Research on Route Optimization of Hazardous Materials Transportation Considering Risk Equity

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Article Research on Route Optimization of Hazardous Materials Transportation Considering Risk Equity

Liping Liu , Jiaming Li , Lei Zhou, Tijun Fan * and Shuxia Li

Business School, East China University of Science and Technology, Shanghai 200237, China; [email protected] (L.L.); [email protected] (J.L.); [email protected] (L.Z.); [email protected] (S.L.) * Correspondence: [email protected]

Abstract: The consequences of a hazmat accident can be catastrophic due to the characteristics of hazardous materials. Different from the models, which are constructed from the perspective of “government-carrier”, this paper considers the three objectives of the risk, the cost, and the compensation cost from the “government-carrier-public” perspective, so as to construct a route optimization model of hazmat transportation considering risk equity. Moreover, considering that the difference in regional emergency response time will significantly affect the risk, this research incorporates the emergency response time into the transportation risk assessment function, and realizes risk equity by minimizing the total compensation cost based on the difference in regional emergency response time. To solve the proposed model, a multi-objective genetic algorithm based on linear weighting is designed. The results obtained from the case study verify the necessity of considering the risk equity in the route optimization model of hazardous materials transportation and prove that the established model and algorithm can find an optimal route that meets the expectations of the government, the carrier, and the public. Keywords: hazardous materials; route optimization; risk equity; multi-objective genetic algorithm; Citation: Liu, L.; Li, J.; Zhou, L.; Fan, emergency response time T.; Li, S. Research on Route Optimization of Hazardous Materials Transportation Considering Risk Equity. Sustainability 2021, 13, 9427. 1. Introduction https://doi.org/10.3390/su13169427 Hazardous material (hazmat) refers to any type of substance that is capable of causing Academic Editor: Armando Cartenì harm to people, property, or the environment. The transportation of hazmat is essential not only for industrial countries like Germany and Canada, but also for developing countries, Received: 7 July 2021 resulting in the fact that the amount of hazmat transportation has reached an unprecedented Accepted: 17 August 2021 level in the past decade. Because many hazardous materials are flammable, explosive, or Published: 22 August 2021 corrosive, the risk generated by an accident during transportation must be considered; otherwise, the consequences will be catastrophic. For example, in July 2013, a driverless Publisher’s Note: MDPI stays neutral train with 72 tank cars of petroleum crude oil derailed in the city center in Lac-Mégantic, with regard to jurisdictional claims in Quebec, Canada, causing the death of at least 42 persons. On 1 July 2019, a tanker truck in published maps and institutional affil- Nigeria overturned and caught fire, leading to 48 deaths, and the number of injuries was iations. greater than 90. On 13 June 2020, a truck transporting liquefied petroleum gas exploded on the Shenhai Expressway in Wenling City, Zhejiang Province, killing 20 people and seriously injuring 24 others. Considering the tremendous consequences of a hazmat accident, many governments have established specific regulations for hazmat transportation. In addition, Copyright: © 2021 by the authors. many studies on hazmat transport have been conducted in terms of risk assessment, routing, Licensee MDPI, Basel, Switzerland. network design, etc. Some literature [1–3] on route optimization of hazmat transportation This article is an open access article usually establish a model considering the transportation risk and transportation cost from distributed under the terms and the perspectives of “government-carrier”. conditions of the Creative Commons However, with the development of society, the public is given increasing importance Attribution (CC BY) license (https:// to equity, and the concept of equity has been introduced into various research fields. For creativecommons.org/licenses/by/ the transportation of hazmat, apart from the total network risk, the risk equity, i.e., the 4.0/).

Sustainability 2021, 13, 9427. https://doi.org/10.3390/su13169427 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 9427 2 of 18

“fairness” of the spatial distribution of risk, should also be considered. When a certain route is selected as the transportation route for hazmat, it will naturally increase the risks around the route. Therefore, some literature [4,5] has begun to add the objective of risk equity to establish a route optimization model of hazmat transportation considering transportation risk, transportation cost, and risk equity from the “government-carrier-public” perspective. When assessing transportation risk in the route optimization model of hazmat transportation, studies [6–9] have adopted the population exposure risk approach. However, they mostly select the optimal route from the perspective of ex-ante planning, ignoring the importance of ex-post processing. When a hazmat accident occurs during transportation, the response of emergency departments near the link will decrease the harm. Therefore, it is of great practical signiﬁcance to consider the impact of the emergency response time on the transportation risk and risk equity. By integrating the emergency response time, we present a more practical risk assessment approach in order to construct a route optimization model of hazmat transportation from the perspective of ex-post processing. The main contributions of this study are that the emergency response time of the emergency departments around the link is included in the transportation risk assessment function. In the risk equity model, the risk compensation is made for the links that exceed the average risk of the selected route from the perspective of the risk compensation cost to highlight the risk equity. The study is structured as follows. The related literature is summarized in Section2 . Model building is presented in Section3. Section4 introduces the Solution produce. The computational results of the numerical study are presented and analyzed in Section5, before ending with the conclusions and future research.

2. Literature Review In this section, we briefly review several streams in hazmat transportation research relevant to this paper: (1) Risk assessment, (2) route optimization, and (3) risk equity consideration.

2.1. Risk Assessment The risk caused by an accident during hazmat transportation makes the transportation problem of hazmat much more complicated than when other materials are moved. How to measure the transportation risk of hazmat is one of the important issues in the field of hazmat transportation, because how to reduce the accidents of hazardous materials has become an important and urgent research topic in the safety management of hazardous materials [10]. The risk makes the transportation problem of hazmat much more complicated than when other materials are moved. Therefore, a variety of models have already been proposed to assess the risk in hazmat transportation. Alp [11] used the approach of Traditional Risk to capture risk. Saccomanno and Chan [12] proposed the Incident Probability model, which focused on using accident probability to represent risk. The Population Exposure model was used to measure the risk in hazmat transportation [13–17]. Erkut and Ingolfsson [18] proposed three risk measurement models based on the avoidance of major disasters. Many popular risk assessment approaches in earlier studies are summarized [19].

2.2. Route Optimization It is necessary not only to evaluate the transportation risk of hazmat to construct a transportation risk assessment function, but also to consider the inﬂuence of road speed limits, trafﬁc restrictions, vehicle capacity, road capacity, and other factors on the route optimization model of hazmat transportation during the transportation, so as to construct a route optimization model that can better comprehend the transportation situation of hazmat in reality. At present, many studies focus on the measurement of population risk in the route optimization of hazmat transportation. Considering factors such as the number of ex- posed people and accident probability in the transportation of hazmat, scholars have Sustainability 2021, 13, 9427 3 of 18

constructed the route optimization models of hazmat transportation that consider population risks [20,21]. Afterwards, Qu et al. [22] made improvements to the traditional model in terms of transportation methods, accident probability, and consequences. Bronf- man et al. [23] maximized the distance from population centers to hazmat transportation routes to reduce risk. Financial risk assessment tools such as VaR and CVaR have also been introduced in the route optimization model of hazmat transportation that consider population risk [24,25]. In addition to considering minimizing the total population risk, scholars also pay more attention to the trade-off between the two goals of risk and cost from the perspective of the government and the enterprise [1–4]. Scholars have begun to pay attention to the inﬂuence of uncertain factors such as road closures and emergencies on the route optimization of hazmat transportation considering population risks. Fan et al. [26] constructed a route optimization model considering road closure to solve the problem of urban hazmat transportation route optimization. Mohammadi et al. [27] studied the route optimization under the random interruption scenario of the multimodal transportation hub of hazmat. Hu et al. [28] established a multi-objective location path optimization model that can solve the problems of risk, cost, and customer satisfaction in the management of dangerous goods transportation under the constraints of trafﬁc restrictions. Su et al. [29] considered the uncertainty of the carrier’s route choice and constructed a model based on the conditional value-at-risk (CVaR) for route choice.

2.3. Risk Equity Consideration Since the transportation of hazmat will bring great potential risks, for the government, the main focus is to minimize the risks in the road transportation network. However, the consequence of such a decision may lead to a situation where hazmat is concentrated in a certain area and flows less frequently in other areas. Although route optimization has been achieved at the government level, for the public, especially those near the section where hazmat is transported, they will think that they are taking more risks than other individuals, and this will be psychologically unfair. Therefore, as the public’s awareness of risk equity increases, in the process of route optimization of hazmat transportation, risk equity should also be considered, that is, to make the spatial distribution of risks more balanced. Holeczek [30] proposed that the fair distribution of risk may appear as a good risk management strategy, especially in the eyes of the public. Keeney [31] first proposed in 1980 that risk equity is the maximum difference of risk levels between a fixed group of individuals. After that, Gopalan et al. [32,33] first introduced risk equity into vehicle path optimization as a constraint condition and established single-path and multi-path models for hazardous materials’ transportation in order to minimize transportation risk and achieve risk distribution equity on the premise that the risk difference assumed through the population region is less than the set threshold. Carotenuto et al. [34] fairly distributed the risk of hazardous materials transportation to the population by setting a risk threshold for each link. Kang et al. [35] introduced the value at risk model (VaR) from the financial field into the risk assessment of hazardous materials’ transportation and set the risk threshold for the risk difference between any two regions. Garrido and Bronfman [36] set an acceptable threshold for accident probability and accident consequences in urban transportation of a variety of hazardous materials, establishing a model accordingly. Fang et al. [37] proposed a risk threshold on each service leg, through which the speed-dependent risk was ensured to be spread equitably in a railway network. Hosseini and Verma [38] imposed threshold restrictions on both the yards and arcs of the railroad network so that equitable distribution of risk across the network was guaranteed. In the above literature, risk equity is described as a constraint condition, and risk equity is realized by directly setting the risk difference threshold. Another approach that has been applied in the literature on risk equity is the minmax method, which minimizes the maximum differential total risk or the risk value. For the purpose of making risk distribution more balanced, Lindner-Dutton et al. [39] proposed a measurement model to Sustainability 2021, 13, 9427 4 of 18

minimize the sum of maximum risk differences between every O-D pair over all shipments. Current and Ratick [40] formulated a mixed-integer program to locate facilities to handle hazmat, such that the maximum hazmat amounts shipped past any individual person and any facility are minimized. List and Mirchandani [41] used the maximum regional risk assumed by each unit of population to measure the equity of the risk distribution of the entire transportation network in the route selection model of hazardous materials transportation. Verter and Kara [42] applied the above method to a case study and discussed the risk equity of natural gas road transportation between Quebec and Ontario. To determine the safest set of routes, Bell [43] used the minmax method in the case of a risk-averse attitude towards hazmat shipments. Bianco et al. [44] formulated a linear bilevel programming model for the design of the hazardous materials’ transportation network, considering the equity of risk by minimizing the maximum link risk of overpopulated links of the entire network. Bianco et al. [5] minimized the maximum total link risk to ensure the spreading of risk in an equitable way. Chiou [45] proposed a stochastic program to reduce maximum time-varying risk over links to promote equity of risk in a spatial distribution. Ke et al. [6] minimized the maximum link risk to attain risk equity under a bi-level problem setting.

3. Model Building 3.1. Model Hypothesis To simplify the problem, the present paper assumes the following: 1. In the constructed model, only one carrier in operation is considered, without considering other carriers. 2. The population density around the link depends on the population density of the geographic area to which it belongs. Considering the uncertainty of the population density, we treat it as an interval number. 3. Assume that the transportation cost of hazmat vehicles on the link is determined by the driving time, that is, the transportation cost is determined by the travel distance and driving speed. 4. Considering that the speed of a hazmat vehicle is an uncertain value, the driving speed of different hazmat types on link are treated as the number of intervals.

3.2. Problem Description In fact, there are many uncertain parameters in the entire transportation network. Al- though the probability of a transportation accident is not only related to the type of hazmat, but also related to weather, time, road conditions, vehicle conditions, and professional skills of transport personnel, the accident probability can be obtained through historical data. So, the probability of transportation accidents is expressed as the product of the accident probability per kilometer when transporting h-type hazmat and the length of link (i, j) in this research. The population density around the link is determined in this research by the population density of the geographical area to which the link belongs. Moreover, we consider the emergency response time of the emergency response departments near the link from the perspective of ex-post-processing and add the emergency response time to the risk assessment function. Considering the risk differences between the different links, risk equity is realized from the perspective of risk compensation cost. Therefore, a multi-objective route optimization model of hazmat considering transportation risk, transportation cost, and risk equity is proposed.

3.3. Parameter Description The transportation network is represented by a graph G = (N, A), where N is the set of nodes and A is the set of links. The transportation of hazmat requires the carrier to transport various hazmat types through the road network from the starting point to the end point. There are multiple feasible routes for the transportation of hazmat between the starting point and end point. The constructed route optimization model of hazmat can select the optimal transportation route in order to meet the expectations of the government, Sustainability 2021, 13, x FOR PEER REVIEW 5 of 19

3.3. Parameter Description The transportation network is represented by a graph 𝐺=(𝑁,𝐴), where N is the set of nodes and A is the set of links. The transportation of hazmat requires the carrier to transport various hazmat types through the road network from the starting point to the Sustainability 2021, 13, 9427 5 of 18 end point. There are multiple feasible routes for the transportation of hazmat between the starting point and end point. The constructed route optimization model of hazmat can select the optimal transportation route in order to meet the expectations of the government,the carrier, the carrier, and the and public. the public. The parametersThe parameters and and variable variable symbols symbols used used in this in this paper paper are aredescribed described in Figurein Figure1. 1.

Figure 1. Cont. Sustainability 2021, 13, x FOR PEER REVIEW 6 of 19 Sustainability 2021, 13, 9427 6 of 18

Figure 1. Cont. SustainabilitySustainability 20212021,, 1313,, x 9427 FOR PEER REVIEW 7 7of of 19 18

FigureFigure 1. 1. MathematicalMathematical notation. notation.

3.4.3.4. Mathematical Mathematical Formulation Formulation G = (N A) TheThe transportation networknetwork isis represented represented by by a grapha graph 𝐺=(𝑁,𝐴), with with a set ofa set nodes of N and a set of links A. According to [33], if λ represents the radius of the spread, people nodes N and a set of links A. According to [33], if 𝜆 represents the radius of the spread, within the λ neighbourhood of a link could potentially be affected. people within the 𝜆 neighbourhood of a link could potentially be affected. Therefore, the area of the affected range is: Therefore, the area of the affected range is: 2 S𝑆ij==2𝜆2λh∗∗𝑑dij++𝜋∗π ∗ (λ(𝜆h)) (1)(1) In this section, considering the uncertainty of population density, 𝜌 is treated as an In this section, considering the uncertainty of population density, ρz is treated as an 𝜌 = 𝜌 −,𝜌 + intervalinterval number, number, that that is, is, ρz = [ρz , ρz ].. Therefore, Therefore, the the population population number number affected affected by by a a hazmathazmat transportation transportation accident accident on on link link i(,𝑖,j ) 𝑗is asis as follows: follows: 𝑃𝑂𝑃h =𝑆 ∗ 𝜌− ,𝜌+ (2) POPij = Sij ∗ ρz , ρz (2) According to [46], 𝑃 is defined as the accident probability per kilometer of h-type hazmat.According When transporting to [46], Ph is h-type deﬁned hazmat, as the accidentthe accident probability probability per on kilometer link (𝑖, of) 𝑗 can h-type be expressedhazmat. When as: transporting h-type hazmat, the accident probability on link (i, j) can be expressed as: 𝑃h =𝑃h ∗𝑑 (3) Pij = P ∗ dij (3) AccordingAccording to to a a standard standard of of emergency emergency response response coverage coverage document document report report prepared prepared byby Portland Portland Fire Fire and and Rescue Rescue (PFR), (PFR), 90% 90% of of hazmat hazmat accidents accidents in in urban urban areas areas can can be be re- re- spondedsponded to to within 18 minmin whilewhile maintainingmaintaining an an acceptable acceptable response response level, level, but but the the delay delay of ofthe the emergency emergency response response time time can can greatly greatly increase increase the harmthe harm generated generated by a by hazmat a hazmat accident. accident.However, However, there are there some are differences some differences in the emergency in the emergency response response time of time emergency of emergency depart- departmentsments near different near different links. Thelinks. shorter The shorter the emergency the emergency response response time, the time, more the effectively more ef- fectivelythe emergency the emergency department department can reduce can the reduce consequences the consequences of an accident of an and accident the possibility and the possibilityof a secondary of a secondary accident; that accident; is, the that transportation is, the transportation risk caused risk by acaused hazmat by accident a hazmat is accidentsmaller, sois smaller, the transportation so the transportation risk in this paper risk in is representedthis paper is by repr theesented product by of the the product accident ofprobability, the accident the probability, accident consequence, the accident and consequence, the emergency and the response emergency time. response time. 𝑅h =𝑃h ∗𝑃𝑂𝑃h ∗𝑡 (4) Rij = Pij ∗ POPij ∗ tij (4) From the perspective of the carrier, the transport cost refers to the cost of fuel. In this paper,From the thetransportation perspective cost of the considered carrier, the by transport the carrier cost is refers expressed to thecost as the offuel. time In cost, this whichpaper, is the related transportation not only to cost the considered travel distance by the and carrier the driving is expressed speed as of the the time vehicle cost, on which the linkis related (𝑖, 𝑗), notbut onlyalso to to the the transportation travel distance cost and per the unit driving time speedof h-type of the hazmat. vehicle Considering on the link that(i, j) ,the but speed also to of the an transportation h-type hazmat cost vehicle per unit travelling time of h-typeon link hazmat. (𝑖, 𝑗) is Considering uncertain, it that is the speed of an h-type hazmat vehicle travelling on link (i, j) is uncertain, it is treated as treated as an interval number, thath is, 𝑣 =𝑣i ,𝑣 . an interval number, that is, vh = vh −, vh + . The transportation cost isij then ijexpressedij as follows: Sustainability 2021, 13, 9427 8 of 18

The transportation cost is then expressed as follows:

h h dij Cij = C ∗ (5) h h − h +i vij , vij

In this paper, risk equity is quantified by means of the risk compensation cost and optimized as one of the multi-objective functions. In this paper, we define risk compensation as follows: In view of the potential risks during transportation and according to the corresponding risk evaluation standards, risk bearers around the links of the transportation network will be compensated with a certain price before an accident occurs to reflect the risk equity. On this basis, this paper makes the following improvements. First, the transportation risk model in this paper takes the difference in the emergency response time of emergency response departments near links into account. Therefore, different from the simple consideration of population exposure risk, the risk equity model in this paper covers the risk injustice caused by the difference in the emergency response time of links. Second, different from the cost of risk compensation for individuals, the risk compensation cost in this paper is for the links that exceed the average risk. Finally, the risk equity model in this paper takes the change in risk equity into account when there is more than one hazmat in the transportation network. In this paper, the risk compensation cost on link (i, j) is the product of the risk compensation coefficient, the unit risk compensation cost, and the risk. The expression of the risk compensation cost is as follows:

h h h fij = lij ∗ Rij ∗ b (6)

h where Rij represents the transportation risk on link (i, j), b represents the compensation h expense per unit risk, and lij represents the coefﬁcient of the risk compensation, which is determined by the difference ratio between the transportation risk on link (i, j) and the average risk of the selected route. The formula is as follows:

 Rh −Rh  ij h − h > h h , Rij R 0 lij = R ∀(i, j) ∈ A, h ∈ H (7) h h  0, Rij − R < 0

Because the objective functions and constraint conditions both contain interval numbers, which cannot be solved directly, the model can be deterministically transformed by the method of interval number sorting. For the interval number, substituting the maximum and minimum values of the interval numbers into the parameters, we can obtain the maximum and minimum values of the parameters containing the interval number, as shown in Formulas (8)–(11).

h − h − Rij = Pij ∗ Sij ∗ ρz ∗ tij (8)

h + h + Rij = Pij ∗ Sij ∗ ρz ∗ tij (9)

dij Ch − = Ch ∗ ij h + (10) vij

dij Ch + = Ch ∗ ij h − (11) vij

h h h − h +i h h h − h +i Therefore, Rij = Rij , Rij and Cij = Cij , Cij . Therefore, the original parameter containing the interval number can be converted into:

h 0 h1 h − h1 h + Rij = ηij Rij + 1 − ηij Rij (12) Sustainability 2021, 13, 9427 9 of 18

h 0 h2 h − h2 h + Cij = ηij Cij + 1 − ηij Cij (13)

h1 h2 where ηij and ηij , respectively, represent the willingness of decision makers to bear the transportation risk and transportation cost in the decision of hazmat transportation. h1 h2 Considering that setting ηij and ηij will cause deviations to the obtained objective variable h1 h2 value, in order to control the deviation, the acceptable deviation values dij and dij are speciﬁed, which represent the deviation between the objective variable value and the minimum variable value, as shown below, where d1max and d2max, respectively, represent the maximum deviation value acceptable to the decision maker.

h1 h 0 h − h1 dij = Rij − Rij , dij ≤ d1max (14)

h2 h 0 h − h2 dij = Cij − Cij , dij ≤ d2max (15) According to the above analysis, the route optimization problem of hazmat transportation considering risk equity can be expressed as the following multi-objective mixed-integer programming model: h 0 h min ∑ ∑ Rij ∗ xij (16) h∈H (i,j)∈A

h 0 h min ∑ ∑ Cij ∗ xij (17) h∈H (i,j)∈A

h min ∑ ∑ fij (18) h∈H (i,j)∈A s.t. h h P ∗ dij ≤ ϕ , ∀(i, j) ∈ A, h ∈ H (19) h 0 h Rij ≤ φ , ∀(i, j) ∈ A, h ∈ H (20)  −1, j = Oh h h  ∑ xij − ∑ xji = 0, otherwise , ∀h ∈ H (21) (i,j)∈A (i,j)∈A  1, j = Dh

h1 h 0 h − h1 dij = Rij − Rij , dij ≤ d1max. (22) h2 h 0 h − h2 dij = Cij − Cij , dij ≤ d2max. (23) h xij ∈ (0, 1), ∀(i, j) ∈ A, h ∈ H (24) There are three optimization objectives in this model. Among them, Equation (16) indicates that the total risk of transportation routes of multitype hazmat is minimized when considering the emergency response time. Equation (17) minimizes the total transportation cost of hazmat in all directions in the entire transportation network considering the difference in the transportation cost per unit time of different types of hazmat. Equation (18) makes use of the risk compensation cost to compensate the links that exceed the average risk and achieves risk equity by minimizing the risk compensation cost. Equation (19) is the transportation accident probability threshold of all links when transporting h-type hazmat, denoting the maximum acceptable accident probability of all links. Equation (20) is the transportation accident risk threshold of all links when transporting h-type hazmat, denoting the maximum acceptable accident risk of all links. Equation (21) is the ﬂow conservation constraint, which ensures that the transportation direction of all hazmat is from the starting point to the end, and the ﬂow direction is balanced throughout the entire transportation h network according to [47]. Constraint (24) is the value range of decision variable xij. Sustainability 2021, 13, 9427 10 of 18

4. Solution Procedure The model constructed in this paper is a route optimization model of multi-variety hazmat transportation considering risk equity in an uncertain environment, which includes the three objectives of transportation risk, transportation cost, and risk equity. First, for the route optimization of multi-variety hazmat transportation, the transportation of different varieties of hazmat are independent of one another; second, because these three objectives are often in conflict, they cannot reach the optimal conditions at the same time; finally, after deterministic transformation of the model constructed under an uncertain environment, a multi-objective genetic algorithm based on linear weighting is designed to solve the problem. Assuming that the route optimization problem of hazmat transportation contains Q objectives, of which the objective function value corresponding to the objective q is zq, the h min maxi objective value range of the objective q is zq , zq . Due to the difference in different objective dimensions, the function values corresponding to the Q objectives are normalized, and the function values are mapped to the interval [0, 1]. Finally, the multi-objective model is converted into a single-objective model in a linearly weighted manner, and then the traditional genetic algorithm is applied to solve the problem. The specific steps are as follows. To facilitate the problem description, it is assumed that the transportation route optimization problem contains Q objectives, of which the objective function value corresponding to objective q is zq, the target value interval of the first k shortest routes of the single- h min maxi objective problem is zq , zq , and the optimal solution is the objective function value min min min when all the single objective optimal values are optimal, namely, z1 , z2 ,..., zq . The specific steps of the algorithm are as follows: min 0 zq−zq (1) Normalize the single-objective functions: zq = max min . zq −zq 0 (2) Use the linear weighting method to weight multiple objectives: minZ = ω1 ∗ z1 + 0 0 ω2 ∗ z2 + ... + ωq ∗ zq. (3) Encoding and initialization: Encoding abstracts the chromosomes and individuals in the genetic space through a certain mechanism in order to solve the problem. Since the problem to be solved is a transportation problem, the N-dimensional vector X = {x1, x2,..., xn} is used to represent the genetic makeup on the chromosome. After the encoding scheme is determined, the genetic algorithm uses a random method to generate a set of several individuals, which is called the initial population. The number of individuals in the population can be freely defined as required. (4) Calculate fitness: Since we consider the shortest route problem in this paper, the relative fitness is calculated by C − f (x), where C is a constant. (5) Selection and replication: Use the roulette algorithm to generate a random value and compare its size with the cumulative relative fitness in order to select good individuals from the population to enter the genetic iteration. (6) Crossover: Since the chromosome code is a set of nonrepetitive numbers, the traditional way of aligning up and down crossing will often produce invalid routes. Therefore, different crossover methods are used, as follows: (a) On the Tx and Ty chromosomes representing routes, two loci are randomly selected as i and j, respectively, the area between the two loci is defined as a cross domain, and the cross content of the two loci is memorized as temp1 and temp2, respectively. (b) According to the mapping relationship in the intersection area, find the same elements as temp2 and temp1 in the individual Tx and individual Ty, respectively, and set the elements to 0, that is, set the cross content to 0. (c) Circulate Tx and Ty to the left, and delete it when it encounters 0, until there are no more zeros at the left end of the cross regions in all coding strings. All the Sustainability 2021, 13, 9427 11 of 18

gaps are then concentrated in the cross region, and the original genes in the cross region are moved backward, that is, the cross content found in the previous step that has been set to 0 is deleted to reorder the chromosome genes. Sustainability 2021, 13, x FOR PEER REVIEW 11 of 19 (d) Insert temp2 into the intersection region of Tx and insert temp1 into the intersection region of Ty, to form a new chromosome, that is, to cross the locus where the intersection content has been deleted. (7)(7) Mutation:Mutation: UsingUsing thethe cross-mutationcross-mutation method,method, twotwo numbersnumbers arearerandomly randomly generated, generated, andand thethe originaloriginal orderorder ofof thethe nodesnodes isis exchanged.exchanged.

5.5. Computational Computational Results Results 5.1.5.1. Overview Overview of of the the Shanghai Shanghai Road Road Transport Transport Area Area ShanghaiShanghai isis oneone of the four four municipalities municipalities directly directly governed governed by by the the Central Central Govern- Gov- 2 ernmentment in China, in China, and and the thetotal total land land area area of the of thecity cityis 6340.5 is 6340.5 kmkm. Shanghai. Shanghai governs governs a total a totalof 16 of municipal 16 municipal districts, districts, including including the Hu theangpu Huangpu District, District, Changning Changning District, District, and Xuhui and XuhuiDistrict. District. According According to the to2020 the Shanghai 2020 Shanghai Statistical Statistical Yearbook, Yearbook, the total the permanent total permanent popu- 2 populationlation of the of city the cityis 24,281,400, is 24,281,400, and andthe average the average population population density density is 3830 is 3830/km/km. In 2020,. In 2020,the total the totallength length of roads of roads opened opened to traffic to trafﬁc in Shanghai in Shanghai reached reached 13,045 13,045 km, km,and andthe road the roaddensity density reached reached 206 km 206 per km 100 per square 100 square kilometers. kilometers. Among Among them, the them, expressway the expressway mileage mileageis 845 km, is 845 and km, the and expressway the expressway density density reaches reaches 13 km 13per km 100 per square 100 square kilometers. kilometers. It is nec- It isessary necessary to pay to payspecial special attention attention to tothe the transp transportationortation risk risk when when transporting hazmathazmat in in ShanghaiShanghai due due to to the the highly highly dense dense population population and and the the distribution distribution of of the the road road network. network. It It isis of of great great practical practical signiﬁcance significance to to use use the the case case of of the the Shanghai Shanghai transportation transportation network network to to verifyverify the the route route optimization optimization model model of of hazmat hazmat transportation transportation considering considering risk risk equity. equity. TheThe distribution distribution of of the the road road network network of of Shanghai Shanghai is is shown shown in in Figure Figure2. 2.

FigureFigure 2. 2.Distribution Distribution map map of of the the Shanghai Shanghai road road network. network.

5.2.5.2. Basic Basic Situation Situation of of the the Case Case TheThe roadroad transportation transportation networknetwork ofof Shanghai Shanghai is is simpliﬁed, simplified, and and the the transportation transportation networknetwork map map of of hazmat hazmat of of Shanghai Shanghai is is obtained, obtained, as as shown shown in in Figure Figure3 ,3, in in which which there there are are 2424 nodes nodes and and 40 40 links. links. Among Among them,them, thethe node node data data come come from from the the cross cross node node in in the the real real road network, and the length data of the links were obtained according to the Baidu map. According to the administrative divisions of Shanghai, links belong to multiple administrative geographic regions, and the population density around the link is improved from the population density of each geographic region in the 2020 Shanghai Statistical Year- book. Sustainability 2021, 13, 9427 12 of 18

road network, and the length data of the links were obtained according to the Baidu map.

Sustainability 2021, 13, x FOR PEER REVIEWAccording to the administrative divisions of Shanghai, links belong to multiple12 administra- of 19 tive geographic regions, and the population density around the link is improved from the population density of each geographic region in the 2020 Shanghai Statistical Yearbook.

FigureFigure 3. Hazmat 3. Hazmat transportation transportation network network map mapof Shanghai of Shanghai.. It is assumed that in the hazmat transportation network of Shanghai, there are two It is assumed that in the hazmat transportation network of Shanghai, there are two types of hazmat that need to be transported from starting point 1 to end point 24. These two types of hazmat that need to be transported from starting point 1 to end point 24. These types of hazmat are explosives and flammable liquids. The two types of hazmat are marked two types of hazmat are explosives and flammable liquids. The two types of hazmat are as H1 and H2, in which the accident influence radiuses are λ = 1.6 km, λ = 0.8 km, the marked as H1 and H2, in which the accident influence radiuses1 are 𝜆 = 1.62 km, 𝜆 = transportation costs per unit time are C1 = 1000, C2 = 600, the compensation expense 0.8 km, the transportation costs per unit time are 𝐶 = 1000, 𝐶 = 600, the compensation per unit risk is b = 20, and the factors in deterministic transformation are ηh1 = 0.8 and expense per unit risk is b = 20, and the factors in deterministic transformation are ij𝜂=0.8 h2 η = 0.5. When transporting hazmat H1 and H2 separately, the transportation accident and 𝜂ij =0.5. When transporting hazmat H1 and H2 separately, the transportation acci- 1 2 dentprobability probability thresholds thresholds of of the the links links are areϕ 𝜑= = 0.045, 0.045, and andϕ 𝜑= = 0.031,0.031, andand the the transportation transpor- 1 2 tationaccident accident risk risk thresholds thresholds of of the the links links are areϕ 𝜑= 1500= 1500 and andϕ 𝜑= 200. = 200. According According to [to48 ],[48], 90% of 90% hazmatof hazmat accidents accidents in urban in urban areas areas can can be responded be responded to within to within 18 min 18 whilemin while maintaining main- an acceptable response level. Therefore, the emergency response time is t = rand(0, 18), and taining an acceptable response level. Therefore, the emergency responseij time is 𝑡 = 𝑟𝑎𝑛𝑑(0,18)the speeds, and of the vehicles speeds transportingof vehicles transporting different types different of hazmat types areof hazmat interval are numbers. interval The numbers.specific The data specific are shown data are in Tableshown1. in Table 1.

Table 1. Description of the transport section. Table 1. Description of the transport section. The Population Emergency Transportation Transportation GeographicThe Population The LengthThe Emergency Length of Transportation Transportation Geographic Density IncludedIncluded Links Response Speed of H1 Speed of H2 Area Density (𝐈𝐧𝐡𝐚𝐛/ 2 of Link LinkResponse (km) Speed of H1 Speed of H2 (𝐤𝐦/ Area (Inhab/km ) Links Time (min) (km/h) (km/h) 𝐤𝐦𝟐) (𝐤𝐦) Time (𝐦𝐢𝐧) (𝐤𝐦/𝐡) 𝐡) 1→2 17 9 [50, 80] [40, 80] 1→2 1→6 17 18 9 7[50, 80] [50, 60] [40, 80] [40, 50] 1→6 1→11 18 12 7 3[50, 60] [40, 50] [40, 50] [70, 80] 1→11 2→7 12 14 3 14 [40, 50] [70, 90] [70, 80] [40, 50] Qingpu District [900, 2700] 2→7 6→714 11 14 7[70, 90] [50, 60] [40, 50] [70, 90] Qingpu 7→13 7 12 [40, 50] [70, 80] [900, 2700] 6→7 11 7 [50, 60] [70, 90] District 11→6 12 3 [40, 50] [70, 80] 7→13 11→12 7 15 12 5[40, 50] [40, 60] [70, 80] [40, 60] 11→6 12→13 12 13 3 8[40, 50] [70, 90] [70, 80] [40, 50] 11→12 15 5 [40, 60] [40, 60] 12→13 13 8 [70, 90] [40, 50] 2→3 15 13 [40, 80] [40, 50] 3→4 4 7 [60, 70] [60, 70] 3→8 15 11 [40, 50] [80, 80] Songjiang [1400, 4300] 4→9 13 9 [40, 60] [40, 60] District 7→8 11 13 [40, 50] [40, 70] 8→9 9 11 [40, 90] [40, 50] 8→14 10 15 [70, 90] [60, 90] Sustainability 2021, 13, 9427 13 of 18

Table 1. Cont.

The Population Emergency Transportation Transportation Geographic The Length of Density Included Links Response Speed of H1 Speed of H2 Area Link (km) (Inhab/km2) Time (min) (km/h) (km/h) 2→3 15 13 [40, 80] [40, 50] 3→4 4 7 [60, 70] [60, 70] 3→8 15 11 [40, 50] [80, 80] 4→9 13 9 [40, 60] [40, 60] Songjiang 7→8 11 13 [40, 50] [40, 70] [1400, 4300] District 8→9 9 11 [40, 90] [40, 50] 8→14 10 15 [70, 90] [60, 90] 9→15 14 9 [50, 60] [40, 50] 13→14 8 7 [40, 60] [70, 80] 14→15 9 15 [50, 70] [70, 90] 4→5 12 13 [40, 70] [50, 50] 5→10 13 4 [80, 90] [50, 50] Jinshan District [600, 2000] 9→10 12 12 [50, 70] [60, 80] 10→16 14 11 [60, 70] [40, 80] 15→16 17 14 [70, 80] [60, 80] 11→17 20 9 [40, 70] [60, 70] Jiading District [1700, 5100] 12→18 12 3 [40, 70] [50, 70] 17→18 14 13 [70, 80] [40, 60] Baoshan 17→19 22 10 [70, 90] [60, 80] [3700, 11,000] District 18→19 15 6 [70, 90] [50, 90] 19→20 17 3 [50, 70] [70, 80] 19→22 18 4 [80, 90] [40, 80] 20→21 8 7 [40, 60] [60, 70] Pudong District [2200, 6800] 20→22 11 13 [40, 70] [50, 80] 21→23 12 6 [40, 60] [40, 90] 22→23 10 7 [70, 90] [60, 70] 23→24 18 11 [50, 60] [80, 90] Minhang [3400, 9200] 14→20 26 9 [70, 80] [50, 60] District 15→21 23 7 [50, 60] [80, 90] Fengxian [800, 2500] 16→24 28 17 [40, 50] [40, 60] District 21→24 23 14 [40, 60] [70, 80]

5.3. Result Analysis The model established in this paper is a multi-objective mixed integer linear programming (MILP) model, which is solved using the multi-objective genetic algorithm based on a linear weighting designed in Section4, and the solution software applied is MATLAB R2018b. Due to the inconsistency of the three objective dimensions, the objective function values of the routes are normalized, and weights are set for different objectives, where the weights of the three objective functions of transportation risk, transportation cost, and risk equity in the ﬁnal objective function are, respectively, set as ω1 = 0.5, ω2 = 0.3, and ω3 = 0.2. We ﬁnd that the optimal transportation route of hazardous material H1 is 1→6→7→13→14→15→21→24 and the optimal objectives value is 27,571.2743, and the optimal transportation route of hazardous material H2 is 1→11→6→7→13→14→15→21→24 and the optimal objectives value is 6579.546345. Although they have most of the same links, there are still some differences, as shown in Figure4. Through the multi-objective genetic algorithm based on linear weighting proposed in this paper, the optimal transportation routes considering the risk equity of two different types of hazmat can be obtained. The following is an analysis of single objectives. Sustainability 2021, 13, x FOR PEER REVIEW 14 of 19 Sustainability 2021, 13, 9427 14 of 18

Figure 4. Optimal routes of H1 and H2 under the multi-objective situation.

Figure 4.When Optimal only routes considering of H1 and theH2 under transportation the multi-objective risk, the situation. optimal transportation route for H1 is 1→11→6→7→13→14→15→21→24 and the optimal objectives value is 7015.794739, andThrough the optimal the multi-objective transportation plangenetic for algoriH2 is 1thm→11 based→6→ on7→ linear13→14 weighting→15→21 →proposed24 and the in thisoptimal paper, objectives the optimal value transportation is 1141.78676. routes For these considering two types the ofhazmat, risk equity the of influence two different radiuses typesof the of hazmat accidentcan be obtained. and the accidentThe following probability is an peranalysis kilometer, of single which objectives. are determined by theWhen type ofonly hazmat, considering are all the different. transportation However, risk, they the are optimal unified transportation in the transportation route for plan H1that is 1→ achieves11→6→7 the→13 optimal→14→15 transportation→21→24 and the risk, optimal which objectives is because value the is transportation 7015.794739, and risk is thelinearly optimal related transportation to the product plan for of theH2 influenceis 1→11→6 radius→7→13 of→ a14 hazmat→15→21 accident→24 and and the the optimal accident objectivesprobability value per is 1141.78676. kilometer, so For normalizing these two ty thepes transportationof hazmat, the influence risk can eliminate radiuses of most the of hazmatthe impact accident of parameterand the accident differences. probability Because per the kilometer, population which density are determined within the influenceby the typerange of hazmat, of a hazmat are all accident different. is However, determined they by are the unified population in the density transportation interval plan of the that area achieveswhere the linkoptimal is located, transportation the uncertain risk, populationwhich is because affected the by transportation the transportation risk ofis theline- two Sustainability 2021, 13, x FOR PEER REVIEW 15 of 19 arlyhazmat related on to the the same product link of remains the influence consistent. radius Therefore, of a hazmat after normalization,accident and the there accident are few probabilitydifferences per in kilometer, the objective so normalizing function values the tr ofansportation the transportation risk can risk eliminate and risk most equity of ofthe the impactH1 and of Hparameter2 optional differences. transportation Because routes, th ase shownpopulation in Figure density5. within the influence range of a hazmat accident is determined by the population density interval of the area where the link is located, the uncertain population affected by the transportation of the two hazmat on the same link remains consistent. Therefore, after normalization, there are few differences in the objective function values of the transportation risk and risk equity of the H1 and H2 optional transportation routes, as shown in Figure 5.

Figure 5. Routes with the least transportation risk of H1 and H2. Figure 5. Routes with the least transportation risk of H1 and H2. When only considering the transportation cost, the optimal transportation route for WhenH only1 is 1 considering→11→17→ 19the→ transportation22→23→24 and cost, the the optimal optimal objectives transportation value isroute 1611.706349, for and H1 is 1→11→17→19→22→23→24 and the optimal objectives value is 1611.706349, and the optimal transportation route for H2 is 1→11→6→7→13→14→15→21→24 and the optimal objectives value is 813.5119048. After normalization, the obtained transportation cost values eliminate the difference caused by the unit time transportation cost, but the two types of hazmat still have a large difference in the transportation routes that achieve the optimal transportation cost, which is because the uncertainty intervals of the transportation speed of the two types of hazmat are different, as shown in Figure 6.

Figure 6. Routes with the lowest transportation cost of H1 and H2.

Finally, when considering the objective of risk equity, comparing the optimal transportation routes under the multi-objective situation with the optimal transportation routes while only considering the transportation risk and the optimal transportation routes while only considering transportation cost separately, we can find that for H2, the optimal transportation routes under the above three situations are consistent, and they are all the route 1→11→6→7→13→14→15→21→24. However, for H1, the route with the Sustainability 2021, 13, x FOR PEER REVIEW 15 of 19

Figure 5. Routes with the least transportation risk of H1 and H2.

Sustainability 2021, 13, 9427 15 of 18 When only considering the transportation cost, the optimal transportation route for H1 is 1→11→17→19→22→23→24 and the optimal objectives value is 1611.706349, and the optimal transportation route for H2 is 1→11→6→7→13→14→15→21→24 and the optimal objectivesthe value optimal is 813.5119048. transportation After route normalizat for H2ion, is 1 the→11 obtained→6→7→ transportation13→14→15→ cost21→ val-24 and the ues eliminateoptimal the objectives difference value caused is 813.5119048.by the unit time After transportation normalization, cost, the but obtained the two transportation types of hazmatcost still values have eliminatea large difference the difference in the causedtransportation by the unit routes time that transportation achieve the cost,optimal but the two transportationtypes of cost, hazmat which still is because have a large the uncertainty difference inintervals the transportation of the transportation routes that speed achieve the of the twooptimal types transportationof hazmat are cost,different, which as is shown because in theFigure uncertainty 6. intervals of the transportation speed of the two types of hazmat are different, as shown in Figure6.

Figure 6. Routes with the lowest transportation cost of H1 and H2. Figure 6. Routes with the lowest transportation cost of H1 and H2. Finally, when considering the objective of risk equity, comparing the optimal trans- Finally,portation when routes considering under thethe multi-objectiveobjective of risk situation equity, withcomparing the optimal the optimal transportation trans- routes portationwhile routes only under considering the multi-objective the transportation situation risk and with the the optimal optimal transportation transportation routes while routes whileonly consideringonly considering transportation the transportation cost separately, risk and we the can optimal ﬁnd that transportation for H2, the optimal routes whiletransportation only considering routes undertransportation the above cost three separately, situations we are can consistent, find that andfor H they2, the are all the optimal routetransportation 1→11→6 →routes7→13 under→14→ the15 →abov21→e three24. However, situations for areH 1,consistent, the route and with they the lowest are all thetransportation route 1→11→ risk6→ is7→ 1→1311→→146→→157→→1321→→1424.→ However,15→21→ 24,for theH1, route the route with with the lowest the transportation cost is 1→11→17→19→22→23→24, and the optimal transportation route under the multi-objective situation is 1→6→7→13→14→15→21→24. Although the difference between the optimal transportation risk route and the optimal multi-objective route is only to change the route 1→11→6 to the route 1→6, there are still some differences. The differences between the optimal transportation routes of H1 and H2 illustrate that it is necessary to consider the differences in the optimal transportation routes caused by the inﬂuence radiuses of hazmat accidents, the accident probabilities per kilometer and the unit time transportation costs of different types of hazmat. On the other hand, for H1, the difference in the optimal transportation risk route, the optimal transportation cost route, and the optimal route of multiple objectives shows that multiple objectives need to be considered comprehensively in the process of optimizing the transportation route of hazmat.

6. Conclusions and Future Research Different from most traditional route optimization models of hazmat transportation, which only consider transportation risk and transportation cost from the perspective of the government and the hazmat carrier and ignore the importance of risk equity, we constructed a multi-objective route optimization model of hazmat transportation considering the transportation risk, transportation cost, and risk equity in this paper. In addition, we considered the impact of the emergency response time on the transportation risk and risk equity and realized the risk equity by setting compensation costs. Subsequently, a multi-objective genetic algorithm based on linear weighting was proposed to solve the constructed multi-objective route optimization model of hazmat transportation. The Sustainability 2021, 13, 9427 16 of 18

solution results obtained by a case show that the constructed model can effectively find a transportation route that satisfies the government, the carrier, and the public. The specific contributions are: (1) Most of the previous transportation risk models of hazmat only evaluate the accident consequences caused by transportation accidents, and few consider that the emergency response time of the emergency departments around the link is an important factor affecting the transportation risk. Therefore, in this paper, the emergency response time of the emergency departments around the link is included in the transportation risk assessment function. In the risk equity model, risk compensation is made for the links exceeding the average risk from the perspective of the risk compensation cost to highlight the risk equity. (2) Since the population density and the transportation speed usually change within an interval, these two uncertain parameters are treated as interval numbers to construct a route optimization model of hazmat transportation considering the risk equity under uncertain environments. The model with interval numbers is transformed into a deterministic model by using the method of interval number sorting. (3) A case transporting different types of hazmat based on the actual road background in Shanghai, China, is constructed. The case data are substituted into the model considering the risk equity, and the model is solved with a multi-objective genetic algorithm based on linear weighting. The results show the necessity of considering risk equity in the route optimization of hazmat. This research will help the management agency of hazmat transportation change the concept from “total risk-total cost” to “total risk-total cost-risk equity”, in which “total risk- total cost” is considered from the perspective of “government-carrier” and “total risk-total cost-risk equity” is considered from the perspective of “government-carrier-public”. To avoid the risk of a certain road section being too high, which may cause irreparable harm to the population of this road section and affect the sustainable development of hazmat transportation, this research constructed the route optimization model to select the route with the least total risk. Moreover, this research not only focuses on the minimum total risk and total cost, but also focuses on how to reduce the risk difference in different road sections and areas and achieve risk equity as much as possible, which promote the sustainable development of hazmat transportation industry because the lack of risk equity is an important reason that more and more people oppose the transportation of hazmat. Moreover, the results of this research can provide scientific guidance for the optimization practice of hazmat transportation and help the hazmat transportation industry achieve sustainability. Several research directions can be explored in the future. First, in this paper, the emergency response time of the emergency response departments near the link is treated as a random number, not real data. In the future, the GIS system can be used to collect links and emergency response department data. Second, the method of processing uncertain parameters with the interval number can only consider a certain degree of uncertainty, and the approaches of processing uncertain parameters should be studied more carefully.

Author Contributions: Conceptualization, S.L.; Data curation, L.Z.; Investigation, J.L.; Methodol- ogy, L.L. and J.L.; Supervision, T.F. All authors have read and agreed to the published version of the manuscript. Funding: This work is funded by the National Natural Science Foundation of China (72032001, 72074076, 71302043); the Shanghai Natural Science Foundation (18ZR1409400), and Ministry of Education, Humanities and Social Sciences Research Planning Foundation (21YJA630057). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data used in this study are accessible at: Baidu map (https: //map.baidu.com/@13520914,3633327,13z (accessed on 3 March 2021)), 2020 Shanghai Statistical Sustainability 2021, 13, 9427 17 of 18

Yearbook (http://tjj.sh.gov.cn/tjnj/20210303/2abf188275224739bd5bce9bf128aca8.html (accessed on 3 March 2021)). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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