Industrial chain multi-objective optimization solving method and computer program product

Abstract

The invention discloses an industrial chain multi-objective optimization solving method and a computer program product, and belongs to the technical field of data processing method.The industrial chain multi-objective optimization solving method comprises the steps that a mathematical model is constructed, and multiple objective functions of an industrial chain are quantized; constructing a swarm intelligence bat optimization algorithm; parameters in the swarm intelligence bat optimization algorithm are initialized; executing a search process, updating the speed and position of each bat individual, and comprehensively evaluating the fitness value of each bat individual by using a plurality of objective functions; a Pareto dominating strategy is adopted to optimize the multiple objective functions, and a Pareto non-dominated solution set is screened out; using a congestion distance algorithm to calculate a congestion distance between solutions in a Pareto non-dominated solution set, and rejecting over-concentrated solutions to form an optimal solution; carrying out back propagation on the optimal solution and the fitness value, and optimizing a next iteration result; and outputting an optimal solution when an iteration termination condition is satisfied. According to the method, the solving precision, the convergence speed and the global search capability of the industrial chain optimization problem can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of data processing methods, and specifically, relates to a multi-objective optimization solution method for an industrial chain and a computer program product. Background Art

[0002] Multi-objective optimization problems in industrial chains are widespread, such as supply chain coordination, production scheduling, inventory control, logistics optimization, etc. These problems involve multiple conflicting goals, such as reducing costs, improving production efficiency, reducing carbon emissions, optimizing inventory turnover, etc. Especially in the context of globalized supply chains, the operation mode of industrial chains has become increasingly complex. Enterprises not only need to make quick decisions in a highly dynamic market environment, but also need to respond to sudden external disturbances, such as market demand fluctuations, supply chain disruptions, policy adjustments, etc. Therefore, how to achieve the optimal configuration of the industrial chain under complex constraints has become a hot topic in current research.

[0003] Early industrial chain optimization methods mainly rely on mathematical programming models, such as linear programming (LP), integer programming (IP), dynamic programming (DP) and other models, which have good optimization effects when the problem scale is small. However, with the expansion of the scale of the industrial chain and the complexity of the constraints, the computational cost of the mathematical programming model has increased significantly, the difficulty of solving has increased dramatically, and its modeling ability is difficult to meet the needs of the actual industrial chain environment. In addition, since the industrial chain involves multiple mutually influential decision-making links, such as procurement, production, inventory, transportation, etc., traditional mathematical programming models are usually difficult to achieve global optimality when dealing with multi-objective and multi-constrained optimization problems, and lack the ability to adapt to dynamically changing environments. Therefore, researchers began to turn to intelligent optimization algorithms to improve the efficiency and flexibility of solving complex optimization problems.

[0004] Intelligent optimization algorithms provide a solution strategy that combines global search and local optimization by simulating biological behaviors or physical phenomena in nature, which can effectively deal with complex industrial chain optimization problems. For example, genetic algorithms (GA) optimize problem solutions by simulating natural selection and genetic variation, and have achieved certain results in solving complex combinatorial optimization problems; particle swarm optimization (PSO) algorithms simulate the foraging behavior of bird flocks to perform global search and gradually approach the optimal solution. They have been used to solve path optimization and production scheduling problems; ant colony optimization (ACO) algorithms simulate the accumulation of pheromones during the foraging process of ants to search for paths, and have shown good results in solving problems such as logistics distribution and network optimization. However, these swarm intelligent optimization algorithms still have certain limitations when solving multi-objective optimization problems in the industrial chain, such as being prone to falling into local optimality, limited solution accuracy, and slow convergence speed. Therefore, studying more efficient and stable intelligent optimization algorithms has become an important direction for improving the optimization capabilities of the industrial chain.

[0005] In recent years, the Bat Algorithm (BA), as an emerging swarm intelligence optimization algorithm, has demonstrated good global search capabilities in solving optimization problems because it combines the characteristics of the Particle Swarm Optimization (PSO) algorithm and the Simulated Annealing (SA) algorithm. The Bat Algorithm simulates the behavior of bats using ultrasonic echolocation to search for prey, and combines frequency regulation, adaptive step size, and local search strategies to enable it to demonstrate strong solution capabilities in single-objective optimization problems. Compared with traditional optimization algorithms, the Bat Algorithm has stronger global search capabilities and can converge to high-quality solutions more quickly.

[0006] However, the existing bat algorithm still has certain shortcomings in the field of multi-objective optimization. For example, in high-dimensional multi-objective optimization problems, the existing bat algorithm is prone to stagnation near the local optimal solution due to the limitations of the search strategy, and it is difficult to further optimize; in the search process, it is difficult to balance the global exploration ability and the local development ability, resulting in slow convergence or insufficient diversity of solutions. In addition, industrial chain optimization problems usually involve discrete decision variables, such as supply chain scheduling and production planning, while the existing bat algorithm is mainly used for continuous optimization problems, has weak adaptability, and is difficult to directly apply to complex industrial chain optimization environments. Therefore, how to further improve the optimization capability of the existing bat algorithm on the basis of its ability to better adapt to the needs of solving multi-objective optimization problems in the industrial chain has become the research focus of this application.

[0007] In addition, there are still some challenges in the application of current intelligent optimization algorithms in industrial chain optimization. First, industrial chain optimization often involves multiple levels of decision-making, including strategic planning, tactical arrangements and specific execution, and existing optimization methods usually find it difficult to take into account the collaborative optimization between different levels. Secondly, the dynamic characteristics of the industrial chain require the optimization algorithm to have strong adaptability to cope with uncertainties such as changes in market demand and supply chain risks. However, many intelligent optimization algorithms still rely mainly on static optimization strategies and lack real-time adjustment capabilities. At the same time, traditional intelligent optimization algorithms often require a large number of parameter adjustments, such as the crossover probability and mutation rate of genetic algorithms, and the inertia weight of particle swarm optimization algorithms. These hyperparameters have a great impact on the solution effect of the algorithm. In actual industrial applications, how to efficiently adjust these parameters is still a problem that needs to be solved. Summary of the invention

[0008] Aiming at the complexity problem existing in the multi-objective optimization process of the industrial chain, the present invention proposes a multi-objective optimization solution method for the industrial chain to improve the solution accuracy, convergence speed and global search capability of the industrial chain optimization problem.

[0009] In order to solve the above technical problems, the present invention adopts the following technical solutions to achieve the above problems: In one aspect, the present invention proposes a method for solving multi-objective optimization of an industrial chain, including the following process: Construct mathematical models for practical problems in the industrial chain and quantify multiple objective functions of the industrial chain; Constructing swarm intelligent bat optimization algorithm: ; ; ; in, and Respectively represent i The bat in the t The speed and position of the iteration; x * Indicates the optimal solution for the current position; α is the step size factor; α initial is the initial step size factor; β is the attenuation coefficient; t is the current iteration number; T is the maximum number of iterations; Initialize the parameters in the swarm intelligence bat optimization algorithm; Execute a search process, update the speed and position of each individual bat, and use the multiple objective functions to comprehensively evaluate the fitness value of each individual bat; The Pareto dominance strategy is used to optimize the multiple objective functions and select a Pareto non-dominated solution set; Use the crowding distance algorithm to calculate the crowding distance between solutions in the Pareto non-dominated solution set, eliminate overly concentrated solutions, and form the optimal solution; Back-propagate the optimal solution and fitness value to optimize the next iteration result; When the iteration termination condition is met, the optimal solution is output.

[0010] In some embodiments of the present application, the mathematical model of the objective function can be constructed as F k ( x );in, k represents the sequence number of the objective function, k= 1,2,3……, M , M is the target number; x is the decision variable.

[0011] In some embodiments of the present application, the process of comprehensively evaluating the fitness value of each individual bat using the multiple objective functions may include: The location of each individual bat , calculate the value of each objective function separately ; Normalize each objective function: ; in, and Respectively represent k The maximum and minimum values ​​of the objective function; right M The objective function is weighted to calculate the fitness value of each bat individual: ; in, w 1. w 2.…… w M Represent weights respectively.

[0012] In some embodiments of the present application, the process of screening the Pareto non-dominated solution set may include: All the normalized objective functions As a solution, if the solution x′ No worse than solution on all objectives x , and is better in at least one objective, then x′ Dominate x , x′ is a non-dominated solution; the superiority and inferiority are determined according to the optimization problem of each objective function; Screen out all non-dominated solutions to form a Pareto non-dominated solution set.

[0013] In some embodiments of the present application, the crowding distance calculation process may include: In the Pareto non-dominated solution set, all solutions are sorted according to the optimization problem of each objective function; Using each solution x The left and right adjacent solutions of x crowding distance; According to the crowding distance, overly concentrated solutions are eliminated to form the optimal solution.

[0014] In some embodiments of the present application, the solutions in the Pareto non-dominated solution set are x The crowding distance calculation formula is: ;in, x prev Yes x The solution on the left side; x next Yes x The solution on the right side; the previous solutions can be retained in descending order of crowding distance to form the optimal solution.

[0015] In some embodiments of the present application, the solutions in the Pareto non-dominated solution set can be arranged in descending order according to the crowding distance; then, the number of retained solutions is set. n Or crowding distance threshold d ; In actual application, you can choose n solutions are retained to form the optimal solution; or, the crowding distance is greater than the threshold d The solutions are retained to form the optimal solution.

[0016] In some embodiments of the present application, the iteration termination condition may be set as: reaching a set maximum number of iterations or a Pareto front change rate being less than a set threshold.

[0017] In some embodiments of the present application, the maximum number of iterations can be set to T =100; the threshold value of the Pareto frontier change rate can be set to ε =e -4 .

[0018] In another aspect, the present invention also proposes a computer program product, including a computer program or instructions, which, when executed by a processor, can implement the steps of the above-mentioned industrial chain multi-objective optimization solution method.

[0019] Compared with the prior art, the advantages and positive effects of the present invention are mainly reflected in: 1. The present invention improves the bat algorithm and enhances the global search capability by introducing an adaptive step size adjustment strategy. The traditional bat algorithm has a fixed step size, which can easily cause the search process to fall into a local optimal solution in complex problems. The present invention dynamically adjusts the step size to enable large-scale global exploration in the early stages of the algorithm to avoid premature convergence; and as the iteration proceeds, the step size gradually decreases, thereby enabling more sophisticated local optimization. This adaptive step size search mechanism effectively avoids the limitations of the fixed step size strategy and improves search efficiency and result quality.

[0020] 2. The present invention adopts the Pareto optimal solution screening method to effectively balance the relationship between different objectives in the multi-objective optimization process. Since these objectives usually conflict, how to find the best balance point between multiple objectives is the core issue of multi-objective optimization. Traditional methods often focus too much on a single objective and ignore the influence of other objectives. The present invention uses the Pareto dominance strategy to select a high-quality solution set that is not dominated by other solutions from the candidate solutions, ensuring that the solution set in the optimization process has good diversity and balance. This not only effectively handles complex multi-objective optimization problems, but also avoids over-optimization of a single objective, thereby improving the comprehensiveness and practicality of the optimization of the entire industrial chain.

[0021] 3. The present invention improves the bat algorithm, combines the adaptive step size adjustment strategy, the improved fitness function design and the multi-objective decision-making method, and significantly improves the solution accuracy, convergence speed and global search capability of the multi-objective optimization problem of the industrial chain.

[0022] 4. The bat optimization algorithm of the present invention has stronger global search capability, higher adaptability and more stable convergence in the multi-objective optimization problem of the industrial chain. Compared with the prior art, the present invention not only has significant advantages in solving efficiency, but also provides a more flexible and comprehensive solution in multi-objective decision-making, which can provide more scientific, reasonable and efficient decision support for the optimization of complex industrial chains, and is particularly suitable for complex industrial chain optimization problems, such as supply chain management, production scheduling, logistics path optimization, etc.

[0023] Other features and advantages of the present invention will become more apparent after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is an overall flow chart of an embodiment of the multi-objective optimization solution method for the industrial chain proposed by the present invention. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] In the description of the present invention, the consecutive numbering of the method steps is for the convenience of review and understanding. Combined with the overall technical scheme of the present invention and the logical relationship between the various steps, adjusting the implementation order between the steps will not affect the technical effect achieved by the technical scheme of the present invention.

[0027] The multi-objective optimization solution method for the industrial chain of this embodiment is proposed based on the bat algorithm. In order to solve the problems that the traditional bat algorithm may have when dealing with multi-objective optimization problems, such as slow convergence speed and easy to fall into local optimal solutions, this embodiment combines the adaptive step size adjustment strategy, the improved design of the fitness function and the multi-objective decision-making method to comprehensively optimize the traditional bat algorithm and proposes a swarm intelligent bat optimization algorithm framework. The framework has stronger global search capabilities, higher convergence speed and more stable solution accuracy, and can more effectively solve the multi-objective optimization problems of complex industrial chains. Compared with the existing intelligent optimization algorithms, it not only improves the efficiency of optimization solutions, but also enhances the algorithm's adaptability to dynamically changing environments, and can provide a more intelligent decision-making solution for industrial chain management.

[0028] Combine the following Figure 1 , the specific execution process of the industrial chain multi-objective optimization solution method of this embodiment is elaborated in detail.

[0029] S101. Aiming at the actual problems of the industrial chain, a mathematical model is constructed to quantify multiple optimization objectives of the industrial chain.

[0030] In the existing industrial chain, common optimization goals include minimizing total cost, maximizing profit, shortening delivery time, etc. Each optimization goal represents an important aspect of the industrial chain, and these optimization goals sometimes compete with each other. Therefore, a multi-objective optimization strategy is needed to balance the relationship between the optimization goals.

[0031] In view of the multi-objective optimization problem of the industrial chain, this embodiment first constructs the objective function F k ( x );in, k Indicates the sequence number of the objective function. Assuming that the multi-objective optimization problem has M goals, such as the total cost, profit, delivery time, etc. of the industrial chain, then k =1,2,3……, M ; x is the decision variable. x The physical meaning of is completely determined by the specific problem and needs to be understood in combination with domain knowledge. x The design of the method is to balance mathematical rigor and engineering feasibility, with the ultimate goal of finding a set of actionable and interpretable variables.

[0032] For each optimization problem, construct an optimization objective function, for example: f 1( x ); f 2( x ); in, F 1( x ) represents the total cost of the industrial chain, including raw material procurement costs, production costs, logistics costs and other expenses; f 1( x ) represents the minimization of total cost; F 2( x ) represents the delivery time, i.e., it is used to measure the product transportation capacity of enterprises in the industrial chain; f 2( x ) represents the minimization of delivery time.

[0033] In some embodiments, the objective function of the total cost can beF 1( x ) is expressed by the following mathematical model: ; in, C represents fixed cost, which can be a constant; c i Indicates i Unit costs of variable costs, such as raw materials, labor, etc.; x i Indicates i The usage of a resource, such as production quantity, transportation volume, etc. n The total number of items representing variable cost items; d j Indicates j Item fixed cost; y j Indicates whether to enable j fixed cost; in this embodiment, y j Can be a variable 0 or 1; 0 means not to start the j Item fixed cost; 1 means starting the j Item fixed cost; m Represents the total number of projects for which you can choose to enable the fixed cost item.

[0034] Delivery time F 2( x ) is usually related to production cycle, transportation time, queuing delay and other issues. In some embodiments, the objective function of delivery time can be F 2( x ) is expressed by the following mathematical model: ; in, t h Indicates h Unit time of each production link; x h It is h The production volume of each production link; p Indicates the total number of production links; t l Indicates l Unit time of transport routes; z l Indicates whether to select l transport paths; in this embodiment, z l Can be a variable 0 or 1; 0 means not to select ltransport path; 1 means select l transport routes; q Indicates the total number of transport routes; t r Indicates r The queuing time of each node; s Indicates the number of nodes.

[0035] There are usually conflicts and trade-offs in the optimization of these objective functions, and multiple factors need to be considered in the optimization process. In some embodiments, a Pareto optimal solution strategy can be used to make multi-objective decisions.

[0036] S102, constructing a swarm intelligent bat optimization algorithm.

[0037] The core idea of ​​the bat algorithm is to simulate the process of bats adjusting their flight paths through echolocation. Through this mechanism, bats can conduct a global search in the search space and gradually develop local solutions to find the optimal solution.

[0038] In this embodiment, in order to make the bat algorithm more suitable for solving multi-objective optimization problems in complex industrial chains, the speed formula and position formula in the bat algorithm are improved and updated to the following formula: ; (1); in, and Respectively represent i The bat in the t The speed and position of the iteration; α is the step size factor, which determines the amplitude of the search; x * represents the optimal solution for the current position, that is, the best solution among all bats.

[0039] The updated position and velocity formulas reflect the echolocation process, in which bats adjust their flight paths by calculating the gap between themselves and the current optimal solution, thereby achieving extensive search of the solution space and meticulous local development.

[0040] In traditional bat algorithms, the step size is usually a fixed value, which may limit the flexibility of the search process, especially when the search space is complex.

[0041] To address this problem, this embodiment introduces an adaptive step size strategy to optimize the flexibility and efficiency of the algorithm, so as to ensure that a large-scale exploration can be performed in the early stage of the search, and more detailed local optimization can be performed in the later stage of the search to accelerate the convergence of the algorithm. To this end, this embodiment proposes the following adaptive step size formula: (2); in, α initial is the initial step size factor; β is the attenuation coefficient; t is the current iteration number; T is the maximum number of iterations.

[0042] It can be seen from the adaptive step size formula (2) that as the number of iterations increases, the step size factor gradually decreases, which can achieve a smooth transition of the optimization target result.

[0043] This adaptive step-size adjustment strategy enables the Bat Algorithm to flexibly balance exploration and development in the solution space. By dynamically adjusting the step-size and optimizing the balance between global search and local development, the early convergence problem caused by the fixed step-size in the traditional Bat Algorithm can be effectively avoided, thereby improving the search efficiency and accuracy.

[0044] S103, initializing parameters in the swarm intelligent bat optimization algorithm.

[0045] When initializing parameters, the complexity of the multi-objective optimization problem of the industrial chain needs to be considered comprehensively to determine the appropriate initial values, including: Bat colony size N :Set according to the complexity of the problem, usually 20≤N≤100 ; If the industrial chain optimization problem involves a large number of decision variables, it is necessary to increase N , to ensure the diversity of the population; Maximum number of iterations T : Can be adjusted experimentally, usually set to 100≤T≤500 , to ensure that the algorithm has enough time to converge; Initial step size factor α initial : can be set to a larger value, for example, according to experiments α initial =0.5 , to support global search; Attenuation coefficient β : can be adjusted through experiments, usually set β=5 .

[0046] The uniform distribution method or Latin hypercube sampling method is used to generate the initial solution set to ensure that the solution set covers the entire search space and avoids local deviation.

[0047] S104, executing the search process, updating the speed and position of each individual bat, and using multiple objective functions to comprehensively evaluate the fitness of each individual bat.

[0048] In this embodiment, the step size factor can be adjusted by using an adaptive step size adjustment strategy (Formula 2). α Perform dynamic adjustment and then adjust the step size factor α Substitute into formula (1) to update the speed and position of each bat individual.

[0049] The fitness value of each individual bat can be obtained by comprehensive evaluation of multiple objective functions. The specific process is as follows: The location of each individual bat , respectively calculate their M The value of an objective function, such as the total cost , Delivery time wait.

[0050] In order to avoid dimensional differences, each objective function is normalized: ; in, and Respectively represent k The maximum and minimum values ​​of the objective function.

[0051] right M The objective function is weighted to calculate the fitness value of each bat individual: ; in, w 1. w 2.…… w M denote weights, and w 1+ w 2+……+ w M = 1. The values ​​of each weight can be adjusted according to the experiment.

[0052] S105. Adopting the Pareto dominance strategy, the normalized multiple objective functions are optimized to screen out the Pareto non-dominated solution set.

[0053] For multi-objective optimization problems, traditional optimization methods may not be able to consider the relationship between multiple objectives at the same time. To solve this problem, this embodiment adopts the Pareto dominance strategy to select the optimal solution by comparing the pros and cons of different solutions.

[0054] The basic principle of the Pareto dominance strategy is: if solution x′ is better than solution x in all objectives, then solution x′ is said to dominate solution x. If no solution x′ dominates solution x in all objectives, then solution x is a non-dominated solution and is part of the Pareto frontier solution.

[0055] In this embodiment, the normalized objective function (For example , The process of multi-objective optimization is to calculate the Pareto non-dominated solution set. x′ No worse than solution on all objectives x , and is better in at least one objective, then x′ Dominate x , x′ This is a non-dominated solution. The quality here can be determined based on the optimization problem of each objective (such as maximization or minimization, etc.).

[0056] Screen out all non-dominated solutions to form a Pareto non-dominated solution set.

[0057] The definition of a non-dominated solution is: in the set of feasible solutions, if there is no other solution that is strictly better than the solution in all objectives (that is, better in at least one objective and not worse in other objectives), then the solution is non-dominated. Its "optimality" is reflected in the following two aspects: (1) Not globally dominated: Non-dominated solutions are the limits of trade-offs. Any attempt to improve one of the objectives will inevitably lead to a deterioration of at least another objective. For example, in a supply chain problem of optimizing cost and delivery time, non-dominated solutions may include: Solution A: The lowest cost, but the delivery time is longer; Solution B: The delivery time is the shortest, but the cost is higher; Solution C: Both cost and time are moderate.

[0058] These three solutions do not dominate each other, and it is not possible to find an "overall better" solution by adjusting the variables.

[0059] (2) Covering all possible trade-off directions The non-dominated solution set represents a reasonable compromise under all conflicting objectives, providing decision makers with a complete trade-off option. Therefore, in multi-objective optimization, due to conflicts between objectives, there is no single optimal solution, and the "optimality" of the non-dominated solution set is relative.

[0060] The Pareto-dominated screening strategy can effectively ensure the diversity and balance of solutions, avoid over-optimization of a single objective while ignoring other objectives, and ensure that the solution set in the multi-objective optimization process is widely representative.

[0061] The introduction of this strategy enables the Bat Algorithm to effectively explore the trade-offs between different objectives when dealing with multi-objective optimization problems and obtain a set of diverse solutions with good performance.

[0062] S106. Use the crowding distance sorting method to sort the solutions in the Pareto non-dominated solution set, eliminate overly concentrated solutions, and form the optimal solution.

[0063] In order to maintain the diversity of the solution set, a crowding distance sorting method can be used to ensure the balance of different objectives. In this embodiment, solutions can be retained in descending order of crowding distance to avoid excessive concentration of Pareto non-dominated solutions (Pareto frontier solutions).

[0064] Specifically, in the Pareto non-dominated solution set, all solutions are sorted according to the value of each objective function in the optimization problem of each objective. F k ( x ), in the solution x Among the adjacent solutions of x prev is the solution (smaller or larger) on its left side, x next is the solution on the right side (larger or smaller value). For example, if the objective function is the total cost of the industrial chain F 1( x ), the optimization problem is to minimize the total cost f 1( x ), then after sorting in ascending order of cost, x prev It is a comparative solution x A lower cost solution, x next It is a comparative solution x A more costly solution.

[0065] Compute solutions in the Pareto non-dominated solution set x Crowding distance: .

[0066] The larger the crowding distance, the more "sparse" the solution is. Retaining such solutions can avoid excessive aggregation of the Pareto front, ensure diversity, and avoid local optimal traps.

[0067] In view of this, this embodiment arranges the solutions in the Pareto non-dominated solution set in descending order of crowding distance. When screening non-dominated solutions, solutions with large crowding distance are preferentially retained, thereby covering a wider optimization space.

[0068] In some embodiments, the number of retained solutions can be set n Or crowding distance threshold d, to filter out solutions that meet the conditions to form the optimal solution. For example, you can select the first n solutions are retained to form the optimal solution; or, the crowding distance is greater than the threshold d The solutions are retained to form the optimal solution.

[0069] Of course, other methods may also be selected to screen non-dominated solutions, and this embodiment is not limited to the above examples.

[0070] S107, back-propagating the optimal solution and fitness value to optimize the next iteration result.

[0071] The selected optimal solution and the calculated fitness value Substitute it into the next iteration process to optimize the next iteration result.

[0072] S108. When the iteration termination condition is met, output the optimal solution.

[0073] In this embodiment, when the maximum number of iterations is reached, T (For example T = 100) or the Pareto front change rate is less than the set threshold ε (for example ε =e -4 ), the iteration process ends and the optimal solution is output for decision makers to choose the final solution based on actual needs.

[0074] The multi-objective optimization solution method for the industrial chain of this embodiment is improved on the basis of the traditional bat algorithm to enhance its ability to solve industrial chain optimization problems, increase convergence speed, and improve the diversity and stability of solutions. By optimizing the search strategy, improving the fitness function design, and combining the multi-objective decision-making method, the bat algorithm can more effectively solve complex industrial chain optimization problems.

[0075] The multi-objective optimization solution method for the industrial chain of this embodiment is written into a computer program or instruction and executed by a processor, which can form a computer program product that solves the multi-objective optimization problem of the industrial chain and provides a reference for decision makers of the supply chain to formulate the final solution.

[0076] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for a person skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to replace some of the technical features therein by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions claimed to be protected by the present invention.

Claims

1. A method for solving multi-objective optimization of an industrial chain, characterized in that: include: Construct mathematical models for practical problems in the industrial chain and quantify multiple objective functions of the industrial chain; Constructing swarm intelligent bat optimization algorithm: ； ； ； in, and Respectively represent i The bat in the t The speed and position of the iteration; x * Indicates the optimal solution for the current position; α is the step size factor; α initial is the initial step size factor; β is the attenuation coefficient; t is the current iteration number; T is the maximum number of iterations; Initialize the parameters in the swarm intelligence bat optimization algorithm; Execute a search process, update the speed and position of each individual bat, and use the multiple objective functions to comprehensively evaluate the fitness value of each individual bat; The Pareto dominance strategy is used to optimize the multiple objective functions and select a Pareto non-dominated solution set; Use the crowding distance algorithm to calculate the crowding distance between solutions in the Pareto non-dominated solution set, eliminate overly concentrated solutions, and form the optimal solution; Back-propagate the optimal solution and fitness value to optimize the next iteration result; When the iteration termination condition is met, the optimal solution is output.

2. The multi-objective optimization solution method for the industrial chain according to claim 1 is characterized in that: Constructing a mathematical model of the objective function F k ( x ); in, x is the decision variable; k represents the sequence number of the objective function, k= 1,2,3……, M , M is the target number; The process of comprehensively evaluating the fitness value of each individual bat using the multiple objective functions includes: The location of each individual bat , calculate the value of each objective function separately ; Normalize each objective function: ； in, and Respectively represent k The maximum and minimum values ​​of the objective function; right M The objective function is weighted to calculate the fitness value of each bat individual: ； in, w 1. w 2.…… w M Represent weights respectively.

3. The method for solving the multi-objective optimization of the industrial chain according to claim 2 is characterized in that: The process of screening the Pareto non-dominated solution set includes: All the normalized objective functions As a solution, if the solution x′ No worse than solution on all objectives x , and is better in at least one objective, then x′ Dominate x , x′ is a non-dominated solution; the superiority and inferiority are determined according to the optimization problem of each objective function; Screen out all non-dominated solutions to form a Pareto non-dominated solution set.

4. The multi-objective optimization solution method for the industrial chain according to claim 3 is characterized in that: The crowding distance calculation process includes: In the Pareto non-dominated solution set, all solutions are sorted according to the optimization problem of each objective function; Using each solution x The left and right adjacent solutions of x crowding distance; According to the crowding distance, overly concentrated solutions are eliminated to form the optimal solution.

5. The method for solving the multi-objective optimization of the industrial chain according to claim 4 is characterized in that: The solution in the Pareto non-dominated solution set x The crowding distance calculation formula is: ； in, x prev Yes x The solution on the left side; x next Yes x Solution on the right side; The previous solutions are retained in descending order of crowding distance to form the optimal solution.

6. The method for solving the multi-objective optimization of the industrial chain according to claim 5 is characterized in that: The process of retaining the previous solutions in descending order of crowding distance includes: Arrange the solutions in the Pareto non-dominated solution set in descending order of crowding distance; Set the number of solutions to keep n Or crowding distance threshold d ; Before selection n solutions are retained to form the optimal solution; or, the crowding distance is greater than the threshold d The solution is retained to form the optimal solution.

7. The method for solving the multi-objective optimization of the industrial chain according to any one of claims 1 to 6, characterized in that: The iteration termination condition is: The maximum number of iterations is reached; or, The Pareto front change rate is less than the set threshold.

8. The method for solving the multi-objective optimization of the industrial chain according to claim 7 is characterized in that: The maximum number of iterations T =100; The Pareto frontier change rate is set to a threshold value ε =e -4 .

9. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the multi-objective optimization solution method for the industrial chain described in any one of claims 1 to 8 are implemented.

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