Knowledge migration method of evolutionary algorithm for solving constrained multi-objective optimization problem

Abstract

The invention provides a knowledge migration method of an evolutionary algorithm for solving a constrained multi-objective optimization problem, and the method comprises the steps: taking the constrained multi-objective optimization problem as a main task, removing constraint conditions in the constrained multi-objective optimization problem, and constructing an unconstrained multi-objective optimization problem as an auxiliary task; randomly selecting partial solutions in the main task population and the auxiliary task population to form a first set and a second set respectively, and generating a first candidate solution and a second candidate solution respectively based on an evolutionary algorithm; generating a main task to-be-screened population and an auxiliary task to-be-screened population based on the first candidate solution and the second candidate solution; and according to the feasibility and the preset sequence of the to-be-screened population of the main task and the to-be-screened population of the auxiliary task, a next-generation main task population and a next-generation auxiliary task population are respectively generated through screening.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence, and in particular to a knowledge transfer method of an evolutionary algorithm for solving constrained multi-objective optimization problems. Background Art

[0002] Constrained Multi-Objective Optimization Problem (CMOP) is widely found in industrial design, manufacturing, energy management, logistics, warehousing and other fields. Such problems usually contain several conflicting optimization objectives and constraints. When optimizing one objective, other objectives may deteriorate. Therefore, the solution of CMOP is a solution set containing multiple independent solutions, any of which represents a solution that trades off various optimization objectives. CMOP usually has the characteristics of high complexity, irregular feasible domain, nonlinearity, etc., and is difficult to solve.

[0003] As an important branch of artificial intelligence, evolutionary optimization algorithm is a widely accepted CMOP solution method in academia. The purpose of CMOP solution is to find a solution that is as close as possible to the optimal trade-off effect on each goal, that is, Pareto Optimal Solutions. At present, CMOP evolutionary optimization algorithms can be divided into penalty function-based methods, goal and constraint separation-based methods, problem type conversion-based methods, and evolution strategy improvement-based methods.

[0004] Among the methods based on problem type conversion, converting CMOP into a multi-task optimization problem (Multi-Task Optimization Problem, MTOP) has relatively ideal performance. It usually uses the information exchange between different tasks to inspire the algorithm to produce high-quality feasible solutions, which are characterized by high convergence performance and strong generalization ability.

[0005] However, when dealing with CMOP with complex optimization objectives and constraints, there are challenges such as insufficient utilization efficiency of optimization results and inability to effectively guide algorithm convergence. It is necessary to fully consider the characteristics of the multi-task CMOP optimization algorithm and design an efficient and stable knowledge transfer strategy to improve the CMOP optimization performance.

[0006] The purpose of the present invention is to analyze the characteristics of a multi-task based CMOP optimization algorithm and to design an efficient knowledge transfer strategy suitable for the mechanism so that the proposed strategy can improve the convergence and generalization ability of the CMOP optimization algorithm. Summary of the invention

[0007] In a first aspect of the present disclosure, a knowledge transfer method of an evolutionary algorithm for solving a constrained multi-objective optimization problem is provided, the method comprising the following steps: Taking a constrained multi-objective optimization problem as the main task, removing the constraints in the constrained multi-objective optimization problem, and constructing an unconstrained multi-objective optimization problem as an auxiliary task; Randomly selecting some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively, and generating a first candidate solution and a second candidate solution respectively based on an evolutionary algorithm; Generate a main task to-be-screened population and an auxiliary task to-be-screened population based on the first candidate solution and the second candidate solution; According to the feasibility and preset order of the main task population to be screened and the auxiliary task population to be screened, the next generation of the main task population and the next generation of the auxiliary task population are respectively generated from them.

[0008] In combination with the first aspect, the randomly selecting some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively comprises: When the number of iterations of the evolutionary algorithm is less than or equal to a first preset condition, randomly selecting solutions from the main task population and the auxiliary task population to form the first set and the second set respectively; Based on the first set and the second set, the first candidate solution and the second candidate solution are generated respectively by using the evolutionary algorithm.

[0009] In combination with the first aspect, the randomly selecting some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively further comprises: When the number of iterations of the evolutionary algorithm is greater than a first preset condition, randomly selecting non-dominated feasible solutions and dominated feasible solutions in the main task population to form the first set, and randomly selecting non-dominated solutions in the auxiliary task population to form the second set; The first candidate solution and the second candidate solution are generated according to the first set and the second set, respectively.

[0010] In combination with the first aspect, generating a main task to be screened population and an auxiliary task to be screened population based on the first candidate solution and the second candidate solution includes: The first candidate solution is obtained by fusing the main task population, the first set and the second set; The auxiliary task population and the two sets are integrated to obtain the second candidate solution.

[0011] In combination with the first aspect, generating a main task to be screened population and an auxiliary task to be screened population based on the first candidate solution and the second candidate solution further includes: The main task population and the first set are integrated to obtain a first set to be migrated, and the auxiliary task population and the second set are integrated to obtain a second set to be migrated; Evaluate the first set to be migrated using all objective functions of the main task, and evaluate the second set to be migrated using all objective functions and constraint functions of the main task; Some solutions of the first set to be migrated are selected to form the first candidate solutions, and some solutions of the second set to be migrated are selected to form the second candidate solutions.

[0012] In combination with the first aspect, if the number of non-dominated solutions in the second set to be migrated is less than a preset value, by generating an angular distance association between a reference vector and the candidate solutions, solutions associated with the unassociated vectors are selected to supplement the preset value.

[0013] In combination with the first aspect, the preset order includes: Feasible non-dominated solution > feasible dominated solution > infeasible non-dominated solution > infeasible dominated solution.

[0014] In combination with the first aspect, the first preset condition includes the number of iterations ,in is the set stage parameter, is the maximum number of iterations of the evolutionary algorithm.

[0015] According to a second aspect of the present disclosure, there is provided an electronic device, comprising: one or more processors; A storage unit is used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors can implement the knowledge transfer method based on the evolutionary algorithm for solving constrained multi-objective optimization problems.

[0016] According to a third aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the knowledge transfer method of the evolutionary algorithm for solving constrained multi-objective optimization problems can be implemented.

[0017] Beneficial effects: The present invention decomposes the constrained multi-objective optimization problem into the main task and the auxiliary task, and improves the population diversity and search efficiency of the main task by means of the auxiliary optimization of the unconstrained problem. At the same time, the screening strategy based on feasibility and non-dominance is used to ensure the superiority of the solution of the main task population under the constraint conditions and the multi-objective optimization performance, thereby achieving the goal of efficiently solving the constrained multi-objective optimization problem in complex constraint scenarios. This method takes into account the feasibility, dominance and population diversity of the solution, and has stronger global search capabilities and higher optimization efficiency than traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1A schematic diagram of a flow chart of a knowledge transfer method of an evolutionary algorithm for solving a constrained multi-objective optimization problem according to an embodiment of the present disclosure; Figure 2 Each test case and corresponding parameter setting of the embodiment of the present disclosure; Figure 3 Comparison of experimental results of various test algorithms in the WM test set of the embodiments of the present disclosure; Figure 4 The experimental results of each test algorithm of the embodiment of the present disclosure on the LIR-CMOP test set are compared; Figure 5 The experimental results of each test algorithm of the embodiment of the present disclosure in the C-DTLZ and DC-DTLZ test sets are compared; Figure 6 An electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0019] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the embodiments of the present disclosure.

[0020] The terms used in the disclosed embodiments are only for the purpose of describing specific embodiments and are not intended to limit the disclosed embodiments. The singular forms of "a", "said" and "the" used in the disclosed embodiments and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0021] It should be understood that although the terms first, second, third, etc. may be used to describe various information in the disclosed embodiments, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the disclosed embodiments, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0022] like Figure 1 The figure is a flow chart of a knowledge transfer method of an evolutionary algorithm for solving a constrained multi-objective optimization problem according to an embodiment of the present disclosure, including: S101: taking a constrained multi-objective optimization problem as a main task, removing constraints in the constrained multi-objective optimization problem, and constructing an unconstrained multi-objective optimization problem as an auxiliary task; S102: Randomly select some solutions in the main task population and the auxiliary task population to form a first set and a second set respectively, and generate a first candidate solution and a second candidate solution respectively based on an evolutionary algorithm; S103: generating a main task to be screened population and an auxiliary task to be screened population based on the first candidate solution and the second candidate solution; S104: According to the feasibility and preset order of the main task population to be screened and the auxiliary task population to be screened, the next generation of the main task population and the next generation of the auxiliary task population are respectively generated.

[0023] Specific: Assume that the main task population when the algorithm iterates to the tth generation is , the auxiliary task population is ; The offspring population generated by the main task is , the offspring population generated by the auxiliary task is . , All included NP A solution.

[0024] When the number of iterations of the evolutionary algorithm is less than or equal to the first preset condition (the number of algorithm iterations ), the specific steps are as follows: S101: taking a constrained multi-objective optimization problem as a main task, removing constraints in the constrained multi-objective optimization problem, and constructing an unconstrained multi-objective optimization problem as an auxiliary task.

[0025] In order to better solve the CMOP problem, the solution proposed in the present invention takes the optimization of CMOP as the main task, and at the same time removes the constraints in the CMOP problem to construct an unconstrained multi-objective optimization problem (MOP) as an auxiliary task.

[0026] S102: Randomly select some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively, and generate a first candidate solution and a second candidate solution respectively based on an evolutionary algorithm.

[0027] (1) Randomly from Select NP / 2 solutions from the set to form the main task (First set); (2) Randomly from Select NP / 2 solutions from the set to form a set for the auxiliary task (Second set); (3) Based on any evolutionary algorithm (such as genetic algorithm (GA), differential evolution algorithm (DE), etc.), Generate NP / 2 new candidate solutions to form a set (first candidate solution); (4) Based on any evolutionary computing operator, Generate NP / 2 new candidate solutions to form a set (Second candidate solution); S103: Generate a main task population to be screened and an auxiliary task population to be screened based on the first candidate solution and the second candidate solution.

[0028] (5) The candidate solutions in are migrated to the main task. At this time, the composition of the population to be screened in the main task is as shown in formula (1):

[0029] (6) The composition of the population to be screened for the auxiliary task is shown in formula (2):

[0030] S104: Generating the next generation of main task population and the next generation of auxiliary task population respectively from the main task population and the auxiliary task population according to their feasibility and preset order.

[0031] (7) Use all objective functions and constraints contained in the main task to Evaluate; use all objective functions included in the auxiliary task to Conduct evaluation; (8) According to the priority order of feasible non-dominated solution-feasible dominated solution-infeasible non-dominated solution-infeasible dominated solution, Select NP solutions, forming the next generation of main task population of the main task ; (9) From Select NP non-dominated solutions, forming the next generation of main task population of auxiliary tasks ; (10) If the number of solutions is not dominated N D < NP , add all non-dominated solutions to , and in Remaining N D In the solution, select NP-ND Add one solution ; (11) If the number of non-dominated solutions among the remaining solutions is less than NP-N D , then continue to select non-dominated solutions from the remaining solutions until is satisfied.

[0032] When the number of iterations of the evolutionary algorithm is greater than the first preset condition (algorithm iteration number ), the specific steps are as follows: (12) For the main task population , randomly select NP / 2 non-dominated feasible solutions to form a set (the first set); (13) If the number of non-dominated feasible solutions N DF <NP / 2, then put all non-dominated feasible solutions into , and then randomly select NP / 2 - N DF dominated feasible solutions and put them into ; (14) If the number of dominated feasible solutions N F <NP / 2 - N DF , then randomly select another NP / 2 - N DF - N F solutions to form a set ; (15) For the auxiliary task population , randomly select NP / 2 non-dominated solutions to form a set (the second set); (16) If the number of non-dominated solutions is less than NP / 2, then according to the method in step (10), until enough solutions are selected to make the number of solutions in satisfy ; (17) According to the methods in steps (3) and (4), based on , generate NP / 2 new candidate solutions for the main task to form a set (the first candidate solution set); (18) Based on , generate NP / 2 new candidate solutions for the auxiliary task to form a set (the second candidate solution set); (19) Combine and to form a set of solutions to be migrated (the first set of solutions to be migrated), that is ; (20) Combine and to form a set of solutions to be migrated (the second set to be migrated), that is ; (21) Evaluate with all objective functions ; (22) Evaluate using all objective functions and constraint functions of the main task ; (23) For , select NP / 2 non-dominated solutions and put them into the set for migration (first candidate solution); (24) If the number of non-dominated solutions is less than NP / 2, let The number of non-dominated solutions is , the MixtureUniform Design method is used to generate a set of reference vectors uniformly distributed in the target space, and each candidate solution is associated with the reference vector with the closest angular distance to it based on the angular distance; (25) Select a candidate solution that is not associated with the selected non-dominated solution and put it into , until The number of intermediate solutions reaches NP / 2; (26) Follow the method in step (11) from Select NP / 2 solutions from the above to form a knowledge transfer population (first candidate solution); (27) At this time, the main task is to select the population The composition of is shown in formula (3).

[0033]

[0034] (28) At this time, the auxiliary task population to be screened The composition of is shown in formula 4.

[0035]

[0036] (29) Follow the methods of steps (8), (9), and (10) to form the next generation population for the main task and auxiliary task respectively. and .

[0037] Exemplarily, four well-known CMOP benchmarks are used in the experimental study: WM, LIR-CMOP, C-DTLZ, and DC-DTLZ. C-DTLZ covers a large target space with a variety of feasible PFs, including regular and irregular PFs. The DC-DTLZ problem presents discontinuous PFs as well as feasible regions in both inner and outer layers, posing a challenge to the convergence ability of CMOEAs. The 14 test cases in LIR-CMOP exhibit a wide range of infeasible regions, which are used to evaluate the ability of the algorithm to avoid local optimal traps. In addition, the 14 test cases of the WM test suite contain four different types of PF geometric relations, which may be constrained or unconstrained.

[0038] Figure 2 The configurations of the population size (N), number of targets (M), decision space dimension (D), and maximum number of function evaluations (maxFEs) assigned for the selected test cases are listed.

[0039] The proposed method is compared with six state-of-the-art CMOEAs: CMOCSO, CMOEA-MS, C-TAEA, EMCMO, LMOCSO, and MSCMO. The parameters of each algorithm are configured as recommended in its original literature. All algorithms use genetic algorithms as optimizers and use simulated binary crossover and polynomial mutation as operators to generate new solutions to ensure the effectiveness of the comparison.

[0040] In order to measure the closeness between the PF output by each algorithm and the actual feasible PF, the present invention adopts the IGD+ index as the performance metric. The IGD+ index calculates the distance between each reference point on the real PF. The closest individual in the population The average distance between them is achieved.

[0041] Figures 3 to 5 The comparative evaluation of the proposed algorithm and the state-of-the-art algorithm on the MW, LIRCMOP and constrained DTLZ test suites is shown respectively. The value in each table cell is the average IGD+ value obtained from 30 independent repeated experiments, and the standard deviation is in brackets.

[0042] The smaller the average IGD+ value and standard deviation value, the better the algorithm performance.

[0043] In addition, based on the mean IGD+ value and standard deviation value, the Wilcoxon rank sum test was used with the significance level set at 0.05 to comprehensively judge the advantages and disadvantages of the algorithm.

[0044] Specifically, the symbols “+”, “-” and “=” after the brackets of other algorithms respectively represent the results of the Wilcoxon rank sum test, indicating whether the results are significantly better than, worse than or equal to the experimental results of the method proposed in the present invention, and “NaN” means there is no feasible solution.

[0045] like Figure 3 As shown, on the WM test set, the method proposed in the present invention achieved the best performance in WM1-9, WM13 and WM14 among the 14 test cases.

[0046] like Figure 4 As shown in the figure, in the LIR-CMOP test set, the method proposed in this invention achieved the best performance in LIR-CMOP1-4, LIR-CMOP6, LIR-CMOP7, LIR-CMOP11, and LIR-CMOP13 among the 14 test cases.

[0047] like Figure 5 As shown in the figure, the proposed method outperforms all the comparison algorithms on C1-DTLZ1, C1-DTLZ3, C2-DTLZ2, C3-DTLZ4, DC1-DTLZ3, DC2-DTLZ1 and DC3-DTLZ1 in 10 constrained DTLZ test cases.

[0048] In addition, on DC1-DTLZ1, the proposed method is significantly better than the four comparison algorithms, and has no significant difference compared with MSCMO and EMCMO. However, on DC2-DTLZ3, although the proposed method is significantly better than the four comparison algorithms, it lags behind EMCMO in terms of performance significance.

[0049] The electronic device 600 may be a desktop computer, a notebook, a PDA, a cloud server, or other electronic device. The electronic device 600 may include, but is not limited to, a processor 601 and a memory 602. Those skilled in the art will appreciate that Figure 6 It is only an example of the electronic device 600 and does not constitute a limitation of the electronic device 600. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the electronic device may also include input and output devices, network access devices, buses, etc.

[0050] Processor 601 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0051] The memory 602 may be an internal storage unit of the electronic device 600, for example, a hard disk or memory of the electronic device 600. The memory 602 may also be an external storage device of the electronic device 600, for example, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 600. Further, the memory 602 may also include both an internal storage unit of the electronic device 600 and an external storage device. The memory 602 is used to store the computer program 603 and other programs and data required by the electronic device. The memory 602 may also be used to temporarily store data that has been output or is to be output.

[0052] In the embodiments provided in the present disclosure, it should be understood that the disclosed devices / electronic devices and methods can be implemented in other ways. For example, the device / electronic device embodiments described above are merely schematic. For example, the division of modules or units is only a logical function division. There may be other division methods in actual implementation. Multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, indirect coupling or communication connection of devices or units, which may be electrical, mechanical or other forms.

[0053] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present disclosure implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. The computer program may include computer program code, and the computer program code may be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electric carrier signals and telecommunication signals.

[0054] The above embodiments are only used to illustrate the technical solutions of the present disclosure, rather than to limit them. Although the present disclosure has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should all be included in the protection scope of the present disclosure.

Claims

1. A knowledge transfer method for an evolutionary algorithm to solve constrained multi-objective optimization problems, characterized in that: The method comprises: Taking a constrained multi-objective optimization problem as the main task, removing the constraints in the constrained multi-objective optimization problem, and constructing an unconstrained multi-objective optimization problem as an auxiliary task; Randomly selecting some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively, and generating a first candidate solution and a second candidate solution respectively based on an evolutionary algorithm; Generate a main task to-be-screened population and an auxiliary task to-be-screened population based on the first candidate solution and the second candidate solution; According to the feasibility and preset order of the main task population to be screened and the auxiliary task population to be screened, the next generation of the main task population and the next generation of the auxiliary task population are respectively generated from them.

2. The method according to claim 1, characterized in that The randomly selecting partial solutions from the main task population and the auxiliary task population to form a first set and a second set respectively comprises: When the number of iterations of the evolutionary algorithm is less than or equal to a first preset condition, randomly selecting solutions from the main task population and the auxiliary task population to form the first set and the second set respectively; Based on the first set and the second set, the first candidate solution and the second candidate solution are generated respectively by using the evolutionary algorithm.

3. The method according to claim 1, characterized in that The randomly selecting some solutions from the main task population and the auxiliary task population to form a first set and a second set respectively further comprises: When the number of iterations of the evolutionary algorithm is greater than a first preset condition, randomly selecting non-dominated feasible solutions and dominated feasible solutions in the main task population to form the first set, and randomly selecting non-dominated solutions in the auxiliary task population to form the second set; The first candidate solution and the second candidate solution are generated according to the first set and the second set, respectively.

4. The method according to claim 2, characterized in that: The generating a main task to be screened population and an auxiliary task to be screened population based on the first candidate solution and the second candidate solution comprises: The first candidate solution is obtained by fusing the main task population, the first set and the second set; The auxiliary task population and the two sets are integrated to obtain the second candidate solution.

5. The method according to claim 3, characterized in that: The generating a main task to be screened population and an auxiliary task to be screened population based on the first candidate solution and the second candidate solution also includes: The main task population and the first set are integrated to obtain a first set to be migrated, and the auxiliary task population and the second set are integrated to obtain a second set to be migrated; Evaluate the first set to be migrated using all objective functions of the main task, and evaluate the second set to be migrated using all objective functions and constraint functions of the main task; Some solutions of the first set to be migrated are selected to form the first candidate solutions, and some solutions of the second set to be migrated are selected to form the second candidate solutions.

6. The method according to claim 5, characterized in that If the number of non-dominated solutions in the second set to be migrated is less than a preset value, then by generating an angular distance association between a reference vector and the candidate solutions, solutions associated with the unassociated vectors are selected to supplement the preset value.

7. The method according to claim 1, characterized in that The preset sequence includes: Feasible non-dominated solution > feasible dominated solution > infeasible non-dominated solution > infeasible dominated solution.

8. The method according to claim 1, characterized in that: The first preset condition includes the number of iterations ,in is the set stage parameter, is the maximum number of iterations of the evolutionary algorithm.

9. An electronic device, characterized in that: include: one or more processors; A storage unit, used to store one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement the knowledge transfer method of the evolutionary algorithm for solving constrained multi-objective optimization problems according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it can implement the knowledge transfer method of the evolutionary algorithm for solving constrained multi-objective optimization problems according to any one of claims 1 to 8.

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