Optimization method of multi-supply point emergency material site selection considering timeliness and fairness

Abstract

The application discloses a multi-supply-point emergency material site selection optimization method considering timeliness and fairness, and comprises the following steps: sequentially constructing a material supply point, a temporary distribution center, a disaster area and a damaged road, constructing a multi-target emergency material distribution model, constructing an initialization individual strategy, constructing a mutation operator and a local search operator based on the initialization individual strategy, constructing a selection strategy and an acceptance criterion, combining the mutation operator and the local search operator, outputting an optimal operator, evaluating the optimal operator, and outputting a best scheme for emergency distribution.The application proposes a double-target multi-supply-point emergency material site selection and distribution model, considers the influence of disasters on a road network in the model, proposes a waiting time concept, introduces a minimum allocated material concept in order to make the allocation result more fair, and introduces related calculation methods; and completes problem domain design of an emergency disaster relief material problem.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of emergency logistics, and particularly relates to a multi-supply-point emergency material site selection optimization method considering timeliness and fairness. BACKGROUND

[0002] Due to the uncertainty of natural disasters, the local reserves of emergency relief materials often cannot meet the demand. Therefore, at the first time after the disaster, optimization scheduling decisions need to be made according to the demand and supply relationship of emergency materials and the damage degree of the disaster area, so as to minimize the loss. In the emergency logistics system, the site selection of the distribution center is very important, which determines whether the emergency system can respond quickly to emergencies. Therefore, the site selection and resource allocation problem of the emergency warehouse has attracted widespread attention in recent years.

[0003] As a kind of efficient and universal intelligent algorithm, hyper-heuristic algorithm has been widely used in various optimization problems, such as education timetable problem, traveling salesman problem, vehicle routing problem, site selection path problem, production scheduling problem, etc. The original hyper-heuristic algorithm is mainly used to solve single-objective problems. With the in-depth research, more and more scholars use it to solve multi-objective problems and have achieved good results. Leng et al. used quantum strategy to select operators to solve the double-objective regional low-carbon site-selection-path problem. Wang et al. proposed a multi-objective hyper-heuristic algorithm to solve the cold chain logistics, which achieved better results than the traditional multi-objective algorithm. Yao et al. proposed a hyper-heuristic algorithm framework for intelligent city walking route planning, and used reinforcement learning mechanism to select operators. Castro integrated hyper-heuristic algorithm into MOPSO and designed four selection strategies for comparison. Zhang et al. proposed a new selection hyper-heuristic operation based on multiple diversity mechanisms, and verified the performance of the algorithm on the MaOP test set of 3-10 objectives. When solving multi-objective problems, scholars have also proposed many excellent high-level acceptance criteria, including full acceptance, only accepting improved solutions, large flood, and Monte Carlo, which ensure the effectiveness of the algorithm. However, no scholar has applied hyper-heuristic algorithm to site-selection-distribution problem, so there is a lack of corresponding problem domain design. In addition, the common hyper-heuristic algorithm generally directly uses operators for optimization, but this method is not ideal in multi-objective problems. SUMMARY

[0004] The purpose of the present application is to provide a multi-supply-point emergency material site selection optimization method considering timeliness and fairness to solve the problems existing in the prior art.

[0005] To achieve the above purpose, the present application provides a multi-supply-point emergency material site selection optimization method considering timeliness and fairness, which comprises:

[0006] sequentially constructing a plurality of material supply points, a plurality of temporary distribution centers, a plurality of disaster areas, and a plurality of damaged roads;

[0007] constructing a multi-objective emergency material distribution model based on the plurality of material supply points, the plurality of temporary distribution centers, the plurality of disaster areas, and the plurality of damaged roads;

[0008] constructing an initial individual strategy based on the multi-objective emergency material distribution model;

[0009] bringing the initial individual strategy into mutation and local search operators to obtain a calculation strategy;

[0010] constructing a selection strategy and an acceptance criterion;

[0011] calculating the calculation strategy based on a hyper-heuristic algorithm, and outputting an optimal operator based on the selection strategy and the acceptance criterion;

[0012] evaluating the optimal operator and outputting an optimal scheme for emergency distribution.

[0013] Optionally, the process of constructing a multi-objective emergency material distribution model comprises:

[0014] judging a waiting condition and calculating a minimum allocation amount, and constructing the multi-objective emergency material distribution model based on the waiting condition and the minimum allocation amount.

[0015] Optionally, the process of judging a waiting condition and calculating a minimum allocation amount comprises:

[0016] The judging method of the waiting condition comprises:

[0017] measuring a supply distance and a distribution distance, the supply distance being a distance from the supply point to the distribution center, and the distribution distance being a distance from the distribution center to the disaster area;

[0018] acquiring a supply time and a distribution time based on the supply distance and the distribution distance respectively, the supply time being a time from the material supply point to the temporary distribution center, and the distribution time being a time from the temporary distribution center to the disaster area;

[0019] calculating a waiting time before the material is transported from the material supply point to the disaster area based on the supply time and the distribution time;

[0020] calculating a repair time of the damaged road, the calculation method of the repair time comprising:

[0021]

[0022] wherein t represents the time needed to repair 1 km of a road with a damage rate of 1, rr ij is the damaged distance of the road, δ ij (0≤δ ij ≤1) is the damage rate of the road, and α is a threshold value;

[0023] If the delivery time is greater than the repair time, no waiting is needed, and if the delivery time is less than the repair time, waiting is needed;

[0024] The method for calculating the minimum allocation amount comprises:

[0025] sorting the disaster areas according to the demand urgency to obtain disaster area levels, setting a span interval for each disaster area level, and calculating the minimum allocation amount based on the disaster area levels and the span interval:

[0026]

[0027] wherein b 0 ×x% represents the proportion of the minimum allocation amount of the first-level disaster area to the demand amount, b is a constant, wherein N represents the disaster area level, M Nk represents the amount of k materials needed by the Nth-level disaster area, y represents the total number of levels, q represents the number of supply points, and c hk represents the inventory of k materials in the supply point h.

[0028] Optionally, the process of constructing an initial individual strategy based on the multi-objective emergency material distribution model comprises constructing a first individual strategy and a second individual strategy, wherein the process of constructing the first individual strategy comprises: randomly allocating materials to the supply points and the disaster areas, then randomly allocating no more than the demand of each disaster area and adjusting to ensure that the amount of materials received by each disaster area does not exceed the demand of the disaster area and that the materials received are the same as the materials sent by the supply points, and then allocating the remaining half of the materials to the distribution centers and adjusting to ensure that the amount of materials received by each distribution center does not exceed the upper limit of the carrying capacity and that the materials received are the same as the materials sent by the supply points;

[0029] The process of constructing the second individual strategy comprises: calculating the materials already received by each disaster area, updating the demand of the disaster area, randomly allocating the materials received by the distribution centers to each disaster area, and adjusting to ensure that the total amount of materials obtained by each disaster area does not exceed the demand.

[0030] Optionally, the process of obtaining the calculation strategy comprises: obtaining the calculation strategy based on the first individual strategy and the second individual strategy.

[0031] Optionally, the method for constructing the selected strategy comprises:

[0032] The selection strategy is constructed based on a non-dominated individual proportion index, a space coverage scale index, a Sapcing index and a UTO index.

[0033] Optionally, the acceptance criteria include AM criteria, GDA criteria and SA criteria.

[0034] Optionally, the process of outputting the optimal operator based on the selection strategy and the acceptance criteria includes optimizing the mutation operator and the local search operator, obtaining selection probabilities of the mutation operator and the local search operator based on the selection strategy, selecting an algorithm for next iteration based on a roulette selection method, and outputting an iteration result.

[0035] Optionally, the process of outputting the optimal operator based on the selection strategy and the acceptance criteria further includes combining the AM criteria, the GDA criteria, the SA criteria and the iteration result respectively, and solving a combination result to obtain a solving result.

[0036] Optionally, the process of evaluating the optimal operator includes evaluating the solving result based on a diversity index, a distance index and a comprehensive index, and outputting a best scheme for emergency distribution.

[0037] The technical effects of the present application are as follows:

[0038] The present application proposes a double-target multi-supply-point emergency material site selection and distribution model, in which the influence of disasters on a road network is considered to propose a waiting time concept, and a minimum distributed material concept is introduced to make the distribution result more fair, and related calculation methods are introduced. The problem domain design of emergency disaster relief materials is completed, corresponding mutation operators and local search operators are proposed, an evolutionary algorithm framework is proposed, the two operators are integrated in the framework to form different bottom evolutionary algorithms, an online learning selection function is proposed as a high-level strategy of a hyper-heuristic algorithm, four common multi-target indexes are used as evaluation bases to select the bottom operators, and three acceptance criteria based on a D matrix are proposed. BRIEF DESCRIPTION OF DRAWINGS

[0039] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and of the related description are used to explain the application and are not intended to limit the application. In the drawings:

[0040] Figure 1 FIG. 3 is a schematic diagram of a three-level emergency material site selection and distribution network in an embodiment of the present application;

[0041] Figure 2 FIG. 6 is a coding diagram of a small-scale problem solution in an embodiment of the present application;

[0042] Figure 3 Figure 1 is a part case operator average usage rate diagram in an embodiment of the present application;

[0043] Figure 4 Figure 2 is a Pareto solution diagram obtained by different algorithms in an embodiment of the present application, wherein Figure 4 (a) in Figure 2 represents a Pareto solution diagram when the scheme 1-2-3-8-3-2 is used, Figure 4 (b) in Figure 2 represents a Pareto solution diagram when the scheme 2-2-4-8-3-2 is used, Figure 4 (c) in Figure 2 represents a Pareto solution diagram when the scheme 3-3-5-12-4-2 is used, Figure 4 (d) in Figure 2 represents a Pareto solution diagram when the scheme 4-3-6-12-4-2 is used, Figure 4 (e) in Figure 2 represents a Pareto solution diagram when the scheme 5-3-6-18-4-2 is used, Figure 4 (f) in Figure 2 represents a Pareto solution diagram when the scheme 6-4-6-20-4-2 is used;

[0044] Figure 5 Figure 3 is a target two iteration diagram in an embodiment of the present application, wherein Figure 5 (a) in Figure 3 represents an average value curve of the target two iteration, Figure 5 (b) in Figure 3 represents a minimum value curve in the target two iteration process;

[0045] Figure 6 Figure 4 is a result diagram when the target two value is minimum in an embodiment of the present application. DETAILED DESCRIPTION

[0046] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0047] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0048] Embodiment One

[0049] As shown in Figures 1-6 , the present embodiment provides a multi-supply point emergency material site selection optimization method considering timeliness and fairness, which includes:

[0050] The present embodiment proposes a double target model, one of which is the time cost. Meanwhile, considering the uncertainty of emergency materials, the present embodiment adds a road network, and sets the damaged road length of the road as rrij , the damage rate of the road is δ ij (0≤δ ij ≤1), when the road damage rate is small, it does not affect the traffic, when it exceeds a certain threshold α, then it needs to be repaired, wherein the repair time of the road is as follows:

[0051]

[0052] Wherein, t represents the time required to repair a 1-kilometer road with a damage rate of 1.

[0053] In addition, since the present embodiment considers the problem of multiple supply points, corresponding to the situation that a sudden public event occurs in a certain place in real life, and other places provide assistance, therefore the road damage problem only occurs between the distribution center and the disaster area, and the supply point directly sent to the disaster area also needs to consider the waiting time. Therefore, the time cost is calculated as follows:

[0054]

[0055] Wherein, represents the amount of the kth material transported from the material supply point h to point i, represents the amount of the kth material transported from the material distribution center i to the disaster area j, represents the amount of the kth material transported from the material supply point h to the disaster area j, t hi represents the time from the material supply point to the temporary distribution center, t ij is the time from the temporary distribution center to the disaster area, as formula (3)

[0056]

[0057] Wherein, r hi and r ij respectively represent the distance from the supply point h to the distribution center i and the distance from the distribution center i to the disaster area j.

[0058] t h is the waiting time of the material at the supply point, that is, the time spent on road repair, t i is the waiting time of the material at the temporary distribution center, the so-called waiting time is the time for unit material to wait for road repair before distribution, mainly considering the road transportation time to the distribution center and the road repair time between the distribution center and the disaster area, if the transportation time is greater than the road repair time, it does not need to wait, if the transportation time is less than the road repair time, it needs to wait.

[0059] Another target is the minimum number of material shortage. The demand urgency of the disaster area is used as the evaluation criterion, and the demand urgency and the amount of the shortage material are considered as the evaluation criterion of fairness. When this value is the minimum, it means that the distribution result takes into account the disaster degree and the demand of the disaster area, and realizes fairness. In order to avoid the situation that the disaster area receives 0 material, the concept of the minimum material allocation is introduced, and the disaster area is classified according to the demand urgency. For disaster areas of different levels, there is a minimum material allocation, to ensure that the material obtained by each disaster area can exceed the minimum allocation. The specific calculation method is as follows:

[0060] First, the disaster area is sorted according to the demand urgency, and the maximum value μ of the urgency is found max , and the minimum value μ min is found, and it is divided into y groups (y is determined according to the number of disaster areas), each group is a level, and its span interval is as follows.

[0061] a = (μ max - μ min ) / y (4)

[0062] Wherein, a is the span interval of each group, by which the range of each level can be determined, and then it can be corresponded to the disaster area one by one. For disaster areas of different levels, the urgency increases with the increase of the level, therefore, the minimum amount of material to be allocated also increases. Assuming that the minimum allocation of the first level disaster area is b 0 × x%, the rest is b 1 × x%, b 2 × x%, b 3 × x%, b is a constant. At the same time, the following conditions are met:

[0063]

[0064] Wherein, N represents the level of the disaster area, M Nk represents the amount of k material required by the disaster area of the N level, and. represents the upward rounding. From the above formula, the minimum allocation of the disaster area of different levels can be calculated, and when the material is allocated, the material allocated to each disaster area should be higher than the minimum material allocation, and on this basis, the minimum number of material shortage is realized, therefore, the second target function of the embodiment is:

[0065]

[0066] Wherein, d jk is the material demand of the disaster area, and the above formula satisfies:

[0067]

[0068] Wherein, a is the minimum demand rate of materials, thus the problem model proposed in this embodiment is:

[0069]

[0070] And subject to the following constraints:

[0071]

[0072] Wherein, formula (8) is a target function representing the minimization of time cost and the minimization of the number of material shortages; formula (9) represents that the number of each type of material delivered to the demand point does not exceed the actual demand, B is a set of disaster areas, C is a set of material types; formula (10) represents that the number of materials received by the distribution center cannot exceed the upper limit of the carrying capacity, D i represents the upper limit of the carrying capacity of the temporary distribution center i, A is a set of distribution centers, Q is a set of supply points; formula (11) represents that in the case of supply shortage, all materials of the material reserve point should be delivered, wherein c hk represents the inventory of the kth type of material in the material reserve h; formula (12) is a non-negative integer constraint for the materials delivered by the distribution center to the disaster area; formulas (13)-(15) are decision variables.

[0073] The problem proposed in this embodiment is a mixed integer nonlinear model. Considering the road damage in reality, the waiting time of materials caused by road repair is added, and the minimum allocation amount is proposed to ensure fair allocation. At the same time, the problem considered is also an NP-hard problem. Therefore, the goal of this embodiment is to design an algorithm, and to propose an effective multi-objective hyper-heuristic algorithm to obtain optimal or near-optimal Pareto solution.

[0074] In the initialization of individual strategies, this embodiment adopts a two-layer structure.

[0075] Wherein the first layer is a (k×q)×(m+n) matrix, representing the number of materials allocated by each supply point to the temporary distribution center and the disaster area, with k×q rows, the first m rows representing the distribution center, and the last n rows representing the disaster area. First, randomly allocate the materials to the supply point and the disaster area. Second, randomly allocate the materials to each disaster area not exceeding its demand and adjust to ensure that the number of materials received by each disaster area does not exceed the demand of the disaster area, and the materials received are the same as the materials sent by the supply point. Then, allocate the remaining half of the materials to the distribution center and adjust to ensure that the number of materials received by each distribution center does not exceed the upper limit of the carrying capacity, and the materials received are the same as the materials sent by the supply point.

[0076] The second layer is a (q+m) x n x k matrix representing the supply points and distribution centers' allocation of goods to the disaster areas. The first q rows of data have been mentioned in the first layer. Next, first calculate the goods each disaster area has received, update the disaster area's demand. Then randomly allocate the goods received by the distribution center to each disaster area and adjust to ensure that the total number of goods obtained by each disaster area does not exceed the demand.

[0077] A small-scale case containing 3 supply points, 2 types of goods, 6 temporary distribution centers, and 6 disaster areas is coded as shown in Figure 2 The yellow and blue parts of the figure are the same, but only to facilitate the calculation of constraints.

[0078] According to the characteristics of the problem coding of this embodiment, three types of operators are designed: mutation operator (LLH-M), local search operator for generating non-dominated solutions (LLH-NDL), and local search operator for generating dominated solutions (LLH-DL). The mutation operator is to optimize the parent individual without considering the dominance relationship between the generated child and the corresponding parent. It can help to expand the search and jump out of the local optimal solution; the local search operator for generating dominated solutions is to generate a child that is not dominated by the corresponding parent. This helps to improve the diversity of the solution; the local search operator for generating non-dominated solutions is to generate a child that must dominate the corresponding parent, which helps the algorithm converge quickly. The specific design of the three operators is as follows:

[0079] LLH-M1: randomly select a distribution center with a certain probability m1, and allocate the goods allocated to a disaster area to another disaster area, while reducing the same goods allocated to the disaster area by the remaining distribution centers, and ensure that it does not exceed the demand of the disaster area.

[0080] LLH-M2: randomly select a distribution center with a certain probability m1, and allocate the goods allocated to a disaster area to another disaster area, and ensure that it does not exceed the demand of the disaster area.

[0081] LLH-M3: randomly select a supply point with a certain probability m1, and allocate the goods allocated to a distribution center to another distribution center, while reducing the same goods allocated to the distribution center by the remaining supply points, and ensure that it does not exceed the capacity limit.

[0082] LLH-M4: randomly select a supply point with a certain probability m1, and allocate the goods allocated to a distribution center to another distribution center, and ensure that it does not exceed the capacity limit.

[0083] LLH-M5: re-allocate the goods allocated by the supply points to the distribution centers and disaster areas, and ensure the feasibility of the solution;

[0084] As for the local search operator, although it is divided into two categories in this paper, there is no difference in the specific operation, only a constraint is added to the final result, so the specific operation has the following several kinds:

[0085] LLH-L1: Select a distribution center with a certain probability m2, and distribute the materials of a certain disaster area to another disaster area, and ensure that it does not exceed the demand of the disaster area.

[0086] LLH-L2: Select a distribution center with a certain probability m2, and distribute the materials of a certain disaster area to another two disaster areas, and ensure that it does not exceed the demand of the disaster area.

[0087] LLH-L3: Select a distribution center with a certain probability m2, and distribute the materials of a certain disaster area A to another disaster area B, and then distribute the same materials of another distribution center to disaster area B to disaster area A, and ensure that it does not exceed the demand of the disaster area.

[0088] LLH-L4: Select a distribution center with a certain probability m2, and distribute the materials of a certain disaster area A to another disaster area B, and then distribute the materials of another distribution center to disaster area B to other disaster areas except disaster area A, and ensure that it does not exceed the demand of the disaster area.

[0089] LLH-L5: Distribute a part of the materials of the supply point to the distribution center, and ensure the feasibility of the solution;

[0090] LLH-L6: Distribute a part of the materials of the distribution center to the disaster area, and ensure the feasibility of the solution;

[0091] The above are six different operations of the local search operator. This embodiment does not directly use it to solve, but integrates the mutation operation and the local search operation in the evolutionary algorithm. Because in the process of solving multi-objective problems, scholars have proposed many efficient algorithms, but evolutionary algorithms have always been favored by scholars because of their high robustness and wide applicability. In the process of evolution, the mutation operator is selected in a random way, and the local search operator is selected by high-level strategy. Since the local search operator is divided into two categories, 12 different evolutionary algorithms will be generated in the end. When updating the solution set of the evolutionary algorithm, the grid density sorting is used to screen the non-dominated solution set, which can effectively ensure the balance between convergence and population diversity.

[0092] In the hyper-heuristic algorithm, the selection strategy is the core of the algorithm, and a good selection strategy can quickly select the appropriate bottom-level heuristic operator to jump out of the local optimal solution. This embodiment proposes a high-level selection strategy based on an online learning selection function (Online Choice Function, OLCF). The specific operation is as follows:

[0093] The strategy is to select the indicators of the generated population. In this problem, because the true Pareto front is unknown, three indicators that do not require the knowledge of the true Pareto front are adopted to evaluate the solution set generated by the operator, and the performance of the operator is reflected in turn, including: the proportion of non-dominated individuals (RNI), the space coverage size (SSC), the Sapcing indicator (S) and the UTO indicator (Usage times of operator). The UTO indicator is defined as the number of times the operator has been used so far, and the smaller this value is, the greater the probability of selecting the operator. Therefore, the proposed online learning selection function comprehensively considers the above four indicators: RNI, SSC, S and UTO. Before selecting the underlying algorithm, each underlying algorithm is used for optimization, and then the four indicators of the solution generated by each underlying heuristic algorithm are calculated, and then the selection probability P(h) of each underlying algorithm h∈M is determined, M represents the set of evolutionary algorithms composed of underlying operators.

[0094]

[0095] wherein a, b, c, d represent the weight coefficients of each indicator, are constants, and satisfy a+b+c+d=1; |M| represents the number of underlying evolutionary algorithms. For the SSC, S and UTO three indicators, the smaller their values are, the greater the probability of selection is, unlike the RNI indicator, so the following equation needs to be satisfied:

[0096]

[0097] After calculating the selection probability of each underlying algorithm, the roulette wheel selection method is used to select the low-level heuristic algorithm for the next iteration.

[0098] The acceptance criterion proposed in this embodiment refers to whether to accept the generated solution set. Before the acceptance criterion is proposed, a definition-D matrix is introduced to represent the dominance relationship between two solution sets.

[0099]

[0100] wherein D(A,B) represents the space that only dominates A but does not dominate B, D(B,A) represents the space that only dominates B but does not dominate A, δ(A+B) represents the common coverage area of the pareto front of solution set A and the front of solution set B, and δ(A) and δ(B) represent the coverage area of the pareto front of solution set A and the coverage area of the pareto front of solution set B, respectively.

[0101] Therefore, the dominance of a solution set can be defined as follows: if D(A, B) < D(B, A), it means that solution set A is closer to the true Pareto front than solution set B, and solution set A is more dominant than solution set B; otherwise, solution set B is more dominant than solution set A.

[0102] Based on the definition, three high-level acceptance criteria are proposed: AM, GDA and SA.

[0103] AM is an acceptance criterion regardless of the dominance of the generated solution set.

[0104] In GDA, there are two important parameters: Level and S. The initial Level is assigned by D(F2, F1), where F1 represents the parent population and F2 represents the child population. According to this acceptance criterion, if D(F2, F1) > Level, the child solution set is accepted, and after accepting the child solution set, the value of Level will be increased by S.

[0105] SA is a variant of the simulated annealing criterion. In the simulated annealing acceptance criterion of single-objective hyper-heuristic algorithms, the change in the objective function value is mainly used to determine whether to accept the child solution. Based on the definition of solution set dominance, a SA acceptance criterion suitable for bi-objective problems is proposed as follows: there are three important parameters: initial temperature T, cooling rate l, and termination temperature T end If D(F1, F2) < D(F2, F1), the child population is accepted, otherwise, the child population is accepted with a certain probability P, as follows:

[0106]

[0107] For the location-distribution model proposed in this embodiment, a multi-objective hyper-heuristic algorithm based on evolutionary algorithm is proposed, which mainly includes two loops: an external large loop determined by the number of iterations, and in each iteration process, an operator is selected to form an evolutionary algorithm, which also has a small loop. In addition, the external archive method is applied to the proposed algorithm, and grid density sorting is used for selection and update of the external archive set. The specific algorithm steps are as follows:

[0108] Step 1: Initialize parameters: including parameters of high-level selection strategy, parameters of high-level acceptance criterion, and parameters of bottom-level heuristic operator.

[0109] Step 2: Initialize the parameters of the population, generate the initial individuals according to the strategy in 2.1, and form the population P.

[0110] Step 3: Establish an external archive set to store non-dominated individuals in each generation (use grid density for selection).

[0111] Step4: Optimizing the generated sub-population P1:

[0112] Step4.1: High-level selection strategy, select operators according to their performance, form the bottom-level evolutionary algorithm, and optimize.

[0113] Step4.2: Determine whether to accept the current solution according to the mechanism in the acceptance criterion.

[0114] Step4.3: Update the performance indicators of the operators.

[0115] Step5: Add non-dominated individuals in the sub-population to the external archive set. Change the sub-population to the parent population.

[0116] Step6: Determine whether the individuals in the external archive set exceed the upper limit. If so, remove the exceeding individuals by grid density sorting.

[0117] Step7: Determine whether the termination condition is met; if so, stop iteration and output

[0118] the external archive set; otherwise, return to Step 4.

[0119] Step8: Remove individuals in the external archive set that exceed the population size by applying grid density sorting, and generate the Pareto front from the remaining individuals.

[0120] Due to the lack of relevant examples, the examples used in this section are randomly generated, with the following specific settings: the demand of each material djk ~ U(5, 25) tons, the urgency of the disaster area μ ~ U(1.5, 2.3), the inventory of the storage point ensures less than the total demand of the disaster area, the distance between each distribution center and the supply point X1 ~ U(300, 900) km, and the distance between the disaster area and the supply point X2 ~ U(50, 200) km, the distance between the disaster area and the supply point X3 ~ U(500, 1000) km, the damage distance of the road between the distribution center and the disaster area X ~ U(0, 15) km, the damage coefficient δ ~ U(0, 1), the damage distance of the road between the supply point and the disaster area is the same as the damage coefficient. The upper limit of the distribution center's transport capacity D ~ U(10, 100) tons. According to the above rules, a total of 6 groups of instances of different sizes are generated: 1-2-3-8-3-2; 2-2-4-8-3-2; 3-3-5-12-4-2; 4-3-6-12-4-2; 5-3-6-18-4-2; 6-4-6-20-4-2, where case 1-2-3-8-3-2 means that instance 1 has 2 supply points, 3 temporary distribution centers, 8 disaster areas, 3 warehouse sizes, and 2 types of emergency resources.

[0121] The experiment of the embodiment is programmed by using MATLAB R2019a, and is run on a computer with Inter(R) Core(TM) i7-6700K CPU @ 4.00GHz 4.01GHz and 20G memory.

[0122] The parameter settings are as follows: since the algorithm framework of this paragraph includes two loops, one is the large loop of the hyper-heuristic framework, and the other is the small loop of the underlying operator, when setting the population size, the population size is set to 40, the maximum number of iterations of the large loop is set to 200, and the maximum number of iterations of the small loop is set to 45. There are several variables in the text, which are the mutation probability Pm, the local search probability Ps, the mutation probability m1 and the local search probability m2 of the underlying evolutionary algorithm, and the parameters a, b, c and d in the high-level selection strategy OLCF. This embodiment gives a value range of these parameters:

[0123] Pm={0.1, 0.2, 0.3,..., 1.0}; Ps={0.1, 0.2, 0.3,..., 1.0}; m1={0.1, 0.2, 0.3,..., 1.0}; m2={0.1, 0.2, 0.3,..., 1.0}; a, b, c, d∈(0, 1). After the initial experiment, when Pm=0.2, Ps=0.9, m1=0.3, m2=0.8, a=0.3, b=0.35, c=0.2 and d=0.15, the algorithm performance is relatively optimal. In addition, for some algorithm parameters, the initial temperature is 1000, the termination temperature is 0.01, and the cooling rate is 0.95 in the SA acceptance criterion. The parameter S in the acceptance criterion GDA follows the default value 0.0003 optimized by Maashi et al.

[0124] In order to understand how the LLH affects the solution of the entire algorithm in the entire algorithm process, the average usage rate of the operator is first calculated, and the algorithm is run for 10 times on the above 6 groups of data, and part of the statistical results are as shown in Table 1. Figure 3 A1-A12 in Table 1 represent the operators LLH1_NDL, LLH2_NDL, LLH3_NDL, LLH4_NDL, LLH5_NDL, LLH6_NDL, LLH1_DL, LLH2_DL, LLH3_DL, LLH4_DL, LLH5_DL and LLH6_DL mentioned in 2.2, respectively.

[0125] Figure 3 ​It can be seen that each operator has a certain probability to be selected in different scale cases, which shows that the operators proposed in this embodiment are effective. However, since the selection function high-level strategy based on online learning is adopted in this embodiment, the selection probability of each operator will be different, and the probability of selecting the operator with good performance will be greater. As can be seen from the figure, under the six cases, the probability of selecting the operator generating non-dominated solutions is slightly lower than that of the operator generating dominated solutions, which shows that the effect of the operator generating dominated solutions will be better in the optimization process. Among them, the usage rate of A8 performs well in the six cases, which shows that this operator is more suitable for solving the problem.

[0126] After verifying the effectiveness of the underlying operator, it is also necessary to verify the effectiveness of the algorithm proposed in this embodiment. In this section, it is mainly divided into two parts, first, verify the performance of different strategies of the proposed algorithm, and second, verify the solving results of the proposed algorithm in this embodiment compared with other classical algorithms under different cases. When comparing the solutions, three indexes are introduced: diversity index (HV), spacing index (Spacing) and comprehensive index (IGD).

[0127] Table 1

[0128]

[0129]

[0130] Note: The optimal solution is generated by integrating all the results as a reference set to solve IGD, and the optimal index value in each case is marked.

[0131] Table 2 is the performance index of the solution obtained by different algorithms. From Figure 4As can be seen, the algorithm proposed in this embodiment achieves superior results under different cases, and its advantages become more pronounced as the case scale increases. Data shows that the average HV index of the solution obtained using the MOHH algorithm is 1805, the average HV index of the solution obtained using the MOPSO algorithm is 1738, and the average HV index of the solution obtained using the NSGA-Ⅲ algorithm is 1674, indicating that the solution obtained using the MOHH algorithm has greater diversity. The average SPACING index of the solution obtained using the MOHH algorithm is 3.143, the average SPACING index of the solution obtained using the MOPSO algorithm is 3.948, and the average SPACING index of the solution obtained using the NSGA-Ⅲ algorithm is 2.9731, indicating that the solution obtained using the NSGA-Ⅲ algorithm has greater uniformity. The average IGD index of the solution obtained using MOHH is 0.4380, the average IGD index of the solution obtained using MOPSO is 2.0714, and the average IGD index of the solution obtained using NSGA-Ⅲ is 2.5337, indicating that the solution obtained using MOHH has stronger convergence. Therefore, when comparing with the other two classic multi-objective algorithms, the algorithm proposed in this embodiment is superior to the other algorithms in terms of diversity and convergence, but slightly inferior to NSGA-Ⅲ in terms of uniformity. Overall, it can be seen that the algorithm proposed in this embodiment is effective.

[0132] Table 2

[0133]

[0134] To further illustrate the impact of introducing the minimum resource allocation on the solution, the data from 4-3-6-12-4-2 above are used to compare the differences before and after introducing the minimum resource allocation. The program is run according to the settings in 3.1, and the average and minimum values ​​of the objective function 2 of the population obtained in each generation are calculated. The convergence is then compared, as follows... Figure 5 (a) and Figure 5 As shown in (b) of the diagram.

[0135] from Figure 5 As can be seen, introducing the minimum allocation number inevitably reduces the minimum function value of objective two. For example... Figure 6 As shown, without the introduction of a minimum allocation quantity, the distribution of supplies is based on the urgency of the disaster area. In this case, supplies with low urgency in the disaster area may be allocated zero supplies. After the introduction of the minimum allocation quantity, although the distribution of supplies is still related to the urgency of the disaster area, the situation of allocating zero supplies will not occur, making the distribution more equitable.

[0136] This embodiment establishes a double objective mathematical model of emergency relief materials location-distribution problem, and uses it to improve the timeliness and fairness of the material distribution system. The first objective of the multi-objective model is to optimize the material distribution time cost, including two-stage transportation time cost and waiting time cost due to road damage. The second objective is to optimize the shortage quantity of disaster area materials while considering the urgency of the disaster area. In order to make the results of material allocation more humanized, the concept and calculation method of minimum allocation quantity are introduced. In order to solve this problem, a MOHH algorithm framework is designed, and an online learning selection function is proposed. Three acceptance criteria are combined to solve the problem. At the same time, three performance indicators are used to evaluate the generated solution in order to obtain the best strategy combination.

[0137] Through experiments, the effectiveness of the bottom operator is verified. According to the strategy comparison of the hyper-heuristic algorithm, it is concluded that OLCF-SA is the best high-level heuristic strategy combination. By comparing with the classical multi-objective solving algorithm NSGA-Ⅲ and MOPSO on different scale cases, the effectiveness of the MOHH proposed in this embodiment is further verified.

[0138] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for optimizing the location of emergency supplies with multiple supply points considering timeliness and fairness, characterized in that, The method comprises the following steps: sequentially constructing a plurality of material supply points, a plurality of temporary distribution centers, a plurality of disaster areas and a plurality of damaged roads; constructing a multi-objective emergency material distribution model based on the plurality of material supply points, the plurality of temporary distribution centers, the plurality of disaster areas and the plurality of damaged roads; constructing an initial individual strategy based on the multi-objective emergency material distribution model; bringing the initial individual strategy into mutation operators and local search operators to obtain a calculation strategy; constructing a selection strategy and an acceptance criterion; calculating the calculation strategy based on a hyper-heuristic algorithm, and outputting an optimal operator based on the selection strategy and the acceptance criterion; evaluating the optimal operator to output an optimal scheme for emergency distribution; the process of constructing the multi-objective emergency material distribution model comprises: judging a waiting condition and calculating a minimum allocation amount, and constructing the multi-objective emergency material distribution model based on the waiting condition and the minimum allocation amount; the process of judging the waiting condition and calculating the minimum allocation amount comprises: the judging method of the waiting condition comprises: measuring a supply distance and a distribution distance, wherein the supply distance is the distance from the supply point to the distribution center, and the distribution distance is the distance from the distribution center to the disaster area; obtaining a supply time and a distribution time based on the supply distance and the distribution distance, wherein the supply time is the time from the material supply point to the temporary distribution center, and the distribution time is the time from the temporary distribution center to the disaster area; calculating a waiting time before the material is transported from the material supply point to the disaster area based on the supply time and the distribution time; calculating a repair time of the damaged road, and the calculation method of the repair time comprises: where t denotes the time required to repair 1 km of a road with a damage rate of 1, rr ij is the damage distance of the road, δ ij is the damage rate of the road, 0 ≤ δ ij ≤ 1, and α is a threshold value; if the distribution time is greater than the repair time, no waiting is needed, and if the distribution time is less than the repair time, waiting is needed; the calculation method of the minimum allocation amount comprises: sorting the disaster areas according to a demand urgency to obtain disaster area levels, and setting a span interval for each disaster area level; calculating the minimum allocation amount based on the disaster area levels and the span interval: where b 0 x% represents the proportion of the minimum allocation of the first level disaster area to the demand, b is a constant, where N represents the level of disaster area, M Nk represents the amount of k materials required by the Nth level disaster area, y represents the total number of grades, q is the number of supply points, c hk is the inventory of k materials in supply point h.

2. The method of claim 1, wherein, the process of constructing the initial individual strategy based on the multi-objective emergency material distribution model comprises constructing a first individual strategy and a second individual strategy, wherein the process of constructing the first individual strategy comprises: randomly allocating the material to the supply points and the disaster areas, then randomly allocating the material to each disaster area without exceeding the demand of the disaster area and adjusting to ensure that the amount of material received by each disaster area does not exceed the demand of the disaster area, and the material received is the same as the material sent by the supply point, and then allocating the remaining half of the material to the distribution centers and adjusting to ensure that the amount of material received by each distribution center does not exceed the upper limit of the carrying capacity, and the material received is the same as the material sent by the supply point; the process of constructing the second individual strategy comprises: calculating the material already received by each disaster area, updating the demand of the disaster area, randomly allocating the material received by the distribution center to each disaster area, and adjusting to ensure that the total amount of material obtained by each disaster area does not exceed the demand.

3. The method of claim 2, wherein, the process of obtaining the calculation strategy comprises: obtaining the calculation strategy based on the first individual strategy and the second individual strategy.

4. The method of claim 3, wherein, The construction method of the selection strategy comprises: The selection strategy is constructed based on a non-dominated individual proportion index, a space coverage scale index, a Sapcing index and a UTO index.

5. The method of claim 4, wherein, The process of outputting the optimal operator based on the selection strategy and the acceptance criterion comprises: optimizing the mutation operator and the local search operator, obtaining selection probabilities of the mutation operator and the local search operator based on the selection strategy, selecting an algorithm for next iteration based on a roulette selection method, and outputting an iteration result.

6. The method of claim 5, wherein, The process of outputting the optimal operator based on the selection strategy and the acceptance criterion further comprises: combining the acceptance criterion and the iteration result respectively, solving the combined results, and obtaining a solving result.

7. The method of claim 6, wherein the method further comprises: The process of evaluating the optimal operator comprises: evaluating the solving result based on a diversity index, a distance index and a comprehensive index, and outputting a best scheme for emergency distribution.

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