Hindawi Computational Intelligence and Neuroscience Volume 2019, Article ID 6192980, 12 pages https://doi.org/10.1155/2019/6192980 Research Article Optimal Operation of the Hybrid Electricity Generation System Using Multiverse Optimization Algorithm Muhammad Sulaiman ,1 Sohail Ahmad,1 Javed Iqbal,1 Asfandyar Khan ,1 and Rahim Khan2 1Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, KP, Pakistan 2Department of Computer Science, Abdul Wali Khan University Mardan, Mardan, KP, Pakistan Correspondence should be addressed to Muhammad Sulaiman; [email protected] Received 12 September 2018; Revised 31 January 2019; Accepted 11 February 2019; Published 11 March 2019 Academic Editor: Antonino Laudani Copyright © 2019 Muhammad Sulaiman et al. *is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. *e ongoing load-shedding and energy crises due to mismanagement of energy produced by different sources in Pakistan and in- creasing dependency on those sources which produce energy using expensive fuels have contributed to rise in load shedding and price of energy per kilo watt hour. In this paper, we have presented the linear programming model of 95 energy production systems in Pakistan. An improved multiverse optimizer is implemented to generate a dataset of 100000 different solutions, which are suggesting to fulfill the overall demand of energy in the country ranging from 9587 MW to 27208 MW. We found that, if some of the power-generating systems are down due to some technical problems, still we can get our demand by following another solution from the dataset, which is partially utilizing the particular faulty power system. According to different case studies, taken in the present study, based on the reports about the electricity short falls been published in news from time to time, we have presented our solutions, respectively, for each case. It is interesting to note that it is easy to reduce the load shedding in the country, by following the solutions presented in our dataset. Graphical analysis is presented to further elaborate our findings. By comparing our results with state-of-the-art algorithms, it is interesting to note that an improved multiverse optimizer is better in getting solutions with lower power generation costs. 1. Introduction them depending on thermal sources [15]. In [14], it is re- ported that the gap between demand and production is Proper management and finding out optimal solutions to utilize expected to increase in the coming years. It is further re- the available power production sources is an important opti- ported in the literature [14, 18] that urban areas are facing a mization problem in Pakistan, which is the main theme of this load shading in summer season as of 10–12 hours, and in paper [1–11]. According to the reports in [12, 13], the demand rural areas, it is even worse as 16–18 hours a day. Urbani- of the power is increasing exponentially and which is causing an zation and rapid increase in population have caused an increase in load shedding each year [14]. *e cause of this increase in the industrial zones [19], and it is worth noting shortage is mismanagement of power production sources. that the demand of electricity was 16000 (MW) during According to a report published by National Electric summer of 2012 while the short fall was 8500 (MW) [20]. Power Regulatory Authority (NEPRA) in 2016 [15], the total In this study, we have explored a scientific decision- capacity of 27240 MW is installed in the country, whereas making approach in terms of mathematical programming the demand rises to 22000 MW in summer [16]. *ese for providing a strategy to utilize the available production production units can produce enough energy if all are sources of Pakistan to meet the demand of energy in dif- managed optimally. In [17], these production units were ferent seasons. However, in [21], a general mechanism was normally producing up to 13240 MW with 4760 MW of presented in terms of 5 major energy production types as X1 shortfall. In nomenclature, we have indicated all the 95 to X5. *ey have fixed the per unit price to estimate the installed capacities of electricity production with majority of overall mathematical model. We have extended the model 2 Computational Intelligence and Neuroscience and included 95 production sources, which generates Table 1: Electricity production constraints on each source. electricity using different means (oil, gas, wind, hydropower, Power unit Lower limit Upper limit and coal). We have implemented per unit price according to x the actual price of fuel used to run these sources. *e 1 0 3478 x production capacities of each source are given in Table 1 2 0 1000 x 0 1450 [22]. Our model will help to reduce the shortfall by utilizing 3 x4 0 243 the power production sources properly. x 0 184 In the last few years, evolutionary algorithms (EAs) are 5 x6 0 130 implemented to solve different real-world optimization x7 0 121 problems. EAs simulate social behavior or natural pro- x8 0 72 cedures in order to handle optimization problems with best x9 0 30 solution. Among the popular EAs are the Bat algorithm x10 0 22 [23, 24], grasshopper optimization algorithm (GOA) [25], x11 0 22 x and firefly algorithm (FA) [26, 27]. *e efficiency of met- 12 0 20 x aheuristics is better as compared to classical optimization 13 0 17 x techniques in solving optimization problems with iterations 14 0 14 x15 0 13.5 and random search behavior. *e main idea behind all EAs x 0 4 is the survival of the fittest, which in return increases the 16 x17 0 1 fitness of individuals in population. EAs are implemented x18 0 1 with different frameworks, which includes population x19 0 1655 structure and search equations [28]. EAs with different x20 0 1350 frameworks generate random populations. *en, all solu- x21 0 850 tions are evaluated according to a given objective function. x22 0 244 *e search space is explored and exploited in two phases. x23 0 195 x EAs get stuck in local optima due to their random search. 24 0 174 x Several papers are published in the literature to overcome 25 0 150 x 0 132 this problem in EAs [29, 30]. 26 x27 0 59 *e multiverse optimization algorithm (MVO) is a x 0 39 nature-inspired optimization technique given in [31]. *e 28 x29 0 35 key idea of MVO is inspired from the theory of multiverses. x30 0 17 Since its invention, it is applied to solve several real-world x31 0 247 problems. In [31], it is shown that MVO obtained very x32 0 100 competitive results compared with other metaheuristic x33 0 100 optimization algorithms. Also, Faris et al. [32] employed the x34 0 1260 MVO for training the multilayer perceptions in neural x35 0 560 x network. *e efficiency of their techniques was evaluated on 36 0 900 x different medical datasets from UCI repository. *e out- 37 0 362 x 0 365 come of their experiments is then compared to different 38 x39 0 29 metaheuristics, namely, Particle Swarm Optimization x 0 225 (PSO), Genetic Algorithm (GA), Differential Evolution (DE) 40 x41 0 165 Algorithm, and Cuckoo Search (CS). It was observed that x42 0 330 MVO was improved in terms of convergence and avoidance x43 0 94 of local optima. MVO still lacks behind in accuracy of results x44 0 152.5 and convergence speed. Fewer studies, like Levy-flight-based x45 0 226.5 MVO [33] and a quantum version of MVO [34], are recently x46 0 157 x proposed to further enhance the capabilities of MVO. Ex- 47 0 110 x perimental results show that they have improved the so- 48 0 179 x 0 165 lutions to some extent. 49 x50 0 188 Currently, as can be seen in the former review, there are x 0 201.5 limited works on improving the performance of MVO. *is 51 x52 0 136 work presents a new method of initialization with the MVO x53 0 140 algorithm called improved multiverse optimization algorithm x54 0 225 (IMVO). *e experimental results on mathematical model of x55 0 225 economic dispatch problem of electricity generation system in x56 0 1292 Pakistan and its three case studies show that IMVO is very x57 0 165 competitive over FA, Bat algorithm, and GOA. x58 0 120 x Furthermore, we have presented solutions to five case 59 0 131 x studies for proper management and production by all the 95 60 0 1638 x 0 232 energy producers in the country. Our model can be 61 Computational Intelligence and Neuroscience 3 Table 1: Continued. Universe (1) Power unit Lower limit Upper limit Universe (2) x 0 202 62 Universe (3) x63 0 660 x64 0 200 . x 0 200 Best universe 65 . x66 0 225 created so far . x67 0 164 x 0 412 68 Universe (n –1) x69 0 114 x70 0 225 Universe (n) x71 0 235 x72 0 350 Wormhole tunnel x73 0 52 White/black hole tunnel x 0 80 74 Figure 1: A sketch of MVO [31]. x75 0 110 x76 0 133.5 x 0 126 77 the white/black hole, and white points represent objects x78 0 990 x 0 137 which move through the wormhole. *ere are 5 assumptions 79 that are applied in MVO to the population/universe [31]: x80 0 325 x 81 0 325 (a) *e probability of having the white holes is directly x 82 0 340 proportional to the inflation rate.