Cold-chain logistics site selection and path planning method based on improved discrete fireworks algorithm

Abstract

The invention discloses a cold-chain logistics site selection and path planning method based on an improved discrete fireworks algorithm, and belongs to the technical field of intelligent decision and logistics management, and the method comprises the steps: S1, building a dual-target stochastic optimization model taking the minimization of the total cost of a system and the minimization of the carbon emission as targets, and taking the output uncertainty into consideration; s2, utilizing opportunity constraint programming to convert the randomly fluctuating yield into deterministic constraint, and setting the confidence level of decision; s3, mixed integer coding is used for generating an initial firework population representing cold storage site selection, vehicle type distribution and a path sequence; s4, in the iteration process of the algorithm, population individuals are searched through an explosion operator and a mutation operator; s5, utilizing a random opportunity constraint adjustment operator to carry out feasibility repair on a new solution generated by explosion and variation, so that the repaired solution meets the confidence level; and S6, performing non-dominated sorting and selection on the population through a Pareto dominating relationship, and outputting a cold storage site selection and path optimal scheme.

Description

Technical Field

[0001] This invention belongs to the field of intelligent decision-making and logistics management technology, specifically relating to a cold chain logistics site selection and route planning method based on an improved discrete fireworks algorithm. Background Technology

[0002] Cold chain logistics for fresh agricultural products is crucial for ensuring food safety and reducing post-harvest losses. However, significant production uncertainties exist at the production end, caused by various uncontrollable factors such as weather and natural disasters. This uncertainty poses a huge challenge to the core decisions of cold chain logistics—the selection of cold storage sites at the production site and the planning of distribution routes.

[0003] Current research largely relies on the assumption of deterministic output for optimization, which is significantly inconsistent with reality. Directly applying deterministic models to uncertain environments easily leads to two types of risks: first, actual output exceeding expectations can cause cold storage overload or vehicle overloading, resulting in operational disruptions; second, lower-than-expected output can lead to idle resources and increased costs. While a few studies have attempted to introduce stochastic programming, their solution algorithms (such as traditional genetic algorithms and particle swarm optimization) typically suffer from difficulties in maintaining feasibility and low search efficiency when dealing with probabilistic constraints like "chance constraints." These algorithms struggle to efficiently find high-quality solutions in complex discrete solution spaces that satisfy conventional constraints such as path and time windows while also guaranteeing a certain probability of not violating capacity constraints.

[0004] Therefore, there is an urgent need for an optimization algorithm specifically designed to handle stochastic output and probabilistic constraints, in order to achieve reliable, economical, and low-carbon planning of cold chain logistics systems under uncertain environments. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies in dealing with cold chain logistics optimization problems with uncertain output, and to provide a cold chain logistics site selection and route planning method based on an improved discrete fireworks algorithm, which can directly output a reliable and efficient cold chain logistics planning scheme under a given risk confidence level.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A cold chain logistics location selection and route planning method based on an improved discrete fireworks algorithm includes the following steps: S1: Establish a bi-objective stochastic optimization model that considers output uncertainty, with the objectives of minimizing total system cost and minimizing carbon emissions; S2: Use chance-constrained programming to transform stochastically fluctuating outputs into deterministic constraints and set the confidence level for the decision. ; S3: Use mixed integer encoding to generate an initial fireworks population representing cold storage location, vehicle type allocation, and path sequence; S4: During the algorithm's iteration process, individuals in the population are searched using the explosion operator and the mutation operator; S5: Using a stochastic chance constraint adjustment operator, perform feasibility repair on the new solutions generated after the explosion and mutation, so that the repaired solutions meet the aforementioned confidence level. ; S6: Perform non-dominated sorting and selection of the population using Pareto dominance relationships, and output the optimal cold storage location and path scheme.

[0007] As a further preferred embodiment of the present invention, S1 includes the following steps: Collection of farmer service points in the production areas of fresh agricultural products Collection of alternative cold storage sites Define farmer service points Fresh agricultural product output Let be a random variable that follows a normal distribution, i.e. ,in This represents the average yield. To determine the variance of output, an optimization model is constructed with the dual objectives of minimizing total system cost and minimizing carbon emissions. The objective function of the bi-objective stochastic optimization model is shown below: in, Expressing expectations, This represents minimizing the total cost of the origin cold storage system. This indicates the location cost of cold storage facilities at the production site. This indicates the transportation cost of fresh agricultural products. This represents the cost of damage incurred during the transportation of fresh agricultural products. This refers to the refrigeration costs incurred by the refrigerated truck during cargo transportation due to the heat load it bears. The penalty cost for violating the service window, This indicates the carbon trading costs incurred during transportation; This indicates minimizing carbon emissions. , , Both represent the upper bound nodes of the summation. This represents the distance between i and j. Indicates the vehicle's weight. Indicates the load-bearing capacity of fresh agricultural products. It is a constant. This indicates the electricity consumption per unit distance for refrigerated new energy vehicles. Indicates the carbon emission factor of electricity. This refers to the carbon emissions during transportation using fuel-powered vehicles. This refers to the carbon emissions during the transportation of new energy vehicles. This is the carbon emission factor coefficient for fuel. This refers to the fuel consumption per unit distance when the vehicle is unloaded. This refers to the fuel consumption per unit distance when the vehicle is fully loaded. The maximum load capacity of the vehicle. For fuel-powered vehicle route decision variables, These are variables for decision-making regarding the path of new energy vehicles.

[0008] As a further preferred embodiment of the present invention, S2 includes the following steps: Chance-constrained programming is used to transform stochastic output constraints. Specifically, for the cold storage capacity and vehicle capacity constraints caused by stochastic output, chance-constrained programming is used to transform them into deterministic constraints, and confidence levels are set. Introducing the standard normal distribution quantiles, the chance constraints are expressed as follows: in, Assign decision variables to farmers and cold storage facilities. For cold storage capacity, For probability, To set the confidence level; This constraint is transformed into an equivalent deterministic linear constraint through the property of the normal distribution: (6) in, It is the inverse function of the standard normal distribution. Indicates variance.

[0009] As a further preferred embodiment of the present invention, The deterministic constraints on cold storage capacity are as follows: in, Assign decision variables to farmers and cold storage facilities. For cold storage location decision variables; The deterministic constraints on the capacity of fuel-powered refrigerated trucks are as follows: in, For fuel-powered vehicle capacity; The deterministic constraints on the capacity of new energy refrigerated trucks are as follows: in, For new energy vehicle capacity.

[0010] As a further preferred embodiment of the present invention, the mixed integer encoding in S3 consists of three concatenated parts, including a facility allocation sequence of length n, a vehicle type allocation sequence of length n, and a vehicle configuration matrix of length m × k, where n is the number of customer points, m is the number of facility alternative points, and k is the number of vehicle type types.

[0011] As a further preferred embodiment of the present invention, the explosion operator is implemented in S4 using a 2-opt exchange operation, and the explosion radius is... Defined as the number of swaps, the mutation operator is implemented through two search mechanisms: insertion and reversal.

[0012] As a further preferred embodiment of the present invention, the specific steps of the random chance constraint adjustment operator in S5 include: S51. For solutions where the cold storage capacity or vehicle load violates the chance constraint due to random production, randomly select a customer point served by the facility or vehicle. S52. Reassign the customer point to another facility or vehicle that satisfies the probability constraints, and update the structure of the solution; S53. Repeat this process until all cold storage facilities and vehicles reach the confidence level. All of them meet the capacity and load-bearing constraints.

[0013] As a further preferred embodiment of the present invention, S6 uses Pareto dominance relations to perform hierarchical sorting of all individuals in the merged population, which includes the current generation, the explosion spark, and the mutation spark; within the same non-dominated hierarchy, individuals with lower crowding are preferentially selected by calculating the crowding degree of each solution.

[0014] The beneficial effects of this invention are as follows: Facing uncertainty head-on: This invention is the first to deeply integrate the improved discrete fireworks algorithm with chance-constrained programming, providing a proprietary solution for handling the randomness of output in cold chain logistics.

[0015] High decision reliability: This invention enables decision-makers to clearly control risks through a confidence level α. All solutions output by the algorithm can guarantee the operational feasibility of the system at this level, greatly improving the robustness of decision-making.

[0016] Achieving both search efficiency and quality: The powerful search capability of the discrete fireworks algorithm in this invention, combined with the adjustment operator designed for probabilistic constraints, enables the algorithm to quickly converge to a high-quality multi-objective optimization solution set in a complex feasible region (the solution space that satisfies probabilistic constraints).

[0017] Highly practical: This invention provides a general methodology and tools for solving the uncertainty problems of resource allocation and path optimization that are widespread in agriculture, logistics and other fields.

[0018] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0019] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 Initial decoding diagram; Figure 2 Initial decoding diagram; Figure 3 Initial population generation flowchart; Figure 4 Improved discrete fireworks diagram; Figure 5 Diagram of the spark generation process; Figure 6 Mutation operator graph; Figure 7 Pareto diagram; Figure 8 Site selection path diagram. Detailed Implementation

[0020] like Figures 1-8 As shown, this invention discloses a cold chain logistics site selection and route planning method based on an improved discrete fireworks algorithm.

[0021] Define the set N of farmer service points in the production area of ​​fresh agricultural products and the set M of cold storage candidate points, and define the output of fresh agricultural products at farmer service point i. Let be a random variable that follows a normal distribution, i.e. ,in This represents the average yield. To minimize the variance of output, an optimization model is constructed with the dual objectives of minimizing the total system cost and minimizing carbon emissions. The objective function is shown in (1-2): Expressing expectations, This represents minimizing the total cost of the origin cold storage system. This indicates the location cost of cold storage facilities at the production site. This indicates the transportation cost of fresh agricultural products. This represents the cost of damage incurred during the transportation of fresh agricultural products. This refers to the refrigeration costs incurred by the refrigerated truck during cargo transportation due to the heat load it bears. The penalty cost for violating the service window, This indicates the carbon trading costs incurred during transportation; This indicates minimizing carbon emissions. , , Both represent the upper bound nodes of the summation. This represents the distance between i and j. Indicates the vehicle's weight. Indicates the load-bearing capacity of fresh agricultural products. It is a constant. This indicates the electricity consumption per unit distance for refrigerated new energy vehicles. Indicates the carbon emission factor of electricity. This refers to the carbon emissions during transportation using fuel-powered vehicles. This refers to the carbon emissions during the transportation of new energy vehicles. This is the carbon emission factor coefficient for fuel. This refers to the fuel consumption per unit distance when the vehicle is unloaded. This refers to the fuel consumption per unit distance when the vehicle is fully loaded. The maximum load capacity of the vehicle. For fuel-powered vehicle route decision variables, These are variables for decision-making regarding the path of new energy vehicles.

[0022] Among them, the carbon emissions during transportation by fuel-powered vehicles are (3): The carbon emissions during the transportation of new energy vehicles are (4): Chance-constrained programming is used to transform stochastic output constraints. Specifically, for the cold storage capacity and vehicle capacity constraints caused by stochastic output, chance-constrained programming is used to transform them into deterministic constraints; a confidence level is set. Introducing standard normal distribution quantiles The core opportunity constraint can be expressed as: In equation (3), where For random output, As decision variables, For cold storage capacity, Represents probability; This constraint is transformed into an equivalent deterministic linear constraint through the property of the normal distribution: The deterministic constraint on cold storage capacity is The deterministic constraint on the capacity of fuel-powered refrigerated trucks is: The deterministic constraint on the capacity of new energy refrigerated trucks is The Assign decision variables to farmers and cold storage facilities (1 represents farmers). From cold storage Service, 0 (conversely). For cold storage site selection decision variables (1 represents the construction of cold storage) (0, conversely) For the path decision variables of fuel vehicles (1 indicates that the fuel vehicle starts from node), to (0 on the contrary) For new energy vehicle path decision variables (1 represents the path of fuel vehicle from node), to (0 on the contrary) These are the capacities for gasoline-powered and new energy vehicles, respectively. Discrete decision schemes are represented using mixed-integer encoding, with a design length of [length missing]. Mixed integer encoding, such as Figure 1 The initial decoding diagram is shown below ( Number of service points for farmers The code (for the number of alternative cold storage locations) is divided into three parts: the first part, of length n, is an integer representing the service cold storage number corresponding to each farmer, mapping the farmer-cold storage allocation relationship; the second part, of length n, is an integer (1 for fuel vehicles, 2 for new energy vehicles) representing the service vehicle type corresponding to each farmer, mapping the farmer-vehicle allocation relationship; the third part, of length m, consists of groups of two integers representing the number of fuel vehicles and new energy vehicles in a cold storage, mapping the cold storage-vehicle number allocation relationship; and so on. Figure 2 The initial solution is decoded from the shown content. The first part of the chromosome, "1-2-2-1-1-2-2-1-2-2", represents the cold storage number selected by the farmer. It can be seen that alternative cold storage 1 and cold storage 2 are open. Corresponding to 10 service points, we can determine which farmers each cold storage serves. The second part of the chromosome, "1-1-1-2-1-2-2-2-2-1", represents the vehicle type served to each farmer. It also corresponds to 10 service points. Combining the information in the first part of the chromosome, we can know the vehicle type corresponding to each farmer served by each cold storage. The third part of the chromosome, "11-21-00", represents the number of vehicles of each type used by each cold storage. That is, cold storage 1 uses 1 vehicle of type 1 and 1 vehicle of type 2; cold storage 2 uses 2 vehicles of type 1 and 1 vehicle of type 2. The set of farmers' points on the service routes of each vehicle type is randomly assigned to each vehicle route. Then, the order of farmers' service on each vehicle route is optimized using the ant colony algorithm to obtain the path scheme, which can be used to obtain the objective function and fitness value of each chromosome.

[0023] To quickly construct an initial feasible solution and increase population diversity, the initial population can be generated by randomly generating initial solutions, such as... Figure 3 As shown, the fireworks population size is set to an empty set of PopSise. Initial solutions are generated according to preset rules. If an initial solution satisfies the cold storage capacity opportunity programming constraint, the first vehicle type load opportunity programming constraint, and the second vehicle type load opportunity programming constraint, then the initial solution is added to the fireworks population. If the number of initial solutions meets the fireworks population size requirement, the initial fireworks population is output. After generating the required initial solutions, the improved discrete fireworks algorithm is used to solve the problem, as follows: Figure 4 As shown.

[0024] Improve the discrete fireworks algorithm: ① Set algorithm parameters: population size Maximum number of iterations Dynamic blast radius ② Generate initial population: Randomly generate mixed integer codes, and select feasible solutions according to the deterministic constraints in step S2 until the population size reaches N; ③ Explosion operation: Based on the dynamic explosion radius The 2-opt swap operator is used to swap the first and second parts of the code, retaining the optimal explosive spark, such as... Figure 5 As shown; ④ Mutation operation: The explosion spark is mutated using the insertion operator (randomly selecting coded segments and inserting them into other positions) and the reversal operator (randomly selecting consecutive coded segments and reversing their order). Both operators have a probability of 0.5, generating mutated sparks, such as... Figure 6 As shown; ⑤ Infeasible solution correction: handle over-constraint solutions by adjusting operators. If the cold storage is overcapacity, the farmers served by the overcapacity cold storage will be reassigned to other open / closed cold storage facilities; if the vehicle capacity is overcapacity, the farmers served by the overcapacity vehicles will be reassigned to other vehicles in the same cold storage facility or new vehicles, and the third part of the coding will be updated; Furthermore, the feasibility of new solutions generated through explosion and mutation is repaired by utilizing stochastic chance constraint adjustment operators. For infeasible solutions in explosion sparks and mutation sparks that do not satisfy the S2 deterministic constraint, the following methods are used for repair: (1) If the cold storage is overcapacity, i.e. : Randomly select one farmer whose cold storage capacity is over-capacity and reassign him to another open cold storage facility; if all open cold storage facilities are over-capacity, open one unopened cold storage facility and assign it to the farmer, until the cold storage capacity meets the constraints; (2) If the vehicle is overloaded, that is, the loading capacity of the fuel vehicle / new energy vehicle exceeds the limit. Randomly select one farmer whose vehicle capacity is exceeded and reassign it to another vehicle of the same type in the same cold storage. If all vehicles of the same type are overloaded, add one vehicle of the same type to the cold storage and update the number of vehicles in the third part of the code to ensure that the repaired solution meets the confidence level set in step S2. ; Furthermore, by using Pareto dominance relationships to perform non-dominated ranking and selection of the population, the optimal cold storage site selection and path scheme are output: ① Perform a fast non-dominated sort on the candidate population consisting of the parent generation feasible solution, the repaired explosion spark and the mutation spark, and divide the domination level (level 1 is a non-dominated solution, and the higher the level, the weaker the domination relationship). ② Calculate the congestion of each solution: For solutions of the same dominance level, sort them according to the two target dimensions of total cost and carbon emissions respectively. Set the congestion of boundary solutions to infinity. The congestion of non-boundary solutions is the sum of the ratios of the difference between the target values ​​of adjacent solutions in each target dimension and the range of the target values ​​of that dimension. ③ Based on the principle of "priority given to dominance level and priority given to crowding within the same dominance level", select from the candidate populations. Each solution forms the next generation population; ④ Repeat S4-S5 until the number of iterations reaches the target. Output all Pareto optimal solutions, such as Figure 7 As shown, the optimal path scheme is as follows: Figure 8 As shown.

[0025] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A cold chain logistics site selection and path planning method based on an improved discrete fireworks algorithm, characterized in that, The method comprises the following steps: S1: a double-objective random optimization model considering yield uncertainty is established with the minimum total cost and carbon emissions as the objectives; S2: transform the stochastic fluctuating production into deterministic constraints using chance-constrained programming and set the confidence level of the decision ; S3: an initial fireworks population representing the cold storage site selection, vehicle type allocation and path sequence is generated using mixed integer coding; S4: in the iteration process of the algorithm, the population individuals are searched through the explosion operator and the mutation operator; S5: adjust the new solution generated by explosion and mutation using the random chance-constrained adjustment operator to make the repaired solution satisfy the confidence level ; S6: the population is non-dominantly sorted and selected through the Pareto dominance relationship, and the optimal cold storage site selection and path scheme are output.

2. The cold-chain logistics location selection and path planning method based on the improved discrete fireworks algorithm according to claim 1, characterized in that: S1 comprises the following steps: Collecting farmer service points of fresh agricultural product origin With cold storage alternative point set , define the farmer service point The yield of fresh agricultural products is a random variable subject to normal distribution, that is , where is the yield mean, is the yield variance; the optimization model is constructed with the double targets of minimizing the total system cost and minimizing carbon emissions; The objective function of the double-objective random optimization model is as follows: wherein, denotes the expectation, denotes the minimization of the total cost of the cold storage system at the origin, denotes the site selection cost of the cold storage at the origin, denotes the transportation cost of the fresh agricultural products, denotes the cost of damage to goods during transportation of the fresh agricultural products, denotes the refrigeration cost of the refrigerated truck compartment during the transportation of goods, the penalty cost for violating the service time window, denotes the carbon trading cost generated during transportation; denotes the minimization of carbon emissions, 、 、 all denote the upper bound node of summation, denotes the distance between i and j, denotes the self-weight of the vehicle, denotes the load of the fresh agricultural products, is a constant, denotes the unit distance electric consumption of the refrigerated new energy vehicle, denotes the carbon emission factor of electricity, is the carbon emission during the transportation of the fuel vehicle, is the carbon emission during the transportation of the new energy vehicle, is the carbon emission factor coefficient of fuel, is the unit distance fuel consumption of the vehicle when empty, is the unit distance fuel consumption of the vehicle when full, is the maximum load of the vehicle, is the path decision variable of the fuel vehicle, is the path decision variable of the new energy vehicle.

3. The cold-chain logistics location and path planning method based on the improved discrete fireworks algorithm according to claim 2, characterized in that: S2 comprises the following steps: The stochastic production constraints caused by the cold storage capacity constraints and the vehicle capacity constraints are transformed into deterministic constraints by using the chance-constrained programming method, and the confidence level is set , and the chance constraint is expressed as follows: wherein, is the farmer - cold storage allocation decision variable, is the cold storage capacity, is the probability, is the set confidence level; The constraint is converted into an equivalent deterministic linear constraint through the property of normal distribution: wherein is the inverse function of the standard normal distribution, denotes the variance.

4. The cold chain logistics site selection and path planning method based on the improved discrete fireworks algorithm according to claim 3, characterized in that: The cold storage capacity deterministic constraint is as follows: wherein, is a decision variable for the farmer and the cold store, is a decision variable for the cold store location. The fuel refrigerated truck capacity deterministic constraint is as follows: wherein, Vf is the fuel tank capacity of the fuel vehicle; The new energy refrigerated truck capacity deterministic constraint is as follows: wherein, is the new energy vehicle capacity.

5. The cold-chain logistics siting and routing method based on the improved discrete fireworks algorithm according to claim 1, characterized in that: The mixed integer coding in S3 is composed of three parts in series, including a facility allocation sequence with a length of n, a vehicle type allocation sequence with a length of n, and a vehicle configuration matrix with a length of m x k, wherein n is the number of customer points, m is the number of facility candidate points, and k is the number of vehicle type categories.

6. The cold-chain logistics siting and routing method based on the improved discrete fireworks algorithm according to claim 5, characterized in that: S4 uses a 2-opt exchange operation to implement the explosion operator and sets the explosion radius. Defined as the number of swaps, the mutation operator is implemented through two search mechanisms: insertion and reversal.

7. The cold-chain logistics siting and routing method based on the improved discrete fireworks algorithm according to claim 1, characterized in that: The specific steps of the random chance constraint adjustment operator in S5 include: S51: for a solution in which the cold storage capacity or vehicle load violates the chance constraint due to random yield, a customer point served by the facility or vehicle is randomly selected; S52: the customer point is reassigned to other facilities or vehicles that satisfy the probability constraint, and the structure of the solution is updated; S53, cycle this process until all cold stores and vehicles are at the confidence level The capacity and weight constraints are satisfied by both.

8. The cold-chain logistics siting and routing method based on the improved discrete fireworks algorithm according to claim 1, characterized in that: S6: all individuals in the merged population including the current generation, the explosion sparks and the mutation sparks are hierarchically sorted using the Pareto dominance relationship; in the same non-dominant level, the individuals with smaller crowding degree are preferentially selected by calculating the crowding degree of each solution.

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