for iteration stopping, one is the number of iterations reaching the value the user defined,There are and two the conditions other is allfor theiteration ants followingstopping, one the is same the routenumber (stagnant of iterations state). reaching the value the user defined, and the other is all the ants following the same route (stagnant state). The flowchart of the modified ACO is shown in Figure7. The flowchart of the modified ACO is shown in Figure 7.

Figure 7. Flowchart of the modified ACO. Figure 7. Flowchart of the modified ACO.

3.2. Modified3.2. Modified Cuckoo Cuckoo Search Search Approach Approach The CSThe is CS inspired is inspired by the by reproductionthe reproduction strategy strate ofgy cuckoos.of cuckoos. The The algorithm algorithm uses uses three three idealized idealized rules: rules: (1) Each(1) Each cuckoo cuckoo lays lays one one egg egg at at a a time time and and dumpsdumps it in in a a random random nest; nest; (2) A(2) fraction A fraction of the of nests the nests containing containing the best the eggs,best eggs or solutions,, or solutions, will carry will overcarry to over the nextto the generation; next (3) The numbergeneration; of nests is fixed and there is a probability that a host will discover an alien egg. If this occurs, the host can either discard the egg or build a new nest in a new location.

Energies 2018, 11, 2675 11 of 23

Because the original CS algorithm was designed to solving the continuous problems, there should be several modifications to suit the algorithm to the heating route selection problem. The modified procedure is shown as follows: (1) Initialization In this study, we set the dimension of the solution matrix as 5 × 35. The initial solutions can be given randomly or by other optimization algorithm, such as the modified ACO. The initial solutions should also follow the angle constraints like the modified ACO did. Similar to the modified ACO, the start point (SP), end point (EP), nodes (N), binary image of HUC (imgC), binary image of HGH (imgH), binary image of building (imgB), binary image of vegetation (imgV), binary image of water (imgW), and the weights of every land cover type (w)were initialized. Then, the distance matrix can be generated by Equation (3). Based on the initial solutions and the distance matrix, the best solution can be chosen and saved by comparing the value of the fitness function. Afterwards, the iterations were conducted and the new solutions by Lévy flights can be generated. The solution generation and updating were also confined from the start point to the end point. (2) Updating the nests by Lévy flights Lévy flight was executed when generating a new solution, and the updating formulation is expressed as Equation (11): t+1 t Xi = Xi + α ⊕ Levy(λ) (11) t t+1 where Xi and Xi represent the nests or the egg locations at time t and time t + 1. ⊕ represents the entry-wise operator. Because the search path hops randomly by Lévy flight, an adjustment called α was introduced according to the size of the problem, and α > 0. The formulation of the Lévy flight can be shown in Equation (12): µ Levy(λ) = (12) |υ|1/β where β is often set as 1.5. The parameters ν and µ are the random numbers following a normal distribution, as shown in Equation (13):

( 2 µ ∼ N(0, σµ) (a) 2 (13) υ ∼ N(0, συ ) (b)

2 2 where σµ and σν can be calculated by Equation (14):   Γ(1+β) sin(πβ/2) o1/β  σµ = (a) 2(β−1)/2Γ[(1+β)/2]β (14)  συ = 1 (b)

The Γ function can be expressed as Equation (15):

Z ∞ Γ(x) = e−ttx−1dt (15) 0

Regarding the specific heat routing problem, the nodes were discretely distributed. The distance by random Lévy flight maybe not exactly match the available nodes. Furthermore, the angle constraint should be considered as well. Referencing the modified ACO algorithm, we determined the alternative nodes by the pseudocode in Figure6. Then, the distances between the current node and the alternative nodes were calculated, the one closest to the Lévy flight distance was selected, and the specific node was chosen as the next visited one. There was also a condition that no eligible point existed for the next generation. If this happened, the solution was declared invalid. After all the solutions were Energies 2018, 11, x FOR PEER REVIEW 12 of 23 the alternative nodes by the pseudocode in Figure 6. Then, the distances between the current node Energiesand the2018 alternative, 11, 2675 nodes were calculated, the one closest to the Lévy flight distance was selected,12 of 23 and the specific node was chosen as the next visited one. There was also a condition that no eligible point existed for the next generation. If this happened, the solution was declared invalid. After all updated, the best solution of this generation was selected and saved by comparing the value of the the solutions were updated, the best solution of this generation was selected and saved by fitness function. comparing the value of the fitness function. (3) Updating the Nests if the Hosts Find the Eggs (3) Updating the Nests if the Hosts Find the Eggs A random matrix that with the same size as the nest matrix was generated and compared with A random matrix that with the same size as the nest matrix was generated and compared with the constant pa. Elements larger than pa should be updated by a random stepsize on condition that the constant pa. Elements larger than pa should be updated by a random stepsize on condition that the angle constraint was satisfied. the angle constraint was satisfied. (4) Iteration Stopping (4) Iteration Stopping There are two conditions for stopping iterations, one is the number of iterations reaching the There are two conditions for stopping iterations, one is the number of iterations reaching the value the user defined, and the other is all the solutions follow the same route (stagnant state). value the user defined, and the other is all the solutions follow the same route (stagnant state). The flowchart of the modified CS is shown in Figure8. The flowchart of the modified CS is shown in Figure 8.

Figure 8. Flowchart of the modified CS. Figure 8. Flowchart of the modified CS.

Energies 2018, 11, 2675 13 of 23 Energies 2018, 11, x FOR PEER REVIEW 13 of 23

3.3. Hybrid Ant Colony & Cuckoo Search (HACCS) Algorithm 3.3. Hybrid Ant Colony & Cuckoo Search (HACCS) Algorithm From the studies mentioned above, we can conclude that the ACO algorithm is good at exploring From the studies mentioned above, we can conclude that the ACO algorithm is good at exploringpromising promising areas of the areas TSP solutionof the TSP space. solution However, space. it However, is not skillful it is in not fine-tuning skillful in as fine-tuning the CS algorithm. as the CSMeanwhile, algorithm. the Meanwhile, performance the of performance the CS algorithm of the might CS algorithm be improved might given be improved good initial given solutions. good initialTherefore, solutions. in this Therefore, study, we coupledin this thestudy, modified we coupled ACO algorithm the modified with theACO modified algorithm CS algorithm,with the modifiednamed HACCS CS algorithm, algorithm. named The HACCS HACCS combines algorithm. the The merits HACCS of ACO comb in exploringines the merits solution of space ACO and in exploringCS in refining solution solutions. space and CS in refining solutions. TheThe HACCS HACCS algorithm algorithm includes includes two two modules: the the ACO ACO module module and and the CS module. The ACO modulemodule was was executed executed first first to to find find the promising so solutionlution areas (global exploration) and transfer the the 55 best solutions to to the the CS CS module module as as the the initial initial so solutions.lutions. Then, Then, the the CS CS module module was was used used to to find find the betterbetter local local optima optima (local exploitation). The The flowchart flowchart is shown in Figure 99..

Figure 9. Flowchart of HACCS. Figure 9. Flowchart of HACCS.

4.4. Results Results InIn reality, reality, the planning of the project was began in 2012, and and the the construction construction of of the the project project was was fromfrom 2017 2017 to to 2018. The The decision decision making making was was a a time consuming task required repeated negotiations with the planning department. Figure 10 shows the final route that was selected manually. The fitness function values of the manually selected route was 234.300.

Energies 2018, 11, 2675 14 of 23 with the planning department. Figure 10 shows the final route that was selected manually. The fitness function values of the manually selected route was 234.300. Energies 2018, 11, x FOR PEER REVIEW 14 of 23

FigureFigure 10. 10.The The manuallymanually selected selected heating heating route. route.

To quantitativelyTo quantitatively evaluate evaluate thethe algorithms, we we compared compared the results the results by the bymodified the modified ACO, the ACO, modified CS, and HACCS with the same number of iteration. The results were compared with the the modified CS, and HACCS with the same number of iteration. The results were compared with the route selected manually. Computer codes were developed in MATLAB for the algorithms. route selected manually. Computer codes were developed in MATLAB for the algorithms. 4.1. Route Analysis by Modified ACO Algorithm 4.1. Route Analysis by Modified ACO Algorithm As there were a total of 35 nodes for the route search, we set 34 ants (solutions) for the route search,As there which were meant a total that of 35the nodes size of for the the visited route matrix search, was we 34 set × 35. 34 The ants start (solutions) point was for set the as route the 1st search, whichnode meant (column that number: the size 41, of row the visitednumber: matrix 1457), while was 34the× end35. point The was start set point as the was 29thset node as (column the 1st node (columnnumber: number: 1411, 41,row row number: number: 31). The 1457), pheromone while the index end point(α) was was predefined set as the as 29th 1.0, nodethe heuristic (column index number: 1411,(β row) was number: 5.0, the evaporation 31). The pheromone index (ρ) was index 0.5, ( αand) was the predefined initial pheromone as 1.0, value the heuristic (τ) was 1.0 index for all (β) was 5.0, thesegments. evaporation To reinforce index the (ρ )pheromones, was 0.5, and a100 the times initial (Q) pheromone magnification value to the ( τvisibility) was 1.0 of forthe segment all segments. To reinforce(η) was added the pheromones, to the pheromone a 100 oftimes the corresponding (Q) magnification segment. to the visibility of the segment (η) was We set the number of iterations as 1000 for the modified ACO algorithm and repeated 20 times added to the pheromone of the corresponding segment. to verify its stability. The final fitness function values after 1000 iterations with 20 repetitions are We set the number of iterations as 1000 for the modified ACO algorithm and repeated 20 times to shown in Figure11. The average value was 240.620, while the best performer was 232.343. Compared verifyto itsthe stability. fitness function The final values fitness of the function manually values selected after route 1000 (234.300), iterations the with modified 20 repetitions ACO derived are showna in Figuredecent 11 solution.. The average However, value the stability was 240.620, was not while good: the among best the performer 20 repetitions, was 232.343.there were Compared 8 times to the fitnessthe fitness function function values values ofwere the still manually high after selected 1000 iterations. route (234.300), the modified ACO derived a decent solution.The detailed However, fitness function the stability value distribution was not good: is shown among in Figure the 20 12. repetitions, From the 3D there diagram, were we 8times the fitnesscan find function the convergence values were of the still modified high after ACO 1000 algorithm iterations. was good. There was an 80% chance that theThe modified detailed ACO fitness algorithm function can valueachieve distribution the minimum is value shown after in no Figure more than12. From400 iterations. the 3D diagram, we can findThe the best convergence route is shown of in the Figure modified 13. The ACO yellow algorithm line shows was the good. manual There route, was the an red 80% line chance is the that best route selected by the modified ACO. We found that the best route selected by the modified the modified ACO algorithm can achieve the minimum value after no more than 400 iterations. ACO preferred straight line instead of the right-angle as the manual route did. The reason may be The best route is shown in Figure 13. The yellow line shows the manual route, the red line is the weights we predefined was not exactly conformed to reality. As to the our knowledge, the the besthypotenuse route selected of a right by triangle the modified is less than ACO. the We sum found of its that two the side bests. However, route selected if the cost by the(weight modified ACOmultiplies preferred length) straight of linethe two instead sides ofis theless right-anglethan the cost as of thethe manualhypotenuse, route then did. it Theis more reason inclined may to be the weightschoose we the predefined two sides was of the not right exactly triangle, conformed as the manual to reality. route As did. to the our knowledge, the hypotenuse of a right triangle is less than the sum of its two sides. However, if the cost (weight multiplies length)

Energies 2018, 11, 2675 15 of 23

of theEnergies two sides 2018, 11 is, x less FORthan PEER theREVIEW cost of the hypotenuse, then it is more inclined to choose the15 two of 23 sides of theEnergies right triangle,2018, 11, x FOR as thePEER manual REVIEW route did. 15 of 23

Energies 2018, 11, x FOR PEER REVIEW 15 of 23

Figure 11. The final fitness function values after 1000 iterations with 20 repetitions of the modified ACO. FigureFigure 11. The 11. finalThe final fitness fitness function function values values after after 10001000 iter iterationsations with with 2020 repetitions repetitions of the of modified the modified ACO. ACO.

Figure 11. The final fitness function values after 1000 iterations with 20 repetitions of the modified ACO.

FigureFigure 12. 12.The The detailed fitness fitness function function values valuesof 1000 iter ofations 1000 with iterations 20 repetitions with of 20the modified repetitions ACO. of the modifiedFigure ACO. 12. The detailed fitness function values of 1000 iterations with 20 repetitions of the modified ACO. Figure 12. The detailed fitness function values of 1000 iterations with 20 repetitions of the modified ACO.

Figure 13. The best route of the modified ACO. Figure 13. The best route of the modified ACO.

FigureFigure 13. 13.The The best bestroute route of the modified modified ACO. ACO.

Energies 2018, 11, x FOR PEER REVIEW 16 of 23 EnergiesEnergies2018 2018, 11, 11, 2675, x FOR PEER REVIEW 1616 of of 23 23 The elapsed time of 20 repetitions is shown in Figure 14. The average elapsed time was 65.46 s. The elapsed time of 20 repetitions is shown in Figure 14. The average elapsed time was 65.46 s. ConsideringThe elapsed the time1000 ofiterations 20 repetitions and 34 is solutions shown in fo Figurer every 14 run,. The the average time consumed elapsed time for wasone solution 65.46 s. Considering the 1000 iterations and 34 solutions for every run, the time consumed for one solution Consideringwas approximately the 1000 1.93 iterations ms. and 34 solutions for every run, the time consumed for one solution was approximately 1.93 ms. was approximately 1.93 ms.

Figure 14. The time consumed for different iteration times of the modified ACO. FigureFigure 14.14.The Thetime timeconsumed consumedfor fordifferent different iteration iteration times times of of the the modified modified ACO. ACO. 4.2. Route Analysis by Modified CS Algorithm 4.2.4.2. RouteRoute AnalysisAnalysis byby ModifiedModified CS CS Algorithm Algorithm Given the initial solutions, the modified CS can be executed individually. Here, we randomly Given the initial solutions, the modified CS can be executed individually. Here, we randomly generatedGiven 5the nests initial (solutions) solutions, for the the modified route search CS ca asn thebe executedinitial solutions, individually. so the Here, size of we the randomly solution generated 5 nests (solutions) for the route search as the initial solutions, so the size of the solution matrix generatedmatrix was 5 5nests × 35. (solutions) The start pointfor the was route set assearch the 1stas thenode initial (column solutions, number: so the41, rowsize ofnumber: the solution 1457), was 5 × 35. The start point was set as the 1st node (column number: 41, row number: 1457), while the matrixwhile thewas end 5 × point35. The was start set pointas the was 29th set node as th (ce olumn1st node number: (column 1411, number: row number: 41, row number:31). Only 1457), three end point was set as the 29th node (column number: 1411, row number: 31). Only three parameters whileparameters the end were point predefined was set asfor the CS: 29th α (0.01), node β (c(1.5)olumn and number:pa (0.25). 1411, row number: 31). Only three were predefined for CS: α (0.01), β (1.5) and pa (0.25). parametersWe also were set predefinedthe number for of CS: iterations α (0.01), as β 1000(1.5) andfor thepa (0.25). modified CS algorithm and repeated 20 We also set the number of iterations as 1000 for the modified CS algorithm and repeated 20 times timesWe to alsoverify set its the stability. number The of finaliterations fitness as functi 1000on for values the modified after 1000 CS iterations algorithm with and 20 repeated repetitions 20 to verify its stability. The final fitness function values after 1000 iterations with 20 repetitions are timesare shown to verify in Figure its stability. 15. The The aver finalage valuefitness was functi 282.000on values while after the be 1000st performer iterations was with 244.247. 20 repetitions Similar shown in Figure 15. The average value was 282.000 while the best performer was 244.247. Similar to areto the shown modified in Figure ACO, 15. the The stability average of value the modified was 282.000 CS waswhile not the quite best well.performer Among was the 244.247. 20 repetitions, Similar the modified ACO, the stability of the modified CS was not quite well. Among the 20 repetitions, tothere the weremodified 15 times ACO, that the the stability fitness of function the modified values CS were was quite not quitehigh after well. 1000 Among iterations. the 20 repetitions, therethere were were 15 15 times times that that the the fitness fitness function function values values were were quite quite high high after after 1000 1000 iterations. iterations.

FigureFigure 15. 15.The The final final fitness fitness function function values values after after 1000 1000 iterations iterations with with 20 repetitions 20 repetitions of the of modified the modified CS. FigureCS. 15. The final fitness function values after 1000 iterations with 20 repetitions of the modified ComparedCS. to the fitness function values of the modified ACO (232.343) and the manually selected route (234.300),Compared the to best the performance fitness function (244.247) values of the of modifiedthe modified CS was ACO not as(232.3 good43) as theand modified the manually ACO. However,selectedCompared route it was (234.300), closerto the tofitness thethe manuallybest function performance selected values route.(244.247)of the As modified of shown the modified inACO Figure (232.3 CS 16 ,was43) the yellowandnot asthe good line manually shows as the theselectedmodified manual route ACO. route, (234.300), However, the red the line it bestwas is the performancecloser best to route the (244.247)manually of the modified of selected the modified CS. route. Both AsCS of shown themwas not overlapped in as Figure good 16,as well thethe exceptmodifiedyellow for line theACO. shows blue However, circle the manual area. it was The route, reasoncloser the to could red the line alsomanually is be the the best selected weights route route. we of setthe As wasmodified shown not exactly CS.in Figure Both conformed of 16, them the toyellowoverlapped reality. line If not showswell considering except the manual for the the weights route,blue circle the of thered area. pixels,line The is the thereason straight best could route lines also of are the be shortest modifiedthe weights between CS. we Both twoset ofwas points. them not overlapped well except for the blue circle area. The reason could also be the weights we set was not

Energies 2018, 11, x FOR PEER REVIEW 17 of 23

Energiesexactly 2018 conformed, 11, x FOR PEER to reality. REVIEW If not considering the weights of the pixels, the straight lines17 of are23 shortest between two points. Energiesexactly2018 conformed, 11, 2675 to reality. If not considering the weights of the pixels, the straight lines17 ofare 23 shortest between two points.

Figure 16. The best route of the modified CS.

The detailed fitness functionFigure value 16. The distribution best route ofis theshown modifiedmodified in Figure CS. 17. From the 3D diagram, we found that the convergence of the modified CS algorithm was not as good as the modified ACO. AlthoughThe detailed there was fitness fitness a 100% function function chance value value that distribution distributionthe modified is is shownCS shown algorithm in inFigure Figure can 17. ac17 Fromhieve. From thethe the3D minimum 3Ddiagram, diagram, value we wefoundafter found nothat more that the the convergencethan convergence 400 iterations, of ofthe the modified the modified final CSfitn CS alessgorithm algorithm value waswas was notstill not as much as good good higher as as the the thanmodified modified the manual ACO. ACO. Althoughselected route. theretherewas Thiswas a asituation 100% 100% chance chance also thatconfirmed that the the modified modi the advantagefied CS CS algorithm algorithm of the can CS can achieve in aca localhieve the search, minimumthe minimum but valuenot asvalue after well noafterin morea globalno thanmore search. 400 than iterations, 400 iterations, the final the fitness final value fitn wasess value still much was higherstill much than thehigher manual than selected the manual route. Thisselected situation route. also This confirmed situation thealso advantage confirmed of the the advantage CS in a local of search,the CS butin a notlocal as search, well in but a global not as search. well in a global search.

FigureFigure 17. 17.The The detailed detailed fitness fitness function function values values of 1000of 1000 iterations iterations with with 20 repetitions 20 repetitions of the ofmodified the modified CS. CS. The elapsed time of 20 repetitions is shown in Figure 18. The average elapsed time was 3.97 s. Figure 17. The detailed fitness function values of 1000 iterations with 20 repetitions of the modified Considering the 1000 iterations and 5 solutions for every run, the time consumed for one solution was CS.The elapsed time of 20 repetitions is shown in Figure 18. The average elapsed time was 3.97 s. approximately 0.794 ms, which was much more quickly than the modified ACO. Considering the 1000 iterations and 5 solutions for every run, the time consumed for one solution wasThe approximately elapsed time 0.794 of 20 ms, repetitions which was is muchshown more in Figure quickly 18. than The theaverage modified elapsed ACO. time was 3.97 s. Considering the 1000 iterations and 5 solutions for every run, the time consumed for one solution was approximately 0.794 ms, which was much more quickly than the modified ACO.

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Figure 18. The time consumed for different iterationiteration timestimes ofof thethe modifiedmodified CS.CS. Figure 18. The time consumed for different iteration times of the modified CS. 4.3. Route Analysis by HACCS Algorithm 4.3. Route Analysis by HACCS Algorithm 4.3. Route Analysis by HACCS Algorithm BasedBased onon thethe workwork describeddescribed inin SectionsSections 4.14.1 andand 4.24.2,, wewe concludedconcluded thatthat thethe modifiedmodified ACOACO cancan escape fromBased local on the optima work relativelydescribed in well Sections but consumed4.1 and 4.2, we more concluded time. Meanwhile,that the modified the modifiedACO can CS escapeescape from from local local optima optima relatively relatively well well but but consumed consumed moremore time. time. Meanwhile, Meanwhile, the themodified modified CS ran CS ran ran more quickly but easily stuck into the premature convergence. In this study, we proposed the moremore quickly quickly but buteasily easily stuck stuck into into the the premature premature convconvergence. In In this this study, study, we we proposed proposed the hybrid the hybrid hybrid algorithm(HACCS) that coupled the ACO and CS algorithms. HACCS was consisted of the algorithm(HACCS)algorithm(HACCS) that that coupled coupled the the ACO ACO and and CS CS algorithms. HACCS HACCS was was consisted consisted of the of modifiedthe modified modifiedACO ACOmodule ACOmodule and module and the themodified and modified the CS modified CS module. module. CS To To module. improveimprove To efficiency,efficiency, improve we we efficiency, set set the the number number we setof iterations theof iterations number as ofas iterations400 and400 andthe as 400 repetitionthe and repetition the repetitiontimes times as as 20 times 2 0for for asthe the 20 ACO forACO the module ACO module andand the the andCS CS module, the module, CS module, according according according to the to the to theconvergence convergenceconvergence study studystudy mentioned mentioned above. above. above. TheThe 55The bestbest 5 best routesroutes routes byby thebythe the ACOACO ACO modulemodule module areare are shown shownshown inin Figure Figure 19. 1919. The. TheThe fitness fitnessfitness function functionfunction values valuesvalues were werewere 232.343, 232.782, 232.782, 232.782, 232.877, respectively. Then, they were transferred to the CS 232.343,232.343, 232.782,232.782, 232.782, 232.782, 232.782, 232.782, 232.877, 232.877, respectively. respectively. Then, Then, they werethey transferredwere transferred to the CSto modulethe CS as themodule initial solutions.as the initial With solutions. the help With ofthe the optimizedhelp of the initialoptimized solutions, initial thesolutions, performance the performance of the modified of modulethe asmodified the initial CS would solutions. be improved. With the help of the optimized initial solutions, the performance of CSthe wouldmodified be improved.CS would be improved.

(a) The(a) The first first route route ((bb)) The The seconsecondd route route (c) ( Thec) The third third rout routee

(d) The fourth route (e) The fifth route (d) The fourth route (e) The fifth route FigureFigure 19. 19.Top Top 5 5 routes routes ofof the modified modified ACO ACO module. module. Figure 19. Top 5 routes of the modified ACO module. FigureFigure 20 shows20 shows the the best best route route byby the modified modified CS CS module. module. It is also It is the also final the best final route best by routethe by HACCS. The red line was the best route by the HACCS, while the yellow line was the manual the HACCS.Figure 20 The shows red linethe best was route the best by routethe modified by the HACCS, CS module. while It is the also yellow the final line best was route the manual by the selected route. We found that the best route by HACCS was the same as the best route by the selected route. We found that the best route by HACCS was the same as the best route by the HACCS.modified The ACO.red line was the best route by the HACCS, while the yellow line was the manual modifiedselected route. ACO. We found that the best route by HACCS was the same as the best route by the modified ACO.

Energies 2018, 11, 2675 19 of 23 EnergiesEnergies 2018 2018, 11, 11, x, FORx FOR PEER PEER REVIEW REVIEW 1919 of of 23 23

FigureFigureFigure 20. 20.20. The The best best route route of ofof the thethe HACCS. HACCS.HACCS.

TheTheThe final finalfinal fitness fitnessfitness function functionfunction values valuesvalues are areare shown shownshown in inin Figure FigureFigure 21. 2121. .Because BecauseBecause the thethe initial initialinitial solutions solutionssolutions were werewere optimized,optimized,optimized, the thethe value valuevalue of ofof the thethe algorithm algorithmalgorithm was waswas stable stablestable and andand maintained maintainedmaintained 232.343 232.343232.343 for forfor 20 2020 repetitions. repetitions.repetitions.

FigureFigure 21. 21. The The final finalfinal fitness fitnessfitness function function values valuesvalues with withwith 20 2020 repetitions repetitionsrepetitions of ofof the thethe HACCS. HACCS.HACCS.

Because the elapsed time for one solution was approximately 1.93 ms by the modified ACO, BecauseBecause the the elapsed elapsed time time for for one one solution solution was was a pproximatelyapproximately 1.93 1.93 ms ms by by the the modified modified ACO, ACO, the the the time consumed for one solution was approximately 0.794 ms by the modified CS, considering the timetime consumed consumed for for one one solution solution was was approximatel approximately y0.794 0.794 ms ms by by the the modified modified CS, CS, considering considering the the 400 iterations as well as the 34 solutions for ACO module and 5 solutions for CS module, the total time 400400 iterations iterations as as well well as as the the 34 34 solutions solutions for for ACO ACO module module and and 5 5solutions solutions for for CS CS module, module, the the total total consumed for the HACCS was approximately 27.836 s, which was more quickly than the modified timetime consumed consumed for for the the HACCS HACCS was was approximately approximately 27.836 27.836 s, s, which which was was more more quickly quickly than than the the ACO (65.46 s). modifiedmodified ACO ACO (65.46 (65.46 s). s). 5. Discussion 5.5. Discussion Discussion This study referenced state-of-the-art SI-based intelligent algorithms, specifically the ACO and ThisThis study study referenced referenced state-of-the-art state-of-the-art SI-based SI-based intelligent intelligent algorithms, algorithms, specifically specifically the the ACO ACO and and CS algorithms. With the modifications of each algorithm and the hybrid strategy, we presented CSCS algorithms. algorithms. With With the the modifications modifications of of each each al algorithmgorithm and and the the hybrid hybrid strategy, strategy, we we presented presented the the modifiedmodified ACO, ACO, the the modified modified CS, CS, as as well well as as th the eHACCS HACCS algorithms algorithms to to solve solve the the heating heating route route optimizationoptimization problem. problem. The The proposed proposed algorithms algorithms we werere applied applied to to the the ZF ZF heating heating engineering engineering project. project.

Energies 2018, 11, 2675 20 of 23 the modified ACO, the modified CS, as well as the HACCS algorithms to solve the heating route optimization problem. The proposed algorithms were applied to the ZF heating engineering project. To verify the modified ACO and modified CS algorithms, we set the number of iterations as 1000 and the repetition times as 20. Comparing to the fitness function value of the manual route (234.300), the best route selected by modified ACO was 232.343, the average value was 240.620 for 20 repetitions, and the elapsed time for one solution was approximately 1.93 ms. There was an 80% chance that the modified ACO algorithm can achieve the minimum value after no more than 400 iterations. Meanwhile, the best route selected by modified CS was 244.247, the average value was 282.000 for 20 repetitions, and the elapsed time for one solution was approximately 0.794 ms. There was a 100% chance that the modified CS algorithm can achieve the minimum value after no more than 400 iterations. We concluded that the modified ACO can find the route with smaller fitness function value, while the modified CS can find the route overlapped to the manual selected route better. The modified CS ran more quickly but easily stuck into the premature convergence. According to the convergence study mentioned above, the HACCS was executed with a 400 iteration and 20 repetition for the ACO module and the CS module. The top five best routes by the ACO module was transferred to the CS module as the optimized initial solutions. The best route selected by the HACCS was the same as the modified ACO algorithm (232.343), but with higher efficiency and better stability. In this study, we devoted to provide the general direction of an alternative optimum route for the preliminary design phase. With the help of our algorithms, we can give a quantitative assessment for the alternative routes. The features and innovations of this study lie in the following: (1) The modification of the original ACO and CS algorithms to solve the heating route optimization problem. By introducing high resolution remote sensing image and heating route selection principle, we extracted the critical discrete nodes, established the distance matrix and the fitness function. Additionally, the updating strategy was improved. (2) The presentation of the HACCS algorithm. By coupling of the ACO and CS algorithm, the advantage of the ACO in global search and the strength of the CS in fine-tuning can be fully displayed. (3) The application of the HACCS for solving the route selection problem in reality We proposed and applied the HACCS algorithm into the ZF heating route engineering project. The comparison and analysis showed that it is a feasible and effective way to solve practical route selection problems. There are several improvements that we can focus on in the future. One is the improvement of the operational efficiency. By introducing parallel computing technology, the computing scale can be enlarged, and the computation time can be significantly shortened. The other is the 3D detailed route optimization with the support of the secondary data, such as other pipeline distribution maps, geological profiles, and the delicate DEM and DSM. Furthermore, with the help of 3D GIS technology, the interaction of the route and the users can be realized. Finally, we expect that the HACCS algorithm can be applied to route selection problems in broader engineering problems.

Author Contributions: Conceptualization, Y.Z., H.Z. and J.W.; Data curation, Y.Z. and M.H.; Methodology, Y.Z. and H.Z.; Software, Y.Z.; Supervision, Y.C., Q.L. and Z.S.; Writing—original draft, Y.Z.; Writing—review & editing, Y.Z., H.Z., Y.C., Q.L., Z.S. and J.W. Funding: This research was funded by the National Key Research and Development Program, grant number 2018YFA0605503, and the Young Scientists Fund of the National Natural Science Foundation of China, grant number 41801257. Acknowledgments: We gratefully acknowledge the anonymous reviewers for their insightful comments on the manuscript. The authors wish to thank Dorigo M et al. and Xin-She Yang et al. for providing the original program for ant colony optimization and cuckoo search. The authors wish to thank Tao Chen et al. from Beijing gas Energies 2018, 11, 2675 21 of 23 and heating engineering design institute for providing valuable suggestions on heating route planning regulations. The authors wish to thank Lei Zhang, and Kuisheng Yang from North China Power Engineering Co., Ltd. of China Power Engineering Consulting Group for the introduction of ZF heating engineering project. Conflicts of Interest: The authors declare no conflicts of interest.

Abbreviations

ACO Ant Colony Optimization ACS Ant Colony System ABC Artificial Bee Colony ASrank Rank-based Ant System CVRP Capacitated Vehicle Routing Problem CSA Cuckoo Search Approach DCS Discrete Cuckoo Search EAs Evolutionary Algorithms FA Firefly Algorithm GA Genetic Algorithms HACCS Hybrid Ant Colony and Cuckoo Search HGH High-Grade Highway HSA-CS Hybrid Self-Adaptive CS HUC Highway Under Construction IIWD Improved Intelligent Water Drops IWD Intelligent Water Drops LSHA Local Search Hybrid Algorithm MMAS Max–Min Ant System PSO Particle Swarm Optimization POHA Post-Optimization Hybrid Algorithm RKCS Random-Key Cuckoo Search SI Swarm-Intelligence TSP Travelling Salesman Problem ZF Zhuozhou–Fangshan

References

1. Lawler, E.L.; Lenstra, J.K.; Kan, A.R.; Shmoys, D.B. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization; Wiley: Chichester, UK, 1985. 2. Shehab, M.; Khader, A.T.; Al-Betar, M. A survey on applications and variants of the cuckoo search algorithm. Appl. Soft Comput. 2017, 61, 1041–1059. [CrossRef] 3. Eiben, A.E.; Smith, J.E. Introduction to Evolutionary Computing; Springer: Berlin/Heidelberg, Germany, 2003. 4. Storn, R.; Price, K.V. Minimizing the real functions of the ICEC’96 contest by differential evolution. In Proceedings of the IEEE International Conference on Evolutionary Computation, Nagoya, Japan, 20–22 May 1996; pp. 842–844. 5. Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P. Optimization by simulated annealing. Science 1983, 220, 671–680. [CrossRef][PubMed] 6. Al-Betar, M.A. β-Hill climbing: An exploratory local search. Neural Comput. Appl. 2017, 28, 153–168. [CrossRef] 7. Beni, G.; Wang, J. Swarm intelligence in cellular robotic systems. In Robots and Biological Systems: Towards a New Bionics, Proceedings of the NATO Advanced Workshop on Robots and Biological Systems, Toscana, Italy, 26–30 June 1989; Springer: Berlin/Heidelberg, Germany, 1993; pp. 26–30. 8. Blum, C.; Merkle, D. Swarm Intelligence: Introduction and Applications, Natural Computing Series; Springer: Berlin/Heidelberg, Germany, 2008. 9. Bolaji, A.L.; Al-Betar, M.A.; Awadallah, M.A.; Khader, A.T.; Abualigah, L.M. A comprehensive review: Krill herd algorithm (KH) and its applications. Appl. Soft Comput. 2016, 49, 437–446. [CrossRef] Energies 2018, 11, 2675 22 of 23

10. Dorigo, M.; Maniezzo, V.; Colorni, A. The Ant System: An Autocatalytic Optimizing Process. Available online: https://pdfs.semanticscholar.org/9649/211474dcfc3a9fd75e5208ffd21d9dcb9794.pdf (accessed on 15 March 2018). 11. James, K.; Russell, E. Particle swarm optimization. In Proceedings of the 1995 IEEE International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; pp. 1942–1948. 12. Karaboga, D. An Idea Based on Honey Bee Swarm for Numerical Optimization; Technical Report; Computer Engineering Department, Engineering Faculty, Erciyes University: Melikgazi, Turkey, 2005. 13. Yang, X.-S. Nature-Inspired Meta Heuristic Algorithms; Luniver Press: Beckington, UK, 2008; pp. 242–246. 14. Yang, X.-S.; Deb, S. Cuckoo search via Lévy flights. In Proceedings of the World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India, 9–11 December 2009; pp. 210–214. 15. Shah-Hosseini, H. The intelligent water drops algorithm: A nature-inspired swarm-based optimization algorithm. Int. J. Bio-Inspired Comput. 2009, 1, 71–79. [CrossRef] 16. Dorigo, M. Optimization, Learning and Natural Algorithms. Ph.D. Thesis, Dipartimento di Elettronica, Politecnico di Milano, Milano, Italy, 1992. (In Italian) 17. Dorigo, M.; Maniezzo, V.; Colorni, A. Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 1996, 26, 29–41. [CrossRef][PubMed] 18. Bullnheimer, B.; Hartl, R.F.; Strauss, C. A new rank-based version of the ant system: A computational study. Cent. Eur. J. Oper. Res. Econ. 1999, 7, 25–38. 19. Stützle, T.; Hoos, H. MAX–MIN ant system and local search for the traveling salesman problem. In Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC’97), Indianapolis, IN, USA, 13–16 April 1997; pp. 309–314. 20. Stützle, T.; Hoos, H. Max–min ant system. Future Gener. Comput. Syst. 2000, 16, 889–914. [CrossRef] 21. Dorigo, M.; Gambardella, L.M. Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1997, 1, 53–66. [CrossRef] 22. Yu, B.; Yang, Z.-Z.; Yao, B. An improved ant colony optimization for vehicle routing problem. Eur. J. Oper. Res. 2009, 196, 171–176. [CrossRef] 23. Tuba, M.; Jovanovic, R. Improved ACO algorithm with pheromone correction strategy for the traveling salesman problem. Int. J. Comput. Commun. 2013, 8, 477–485. [CrossRef] 24. Chen, S.-M.; Chien, C.-Y. Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst. Appl. 2011, 38, 14439–14450. [CrossRef] 25. Deng, W.; Chen, R.; He, B.; Liu, Y.Q.; Yin, L.F.; Guo, J.H. A novel two-stage hybrid swarm intelligence optimization algorithm and application. Soft Comput. 2012, 16, 1707–1722. [CrossRef] 26. Mahi, M.; Baykan, Ö.K.; Kodaz, H. A new hybrid method based on particle swarm optimization, ant colony optimization and 3-opt algorithms for traveling salesman problem. Appl. Soft Comput. 2015, 30, 484–490. [CrossRef] 27. Zhang, X.; Tang, L. A new hybrid ant colony optimization algorithm for the traveling salesman problem. In Proceedings of the 4th International Conference on Intelligent Computing, Shanghai, China, 15–18 September 2008; pp. 148–155. 28. Kaabachi, I.; Jriji, D.; Krichen, S. A DSS Based on Hybrid Ant Colony Optimization Algorithm for the TSP. In Proceedings of the International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland, 11–15 June 2017; pp. 645–654. 29. Liu, W.; Zhou, Y. An effective hybrid ant colony algorithm for solving the traveling salesman problem. In Proceedings of the 2010 International Conference on Intelligent Computation Technology and Automation, Changsha, China, 11–12 May 2010. 30. Yang, X.-S.; Deb, S. Engineering optimisation by cuckoo search. Int. J. Math. Model. Numer. Optim. 2010, 1, 330–343. [CrossRef] 31. Gandomi, A.H.; Yang, X.-S.; Alavi, A.H. Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems. Eng. Comput. 2013, 29, 17–35. [CrossRef] 32. Chiroma, H.; Herawanb, T.; Fister, I., Jr.; Fister, I.; Abdulkareem, S.; Shuib, L.; Hamza, M.F.; Saadi, Y.; Abubakar, A. Bio-inspired computation: Recent development on the modifications of the cuckoo search algorithm. Appl. Soft Comput. 2017, 61, 149–173. [CrossRef] Energies 2018, 11, 2675 23 of 23

33. Mlakar, U.; Fister, I., Jr.; Fister, I. Hybrid self-adaptive cuckoo search for global optimization. Swarm Evol. Comput. 2016, 29, 47–72. [CrossRef] 34. Saelim, A.; Rasmequan, S.; Kulkasem, P.; Chinnasarn, K.; Rodtook, A. Migration planning using modified cuckoo search algorithm. In Proceedings of the 13th International Symposium on Communications and Information Technologies (ISCIT), Surat Thani, Thailand, 4–6 September 2013; pp. 621–626. 35. Ouaarab, A.; Ahiod, B.; Yang, X.-S. Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput. Appl. 2014, 24, 1659–1669. [CrossRef] 36. Ouaarab, A.; Ahiod, B.; Yang, X.-S. Random-key cuckoo search for the travelling salesman problem. Soft Comput. 2015, 19, 1099–1106. [CrossRef] 37. Abu-Srhan, A.; Daoud, E.A. A hybrid algorithm using a genetic algorithm and cuckoo search algorithm to solve the traveling salesman problem and its application to multiple sequence alignment. Int. J. Adv. Sci. Technol. 2013, 61, 29–38. [CrossRef] 38. Teymourian, E.; Kayvanfar, V.; Komaki, G.H.M.; Zandieh, M. Enhanced intelligent water drops and cuckoo search algorithms for solving the capacitated vehicle routing problem. Inf. Sci. 2016, 334–335, 354–378. [CrossRef] 39. Feng, Y.; Wang, G.; Feng, Q.; Zhao, X. An effective hybrid cuckoo search algorithm with improved shuffled frog leaping algorithm for 0–1 knapsack problems. Comput. Intell. Neurosci. 2014, 2014, 1–17. [CrossRef] [PubMed] 40. Feng, Y.; Wang, G.; Gao, X. A novel hybrid cuckoo search algorithm with global harmony search for 0–1 knapsack problems. Int. J. Comput. Intell. Syst. 2016, 9, 1174–1190. [CrossRef] 41. Alkhateeb,F.; Abed-alguni,B.H.Ahybridcuckoosearchandsimulatedannealingalgorithm. J. Intell. Syst. 2017. [CrossRef] 42. Elkhechafi, M.; Hachimi, H.; Elkettani, Y. A new hybrid cuckoo search and firefly optimization. Monte Carlo Methods Appl. 2018, 24, 71–77. [CrossRef] 43. People’s Republic of China Ministry of Housing and Urban-Rural Development. Design Code for City Heating Network (CJJ 34-2010); China Building Industry Press: Beijing, China, 2011.

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