1. Introduction
At present, China’s chemical and petrochemical industries have made great progress in terms of their economic efficiency, with a steady upward trend [
1]. To continue promoting the vigorous development of the national chemical industry, large-scale chemical parks such as Shanghai, Ningbo and Huizhou have been built and continue to emerge in medium and small cities. A CIP is a product of the modern chemical industry that uses the industrial agglomeration model to achieve the optimal efficiency [
2]. It can reduce the infrastructure costs and accelerate the conversion of raw chemical materials into others. Thus, the purpose of the internationalization of the chemical industry, maximization of the economic benefits and optimization of enterprise development is achieved. However, inside the park, the industrial operation also incorporates a large number of pipelines used for transporting chemical liquids, and many large storage tanks for chemical materials have been set up, many of which are flammable, explosive, highly toxic and corrosive and carry the radiation characteristic of hazardous materials. These hazardous sources are superimposed onto one another because of industrial clustering, and sudden accidents such as fires, explosions, toxic gas diffusion, toxic liquid leakage, radioactive material leakage, etc., produce great destructiveness in the park and also threaten the safety, lives and property of people near the park, as well as the conditions of the surrounding ecological environment. Through the statistics and analysis of 207 chemical accidents [
3], it was found that the chemical accidents that can produce the domino effect account for 38.6%. Additionally, the domino effect [
4] is very likely to occur in a situation of high temperature, high pressure and chemical reactions, such as oxidation reduction, brought about by different kinds of hazardous chemicals, which leads to the spreading of accidents affecting enterprises in the adjacent area and the occurrence of secondary accidents, thus expanding the scale of the accidents. Since 2015, there have been more than 10 cases of serious accidents concerning hazardous chemicals in China. For example, in March 2019, a particularly serious explosion occurred in a chemical park in Yancheng City, Jiangsu Province, killing seventy-eight people immediately, injuring more than seven hundred people, and causing economic losses of RMB 1.9 billion. When a sudden accident occurs in a chemical park, all the people in the park need to be evacuated to a safe area immediately in order to avoid their prolonged exposure to dangerous factors, such as thermal radiation and strong air currents, and emergency supplies from outside the park need to be transported to the accident site so as to improve the rescue efficiency and greatly reduce the human casualties and property damage.
However, most of the existing emergency studies have focused on the field of natural disasters, such as earthquakes, typhoons, floods, etc., with respect to multi-objective and multi-disaster emergency material deployment. For example, Liu et al. [
5] examined several different passage periods, minimized the total time for dispatching paths in each period, maximized the matching of the material requirements at the distribution points and ensured the fairness of the relief material distribution. Feng et al. [
6] took into account the efficiency and fairness and established a transportation deployment model for multiple types of emergency supplies throughout multiple cycles, considering the transportation cost minimization while ensuring that the first batch of emergency supplies could be fairly deployed to the disaster sites. Li et al. [
7] constructed a multi-period, two-level planning model to solve the scheduling problem of post-disaster road network repair work, designed a genetic algorithm to solve the model considering the maximum relative satisfaction, and verified that the model could complete the repair of the damaged road network before the end of the planning time horizon in the case of the Wenchuan earthquake. Yu et al. [
8] optimized the UAV path planning model using three constraints to understand the disaster situation and immediately carry out rescue work. Ng et al. [
9] designed a model for different risk groups (children, women, elderly, etc.) and an emergency model for the rescue evacuation of people at sea among different risk groups (children, women, elderly, etc.) and different evacuation tools (lifeboats, rescue boats, marine robots, helicopters, etc.). Feng et al. [
10] constructed a multi-objective optimization model for the purpose of rescue station site selection to improve the emergency response capability of each rescue team and its efficiency in emergencies. The optimization was carried out from three perspectives: the timeliness, economic efficiency and workload of rescue teams. The superiority of the model was verified by heuristic methods. Huang et al. [
11] established an emergency logistics distribution path model based on uncertainty theory and used a cellular genetic algorithm to verify the feasibility of the model, considering the suddenness of the emergency events and the lack of historical data as a reference in the deployment of emergency logistics. El Sayed et al. [
12] extended Zimmerman’s approach to maximize the membership and minimize the non-membership functions in the solution model and developed a novel approach for solving the fully intuitionistic fuzzy multi-objective fractional transportation problem (FIF-MOFTP). Sun et al. [
13] designed a multi-objective positioning emergency logistics center model for sudden disasters with minimum total costs and the maximum satisfaction of the disaster victims. Additionally, the IABC algorithm was proposed to effectively calculate the optimal location of the emergency logistics center in sudden disasters, which can help the rescue time for different rescue locations to meet the satisfaction requirements. It is also proved that the global search capability and stability of the IABC algorithm are better than those of the ABC and GABC algorithms. Zhang et al. [
14] used a hybrid optimization algorithm of an ant colony algorithm and NSGA-II to design an individual correction strategy for the multi-objective deployment of emergency supplies within a reasonable timeframe. The above studies all took natural disasters as their emergency situations and considered the distribution and dispatch of relief materials throughout different time cycles. Once a natural disaster occurs, the emergency centers in multiple locations will respond to the emergency situation at the same time and distribute a single type or multiple types of materials stored in the emergency centers and then enter the transportation link. This emergency response model pursues fairness in distributing the relief materials, minimizing the transportation time and optimizing the dispatching efficiency. However, the industries in the chemical park are complex and connected by pipelines, and the raw materials, intermediates and even the finished products used in the park are all highly dangerous sources. If an accident occurs in one chemical company, the domino effect will bring safety risks to the neighboring chemical companies in the park at the same time, causing the scale of the accident to increase geometrically. The traditional emergency response model for natural disasters is not applicable to the emergency dispatch model of chemical parks.
In recent times, the model of multi-objective decision optimization and facility siting has been widely used in various fields and has made good progress in public service facilities. For example, Wang et al. [
15] established a hybrid model of an open site path considering the minimization of the post-earthquake emergency time and the minimization of the total cost of the emergency system, and they derived several non-dominated Pareto solution sets to provide a solution for decision makers. Elsisy et al. [
16] introduced the modified Hungarian method for solving the interval and fuzzy assignment problem. It is used for the problem of the reuse of valuable buildings. The proposed algorithm requires less effort and time in order to reach optimality and offers a solution based on a scientific and realistic basis. Yu et al. [
17] designed a bat algorithm incorporating a chaotic search mechanism to establish a time-satisfied site allocation model. J Burek [
18] et al. developed a multi-objective optimization model based on life cycle assessment to identify cost efficiency optimization solutions so as to minimize the use of fossil energy and mitigate the climate change impact of Wal-Mart’s distribution center network. A Monte Carlo uncertainty analysis was also introduced to compare the solutions and evaluate the superiority of the Pareto optimal solution. Tao Wu [
19] et al. raised the question of choosing the location of market hubs to maximize the total profit based on the meeting of the market demand. The validity of the results of the Lagrangian relaxation-based heuristic algorithm, compared with the CPLEX solver and the Benders decomposition method, are demonstrated by a large number of test examples. El Sayed et al. [
20,
21] assessed the client’s demands and vague demand for the supply of the items, adopting an interactive approach for a bi-level multi-objective supply chain model (BL-MOSCM). The proposed model assists the DM in minimizing the transportation expenses and conveyance time of a large SCN. Additionally, the paper discusses a new algorithm for generating the Pareto frontier for the bi-level, multi-objective, rough nonlinear programming problem (BL-MRNPP). This approach is mainly based on transforming the BL-MRNPP into a single-level nonlinear programming problem using the weighting method and KKT optimality conditions. Additionally, it can be applied to problems such as supply chain models, bi-level transportation models and bi-level industrial production planning problems. Kaveh [
22] et al. used an improved genetic algorithm to optimize the siting layout of hospitals, aiming to select the points out of hundreds of candidate locations that could achieve the best coverage. A hierarchical analysis was introduced to limit the search space and compare the options using the genetic algorithm and particle swarm algorithm. Hu et al. [
23] constructed a dual-objective, two-stage model for siting waste-to-energy facilities, considering the sustainability and economic aspects of the urban environment to help the government to identify the most cost-efficient and environmentally friendly location for siting waste-to-energy facilities under conditions of uncertainty. Kaveh et al. [
24] identified vulnerable urban infrastructure in regard to cascading hazards and used GIS to prioritize urban areas according to the severity of the cascading hazards. A bi-objective multi-material distribution center siting model was constructed under uncertainty conditions. The model was solved using an invasive weed optimization algorithm. Wu et al. [
25] used microblogging big data to obtain public opinion information on urban stormwater flooding disasters, while constructing a model for siting urban emergency logistics in stormwater flooding disaster situations. The NSGA-III algorithm was used to identify the optimal deployment path of the emergency logistics, which provides a reference for cities to cope with storm waterlogging disasters. The abovementioned research on urban infrastructure siting is making good progress, but emergency siting studies related to chemical parks are relatively rare. In the context of the vast territory of China, which has the largest population in the world and dense and complex urban planning lines, it is difficult for the firefighting and rescue forces to access the chemical parks established in the suburbs around the cities and almost impossible to meet the requirements for achieving the rescue within minutes. Additionally, different regions have relatively different levels of firefighting resource allocation because of differences due to economic and cultural factors. If the rescue is not timely, in addition to the accident point, the enterprises adjacent to the accident point will also be affected by the domino effect, making the situation more serious. Therefore, the establishment of multiple reasonably sized emergency centers in the vicinity of chemical parks can aid in the immediate initiation of the emergency response.
By referring to the above research results, it is found that there are few studies on emergency siting in the case of chemical parks, and few of them investigate how to prevent the domino effect in order to prevent the accident scale from expanding, and there is a lack of targeted mathematical models. Therefore, based on the previous academic research, this paper uses NSGA-II to solve a siting model of the chemical park emergency center that can effectively prevent the domino effect and satisfy the timeliness, economic and safety requirements so as to optimize the layout of the chemical park emergency center and provide a basis for decision makers involved in siting decisions. The CPLEX method is also introduced to verify the superiority of the NSGA-II algorithm in solving this model.
2. Siting Model
2.1. Description of the Problem
The establishment of an emergency center of a certain scale near the chemical park can improve the rescue efficiency, shorten the emergency time and greatly help to save lives and properties. At the same time, a reasonably located emergency center can also quickly deploy relief supplies to prevent secondary accidents caused by the domino effect. As the main dispatching point for rescue and relief when an accident occurs, individuals deciding on the location of the emergency center need to consider various factors, such as safety, timeliness, emergency costs and other factors.
If the emergency center aims to provide long-term and stable services during an accident, it must first ensure its own safety before it can effectively carry out rescue tasks for each accident site. The safety aspects are based on the “Design Code for Disaster Prevention and Sheltering Places” and, combined with the layout factors of the chemical park itself, different safety levels of the emergency center in the chemical park are obtained. A variety of safety factors need to be considered in regard to the site selection safety factor, such as the distance of the risk radius between the emergency center and the accident-prone area, the proximity of water sources for a sufficient water supply, the capacity for protection against extensive damage and wind direction problems, all of which can be used as references for the scoring of the emergency center site selection safety factor.
In the case of a sudden hazardous chemical accident in a chemical park, if the relief is not timely, the chain reaction brought about by the domino effect will allow the thermal radiation, strong airflow and flying debris generated in the accident area to impact the neighboring areas, leading to secondary accidents. Therefore, in terms of timeliness, the emergency response needs to be carried out immediately upon the occurrence of the accident. When deploying emergency forces for the rescue of the accident site, emergency measures should also be carried out for the nearby potential accident sites, such as spraying cool water to reduce the heat radiation affecting the storage tanks and burying the leaking chemicals with sand to prevent the further expansion of the accident scale. Additionally, the average travel time of emergency vehicles and the maximum travel time that can be taken to reach the accident point need to be considered in the case of a disaster.
The cost of establishing emergency centers of different sizes and capacities varies, but regardless of the size, the cost of establishing an emergency center is relatively high; thus, the cost of site selection is such that once the emergency center is established, the location of the emergency center will not be changed for a long period of time. Additionally, the number of emergency centers should be balanced according to the size of the incident, and the costs of transportation from the emergency center to the incident point should be as small as possible if all the incident points are covered.
In order to highlight the focus, the following basic agreement on the siting of the emergency center in the chemical park is reached:
(a) All emergency rescue vehicles can reach the accident point, without considering the damage to the road network.
(b) All types of emergency rescue vehicles have the same travel speed and their unit travel costs are the same.
(c) The construction cost of the emergency response center is known and there is sufficient financial support available for the establishment of the emergency response center.
(d) The emergency centers are distributed in a point pattern, with each point representing a site building area, and the actual distance from the emergency center to the incident point is known.
(e) Each emergency center is capable of meeting the material needs of each demand point.
2.2. Mathematical Model
The meanings of the symbols used in the modeling are as follows:
① Decision-making variables:
, is a 0–1 decision variable with the value of 1 if the emergency center is established at the candidate site j of the emergency center, and 0 otherwise.
, is a 0–1 decision variable with a value of 1 if incident point i is provided with rescue by the emergency center candidate site j, and 0 otherwise.
, is a 0–1 decision variable with a value of 1 if incident point i is rescued by emergency center candidate site j and the rescue is provided by a vehicle of type k. Otherwise, it is 0.
② Subscripts
, ( = 1, 2…) emergency accident site number.
, ( = 1, 2…) emergency center candidate site number.
, ( = 1, 2…) rescue vehicle type serial number.
, ( = 1, 2…) rescue material type serial number.
③ Constants
represents the construction cost of establishing an emergency center.
represents the risk radius at accident point i.
represents the total number of sites eventually built for the emergency response center.
represents the distance from emergency center j to accident point i.
represents the maximum number of rescue vehicles k.
represents the safety factor for siting emergency centers.
represents the time of tank failure at accident point i.
represents the unit travel speed of the rescue vehicle k.
represents the unit travel cost of rescue vehicle k.
represents the demand for the sth material at incident point i.
represents the upper load capacity of the kth type of vehicle.
From the definition of the abovementioned modeling parameters, the siting model of the chemical park emergency center is established as follows:
S.t.
Equation (1) is the objective function of minimizing the cost of siting the emergency center, and the cost of siting the emergency center includes the cost of building the emergency center and the cost of transporting the emergency vehicles. Equation (2) is the objective function of maximizing the safety of the emergency center siting, which is defined by the product of the safety factor and the distance of the risk radius. Equation (3) ensures that each incident point can be rescued. Equation (4) ensures that only the selected emergency center can provide rescue to the incident point. Equation (5) is the total number of final sites for the emergency center, ensuring that only a maximum of one emergency center can be built at each site selected. Equation (6) ensures that the distance between the emergency center and the incident point is greater than the risk radius at the incident point so as to ensure that the result of Equation (2) is a constant positive. Equation (7) is the upper limit of the number of rescue vehicles of the first kind and determines the number of vehicles that can be dispatched from the emergency center. Equation (8) is the constraint used to prevent the domino effect. It is necessary to control the time of the travel of the rescue vehicles to the accident point within the tank failure time. Equation (9) ensures that the number of supplies meets the demand at the accident point. Equation (10) is the constraint range under a given determination condition.
2.3. Tank Failure Time Formula
The constraint time in formula (11) is the time taken for the failure of the tank at the accident point due to thermal radiation. Emergency rescue vehicles arrive at the rescue site within the tank failure time to cool the tank by sprinkling water on and cooling the tank to extend the failure time, thus achieving the purpose of reducing the occurrence of domino accidents. Since the failure time involves thermodynamic and transport properties and requires a great deal of computational time, it is difficult to obtain accurate scenario data. Therefore, Landucci [
26] obtained an equation to conservatively estimate the failure time of the tank based on experimental data, where the equation is the thermal radiation (in units) received by the tank at the accident point and the volume of the tank. The specific equation is as follows:
4. Algorithm Performance Comparison
To verify the effectiveness of using NSGA-II to solve the siting model constructed in this paper, this section compares the results obtained using the two methods. Both NSGA-II and CPLEX can solve siting problems with multiple constraints. CPLEX, as a commercial optimization engine, can solve four basic types of problems, including large-scale linear programming (LP), quadratic programming (QP), and quadratic programming with constraint (CPLEX can be called by the environments of Matlab, Java, Python and C++). In the case of larger models, its support for multi-threaded and distributed parallel optimization is usually beneficial in improving the speed of the solution. Here, we presume two emergency scenarios for the chemical parks. In Scenario 1, there are six accident points and five emergency center candidate sites. In Scenario 2, there are 15 accident points and 10 emergency center candidate sites. In these two scenarios, two and three sites are selected as the final sites for the emergency center. In each scenario, the values of the fitness functions obtained using the two methods are compared. For comparative purposes, the two max–min objective functions are weighted here. The first objective function is weighted by 0.7, and the second objective function is taken as the opposite value and weighted by 0.3. For the most part, TOPSIS exchange objectives, which are clashing and non-commensurable, are transformed into bi-objective commensurable and, most of the time, clashing functions. Then, the max–min [
31] operator is deemed to disband the incongruity of both criteria. This study used Visual Studio 2019 as the runtime environment for NSGA-II and CPLEX, respectively, to design code programs for the two abovementioned methods so as to solve the optimization problem for the siting model, and the values of the two scenarios were factored into the siting model in the model, and the solution results are shown in
Figure 4 and
Figure 5.
The optimal fitness values obtained by comparing NSGA-II and CPLEX after several iterations with different generations are compared. It can be seen from
Figure 4 that the optimal solution obtained by NSGA-II is better than the optimal solution obtained by CPLEX for Scenario 1, with six incident points and five emergency center candidate sites. Therefore, NSGA-II outperforms the CPLEX method in Scenario 1. As can be seen in
Figure 5, the optimal solution obtained by CPLEX almost overlaps with the optimal solution obtained by NSGA-II in Scenario 2, with 15 accident points and 10 emergency center candidate sites, but the performance of NSGA-II is still slightly better than that of the CPLEX method. By comparing the results of the NSGA-II and CPLEX methods by designing two emergency scenarios for chemical parks of different scales, the effectiveness of NSGA-II in solving the emergency center siting model can be verified.