A method for allocating electronic product recycling orders based on fast non-dominated sorting method

Abstract

The present invention provides an electronic product recycling order allocation method based on a fast non-dominated sorting method, which belongs to the field of electronic order allocation, and includes: modeling the electronic order allocation problem, initializing a fast non-dominated sorting algorithm, performing chromosome crossover mutation, judging whether the maximum number of iterations has been reached, and determining the Pareto optimal path. The present invention is based on the concept of Pareto dominance, and a set of Pareto optimal solutions can be obtained by one allocation, which has strong flexibility; this order allocation method is different from the traditional order allocation method for a single target and the order allocation method that uses a weighted method to convert multiple targets into a single target, and can better meet the actual needs of order allocation.

Description

Technical Field

[0001] The present invention relates to the field of order allocation, in particular to an electronic product recycling order allocation method based on a fast non-dominated sorting method, and in particular to an electronic product recycling multi-objective order allocation method based on a fast non-dominated sorting genetic algorithm NSGA-Ⅱ. Background Art

[0002] In recent years, with the rapid development of electronic technology, the speed of electronic product replacement has accelerated, and a large number of waste electronic products are in urgent need of recycling. At the same time, with the application of "Internet +", the online to offline model (Online to Offline, O2O) has received widespread attention.

[0003] In the O2O model, users submit recycling orders online, and the order allocation system allocates the collected orders to offline recycling vehicles, which then recycle the electronic products to be recycled. Generally speaking, order allocation is to find a solution that allocates existing orders to recycling vehicles and plans recycling routes for each recycling vehicle based on certain task requirements (shortest recycling vehicle travel path, shortest travel time, minimum number of recycling vehicles, etc.). Traditional order allocation usually only considers the optimization of a single goal, and finds an order allocation solution that can meet the goal requirements in the decision space based on a certain optimization goal. However, in practical applications, it is usually necessary to consider multiple optimization goals, such as the minimum number of vehicles used, the minimum transportation cost, the time cost, etc., and multiple constraints must be met at the same time, such as service time constraints, vehicle loading constraints, etc. It is essentially an NP-complete problem with multiple goals. Therefore, the online order allocation problem for electronic product recycling can be modeled as a multi-objective optimization problem with constraints.

[0004] Different from single-objective order allocation, multiple objectives in multi-objective order allocation problems often conflict with each other. A solution that is good for one objective may be poor for other objectives. This makes it so that there is generally no unique optimal allocation solution for multi-objective electronic product recycling order allocation problems. Instead, it is a collection of allocation solutions with different objective function values. Decision makers can choose the appropriate solution according to actual needs. However, due to the NP-hard nature of multi-objective order allocation problems, its solution is often difficult to obtain accurately.

[0005] Evolutionary algorithm is a meta-heuristic optimization algorithm based on population, which can avoid searching the entire problem space and find the optimal or suboptimal order allocation solution within a reasonable time. In view of the fact that integer coding is required for path planning problems, particle swarm or genetic algorithm is often used. For the electronic product recycling order allocation problem with two objective functions in the model, the fast non-dominated sorting genetic algorithm NSGA-Ⅱ with outstanding performance is used. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes an electronic product recycling order allocation method based on a fast non-dominated sorting method. Based on the background of electronic product recycling, a multi-objective optimization model for online order allocation for electronic product recycling is established. NSGA-Ⅱ is used to select the optimal solution set that balances total transportation cost and customer satisfaction from a variety of order allocation schemes. The appropriate solution is selected according to actual needs, and has good allocation rationality and computational efficiency. The significant features of the present invention that distinguish it from existing methods are: First, the present invention models the customer experience in the electronic product recycling process as an order allocation performance indicator for the first time; Second, the present invention is aimed at the online order allocation problem for electronic product recycling, and considers multiple performance indicators at the same time in the allocation process. A set of Pareto optimal solutions can be obtained by solving it once, which has strong flexibility and can better meet actual needs.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for allocating electronic product recycling orders based on a fast non-dominated sorting method is characterized by comprising the following steps:

[0009] Step 1: Mathematical modeling of the electronic product recycling order allocation process:

[0010] Mathematically model the environment for allocating electronic product recycling orders, obtain the locations of the orders to be allocated and the different pickup vehicles available, as well as the expected service time windows of each order to be allocated, and mathematically model the constraints and objective functions;

[0011] The modeling process is as follows:

[0012] Mathematical modeling is performed on the environment of electronic product recycling order distribution. Mathematical modeling is performed in a two-dimensional plane, and a global coordinate system O-XY is established within the order distribution range, where C = {v1, v2, ..., v n} is the location set of all orders to be allocated, L = {v n+1 ,...,v n+m} is the location set of the recovered vehicles, V = {v1,v2,...,v n+m} is the set of all recovered vehicles and locations of orders to be allocated, D = {(v i ,v j ),v i ,v j ∈V,i≠j} is the set of arcs within the order allocation range, and the allocation result received by each pickup vehicle is a set of several arcs;

[0013] The specific steps include:

[0014] S1. First, the following assumptions are made:

[0015] First, in the above problems, all the vehicles used have exactly the same performance, including loading capacity, driving speed, working time, use cost, etc.;

[0016]

[0017] Among them, Q l is the maximum load of a single vehicle, Q is a constant;

[0018] Second, all customers can be served and their orders will not be split, i.e. the sum of customers’ loading requirements will not exceed the sum of all vehicles’ loading capacities;

[0019] q j ≤Q l ,j∈C,l∈L

[0020]

[0021] Among them, q j Represents the loading requirement of a single order;

[0022] Third, in this two-dimensional plane, the two positions V i and V j The distance between them is expressed using the Euclidean distance:

[0023]

[0024] Where (X i , Y i ) and (X j , Y j ) are V i and V j Coordinates on a two-dimensional plane;

[0025] The expected service time of an order is divided into two types: one is a time window with a time span of two hours, and the other is the vehicle working time during any period. When a customer submits an order, he or she can choose one of the five time windows: [0:00, 2:00], [2:00, 4:00], [4:00, 6:00], [6:00, 8:00], [8:00, 10:00]. If no time window is selected, it will be regarded as [0:00, 10:00].

[0026] S2. Modeling decision variables:

[0027] Decision variables

[0028]

[0029] Decision variables

[0030] represents the actual service time of vehicle l for order j;

[0031] S3. Model the constraints involved in the above problem:

[0032] First, we model the actual scenarios involved in this problem under normal execution constraints: any order will be served once and only once, and the sum of the load requirements of all orders in each allocation is less than the sum of the loads of all pickup vehicles;

[0033]

[0034]

[0035] Then, the constraints of the spatial dimension are modeled: the starting position of each order allocation scheme can only be the location of the pickup vehicle and the pickup vehicle does not need to be assigned an order;

[0036]

[0037]

[0038] Finally, the constraints of the time dimension are modeled: the service time for the next order must be later than that for the previous order, and the service time for each order must be within the working hours of the pickup vehicle;

[0039]

[0040]

[0041]

[0042] in, represents the service time of vehicle l for order i, T max Indicates the latest working time of the vehicle;

[0043] S4. Model the objective function:

[0044] First, the system transportation cost is modeled: In this problem, the system transportation cost consists of two parts, one part is related to the vehicle driving distance, and the other part is related to the vehicle fixed use cost and the number of pickup vehicles used;

[0045]

[0046] Among them, C d is the transportation cost per vehicle per unit distance, C f is the fixed cost of using a single vehicle; dij is the position V i and V j The Euclidean distance between

[0047] Then model customer satisfaction:

[0048] Customer satisfaction is composed of the average of the sum of customer satisfaction, n is the total number of orders in the order allocation process, where the individual customer satisfaction is a piecewise function associated with the expected service time and the actual service time of the order

[0049]

[0050] Among them, [a j ,b j ] is the expected service time range of the order submitted by customer j. In order to adapt to the calculation process of the genetic algorithm, customer satisfaction is converted into customer dissatisfaction. The customer dissatisfaction value is 1 minus the customer satisfaction value.

[0051]

[0052] Step 2: Initialize the fast non-dominated sorting genetic algorithm:

[0053] Initialize the relevant parameters in the fast non-dominated sorting genetic algorithm, and at the same time initialize the chromosomes in the fast non-dominated sorting genetic algorithm according to the orders to be assigned and the available pickup vehicles, generate chromosomes of a certain size that meet the constraints, use integer coding for the orders to be assigned and the available pickup vehicles, randomly generate chromosomes that meet the constraints, each chromosome represents an order allocation plan, and initialize the order allocation sample population based on the coding method;

[0054] Step 3: Update the chromosomes in the population and generate offspring chromosome populations through crossover and mutation operations:

[0055] Using the crossover operator and mutation operator, the chromosomes in the initialized population are used to generate a new offspring chromosome population that meets the constraints and has the same size as the parent population. The target value of the order allocation scheme represented by each chromosome is calculated, which are the system transportation cost and customer dissatisfaction.

[0056] Step 4: Select excellent chromosomes from the existing chromosomes according to the concept of Pareto dominance and keep them as the parents for the next update;

[0057] Step 5: Determine whether the maximum number of iterations has been reached;

[0058] Repeat step 3 and step 4 and determine whether the number of iterations reaches the preset maximum number of iterations. If not, continue to repeat. If it has reached, proceed to step 6.

[0059] Step 6: Select the most appropriate order allocation plan from the optimal solution set according to actual needs;

[0060] Step 7: Update the pickup vehicle’s geographic location;

[0061] Updates the pickup vehicle location to the geographic location of the last order it served.

[0062] The population size is generally 200-1000. The larger the population size, the more optimal solutions in the iterated Pareto optimal solution set, but the calculation time will also increase accordingly. The crossover and mutation probabilities are 0.8 and 0.9 respectively, and the maximum number of iterations is 1000.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] Firstly, the electronic product recycling order allocation model proposed in the present invention models the customer usage experience in the process of waste electronic product recycling, and considers customer satisfaction in the order allocation process, which can effectively improve the system's usage experience and market competitiveness, and meets the needs of practical problems; secondly, different from the traditional order allocation process that only considers a single objective function, the present invention considers both the system transportation cost and customer satisfaction, and adopts a fast non-dominated algorithm to quickly solve the order allocation problem that considers multiple performance indicators at the same time, providing decision makers with a reasonable Pareto optimal solution set. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A flowchart of the allocation method of the present invention;

[0066] Figure 2 This is a schematic diagram of order allocation of the present invention;

[0067] Figure 3 This is a schematic diagram of the order execution sequence of this embodiment;

[0068] Figure 4 This is one of the schematic diagrams of performing crossover and mutation operations on chromosomes of an existing population in this embodiment;

[0069] Figure 5 This is the second schematic diagram of the crossover and mutation operation on the chromosomes of the existing population in this embodiment;

[0070] Figure 6 This is a schematic diagram of the process of forming a new parent chromosome population in this embodiment. DETAILED DESCRIPTION

[0071] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0072] Example 1

[0073] This embodiment describes a method for allocating electronic product recycling orders based on a fast non-dominated sorting method. Figure 1 As shown, it mainly includes the following steps:

[0074] Step 1:

[0075] Mathematically model the order allocation problem:

[0076] like Figure 2 As shown in the figure, order allocation is performed in a two-dimensional plane. The blue solid box is the starting point of the order allocation result and the location of the pickup vehicle. The blue hollow circle represents an unused vehicle. The red hollow circle represents orders at different locations. The expected service time of the order is marked next to the order. The broken lines of different colors are the order allocation results assigned to each vehicle. The customer points passed by each broken line and the connection order are the optimization goals.

[0077] 1. The following basic assumptions are made for this problem:

[0078] (1) In this problem, all vehicles used have exactly the same performance, including loading capacity, driving speed, working time, and operating cost;

[0079]

[0080] Among them, Q l is the maximum load of a single vehicle, and Q is a constant.

[0081] (2) All customers can be served and their orders will not be split, that is, the sum of the customers’ loading requirements will not exceed the sum of the loading capacities of all vehicles;

[0082] q j ≤Q l ,j∈C,l∈L

[0083]

[0084] Among them, q j Represents the loading requirement for a single order.

[0085] (3) In this two-dimensional plane, two positions V i and V jThe distance between them is expressed using the Euclidean distance:

[0086]

[0087] Where (X i , Y i ) and (X j , Y j ) are V i and V j Coordinates on a two-dimensional plane.

[0088] (4) The expected service time of an order is divided into two types: one is a time window with a time span of two hours, and the other is the vehicle working time during any period. When a customer submits an order, he or she can choose one of the five time windows: [0:00, 2:00], [2:00, 4:00], [4:00, 6:00], [6:00, 8:00], [8:00, 10:00]. If no time window is selected, it is considered to be [0:00, 10:00].

[0089] 2. Model the decision variables;

[0090] (1) Decision variables

[0091]

[0092] (2) Decision variables

[0093] represents the actual service time of vehicle l for order j;

[0094] 3. Model the constraints involved in this problem:

[0095] (1) Model the normal execution constraints of the actual scenarios involved in this problem:

[0096] Any order will be served once and only once, and the sum of the load requirements of all orders in each distribution is less than the sum of the load capacities of all pickup vehicles.

[0097]

[0098]

[0099] (2) Modeling the constraints of the spatial dimension:

[0100] The starting position of each order allocation plan can only be the location of the pickup vehicle and the pickup vehicle does not have to be assigned an order.

[0101]

[0102]

[0103] (3) Modeling the constraints of the time dimension:

[0104] The service time for the latter order must be later than that for the previous order, and the service time for each order must be within the working hours of the pickup vehicle.

[0105]

[0106]

[0107]

[0108] in, represents the service time of vehicle l for order i, T max Indicates the latest working time of the pickup vehicle.

[0109] 4. Model the objective function;

[0110] (1) Modeling system transportation costs;

[0111] In this problem, the system transportation cost consists of two parts, one part is related to the vehicle driving distance, and the other part is related to the vehicle fixed usage cost and the number of pickup vehicles used.

[0112]

[0113] Among them, C d is the transportation cost per vehicle per unit distance, C f is the fixed cost of using a single vehicle

[0114] (2) Model customer satisfaction;

[0115]

[0116] Customer satisfaction is composed of the average of the sum of customer satisfaction, n is the total number of orders in the order allocation process, where the individual customer satisfaction is a piecewise function associated with the expected service time and the actual service time of the order

[0117]

[0118] Among them, [a j ,b j ] is the expected service time range of the order submitted by customer j. In order to adapt to the calculation process of the genetic algorithm, customer satisfaction is converted into customer dissatisfaction. The customer dissatisfaction value is 1 minus the customer satisfaction value.

[0119]

[0120] Step 2: Initialize the fast non-dominated sorting algorithm to generate the parent chromosome population;

[0121] First, initialize the parameters of the fast non-dominated sorting algorithm: population size, maximum number of iterations, crossover probability, mutation probability, initialize the chromosomes in the population, and generate an initial population of a certain size. In this problem, each chromosome represents an electronic product recycling order allocation plan. The chromosome is encoded using integers. The internal gene encoding information in each chromosome represents the allocation of orders to vehicles and the order execution order. If there are N orders to be allocated and M vehicles available, the initial chromosome length is N+M-1, where the chromosome is divided into M segments, each segment represents an order assigned to the same pickup vehicle, and the order within the segment represents the order execution order. Figure 3 As shown, the chromosome at the top is divided into four segments by numbers greater than 10, namely (2,3), (4,6,9), (7,1,10), and (5,8). This means that orders 2 and 3 are assigned to the same pickup vehicle, and their service order is 2 first and then 3. Similarly, the chromosome at the bottom means that all ten orders are assigned to the same pickup vehicle, and their execution order is shown in the chromosome.

[0122] Step 3: Produce daughter chromosomes;

[0123] Perform crossover and mutation operations on the existing population chromosomes, such as Figure 4 , as shown in 5, where Figure 4 For single-segment switching crossover, two parent chromosomes cross over to produce a new daughter chromosome. Figure 5 In order to exchange and mutate, genes at two positions in a parent chromosome are exchanged to produce a daughter chromosome. After crossover and mutation operations, a new daughter chromosome population of the same size as the parent population is generated.

[0124] Step 4: Update the chromosome and determine the non-dominated solution set;

[0125] like Figure 6 As shown in the figure, first, the generated parent chromosome population is combined with the daughter chromosome population to form a new population. Secondly, for each chromosome, the two objective functions of system transportation cost and customer dissatisfaction are calculated to obtain the corresponding objective function values. For any chromosome in the population, based on the concept of Pareto dominance, the Pareto dominance relationship between chromosomes is judged. If chromosome i dominates chromosome j, it means that the order allocation scheme represented by i is better and is retained first. The chromosomes in the population are quickly non-dominated sorted, and half of the chromosomes in the existing mixed population are retained to form a new parent chromosome population.

[0126] Step 5: Determine whether the preset maximum number of iterations has been reached;

[0127] Repeat steps 3 and 4 and determine whether the maximum number of iterations has been reached. If the preset maximum number of iterations has been reached, proceed to the next step; otherwise, continue to repeat steps 3 and 4.

[0128] Step 6: Determine the Pareto optimal allocation plan and the order allocation is completed;

[0129] Output the chromosomes with non-dominated level 1 in the final population, and obtain a set of Pareto optimal allocation solutions. According to the actual problem needs, select a Pareto optimal solution for decoding as the final order allocation result. At this point, the order allocation process ends, and the vehicle location is updated to the geographic location of the last order it served.

[0130] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only preferred examples of the invention and are not intended to limit the present invention. Without departing from the novel spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for allocating electronic product recycling orders based on a fast non-dominated sorting method, characterized in that: The specific steps include the following: Step 1: Mathematical modeling of the electronic product recycling order allocation process: Mathematically model the environment for allocating electronic product recycling orders, obtain the locations of the orders to be allocated and the different pickup vehicles available, as well as the expected service time windows of each order to be allocated, and mathematically model the constraints, objective functions, and decision variables; The modeling process is as follows: Mathematical modeling is performed on the environment of electronic product recycling order distribution. Mathematical modeling is performed in a two-dimensional plane, and a global coordinate system O-XY is established within the order distribution range, where C = {v1, v2, ..., v n } is the location set of all orders to be allocated, L = {v n+1 ,...,v n+m } is the location set of the recovered vehicles, V = {v1,v2,...,v n+m } is the set of all recovered vehicles and locations of orders to be allocated, D = {(v i ,v j ),v i ,v j ∈v,i≠j} is the set of arcs within the order allocation range, and the allocation result received by each pickup vehicle is a set of several arcs; The specific steps include: S1. First, the following conditions are proposed: First, in the above problems, all the vehicles used have exactly the same performance, including loading capacity, driving speed, working time, and use cost; Among them, Q l is the maximum load of a single vehicle, Q is a constant; Second, all customers can be served and their orders will not be split, i.e. the sum of customers’ loading requirements will not exceed the sum of all vehicles’ loading capacities; q j ≤Q l ,j∈C,l∈L Among them, q j Represents the loading requirement of a single order; Third, in this two-dimensional plane, the two positions v i and v j The distance between them is expressed using the Euclidean distance: Where (x i ,y i ) and (x j ,y j ) are v i and v j Coordinates on a two-dimensional plane; Fourth, the expected service time of the order is divided into two types: one is a time window with a time span of two hours, and the other is the vehicle working time in any period; when the customer submits an order, he can choose one of the five time windows: [0:00, 2:00], [2:00, 4:00], [4:00, 6:00], [6:00, 8:00], [8:00, 10:00]. If no time window is selected, it will be regarded as [0:00, 10:00]; S2. Modeling decision variables: Decision variables Decision variables represents the actual service time of vehicle l for order j; S3. Model the constraints involved in the above problem: First, we model the actual scenarios involved in this problem under normal execution constraints: any order will be served once and only once, and the sum of the load requirements of all orders in each allocation is less than the sum of the loads of all pickup vehicles; Then, the constraints of the spatial dimension are modeled: the starting position of each order allocation scheme can only be the location of the pickup vehicle and the pickup vehicle does not need to be assigned an order; Finally, the constraints of the time dimension are modeled: the service time for the next order must be later than that for the previous order, and the service time for each order must be within the working hours of the pickup vehicle; in, represents the service time of vehicle l for order i, T max Indicates the latest working time of the vehicle; S4. Model the objective function: First, the system transportation cost is modeled: In this problem, the system transportation cost consists of two parts, one part is related to the vehicle driving distance, and the other part is related to the vehicle fixed use cost and the number of pickup vehicles used; Among them, C d is the transportation cost per vehicle per unit distance, C f is the fixed cost of using a single vehicle; d ij is the position V i and V j The Euclidean distance between Then model customer satisfaction: Customer satisfaction is composed of the average of the sum of customer satisfaction, n is the total number of orders in the order allocation process, where the individual customer satisfaction is a piecewise function associated with the expected service time and the actual service time of the order Among them, [a j ,b j ] is the expected service time range of the order submitted by customer j. In order to adapt to the calculation process of the genetic algorithm, customer satisfaction is converted into customer dissatisfaction. The customer dissatisfaction value is 1 minus the customer satisfaction value. Step 2: Initialize the fast non-dominated sorting genetic algorithm: Initialize the relevant parameters in the fast non-dominated sorting genetic algorithm, and at the same time initialize the chromosomes in the fast non-dominated sorting genetic algorithm according to the orders to be assigned and the available pickup vehicles, generate chromosomes of a certain size that meet the constraints, use integer coding for the orders to be assigned and the available pickup vehicles, randomly generate chromosomes that meet the constraints, each chromosome represents an order allocation plan, and initialize the order allocation sample population based on the coding method; Step 3: Update the chromosomes in the population and generate offspring chromosome populations through crossover and mutation operations: Using the crossover operator and mutation operator, the chromosomes in the initialized population are used to generate a new offspring chromosome population that meets the constraints and has the same size as the parent population. The target value of the order allocation scheme represented by each chromosome is calculated, which are the system transportation cost and customer dissatisfaction. Step 4: Select excellent chromosomes from the existing chromosomes according to the concept of Pareto dominance and keep them as the parents for the next update; Step 5: Determine whether the maximum number of iterations has been reached; Repeat step 3 and step 4 and determine whether the number of iterations reaches the preset maximum number of iterations. If not, continue to repeat. If it has reached, proceed to step 6. Step 6: Select the most appropriate order allocation plan from the optimal solution set according to actual needs; Step 7: Update the pickup vehicle’s geographic location; Updates the pickup vehicle location to the geographic location of the last order it served.

2. The electronic product recycling order allocation method based on the fast non-dominated sorting method according to claim 1 is characterized by: The population size is 200-1000. The larger the population size, the more optimal solutions in the iterated Pareto optimal solution set, but the calculation time will also increase accordingly. The crossover and mutation probabilities are 0.8 and 0.9 respectively, and the maximum number of iterations is 1000.

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