Constraint multi-task optimization method and system based on task cooperation and resource self-adaption

Abstract

The invention discloses a constrained multi-task optimization method and system based on task cooperation and resource self-adaption, and belongs to the technical field of evolutionary computation and multi-task optimization. The method comprises the steps that two populations are established based on each task; a feasibility priority strategy is adopted to evolve one population, and a domain adaptation strategy based on constraint relaxation is adopted to evolve the other population; after each evolution cycle, individuals in a preset proportion are selected for evolution based on the two populations of the same task, and progenies generated by evolution are included in a progeny set; later generations generated by evolution are evaluated through environment selection, and a roulette algorithm is adopted to carry out resource adaptive allocation on an evaluation result until an evaluation counter reaches the maximum function evaluation frequency; mating is carried out based on the populations corresponding to different tasks, and generated offspring is used for randomly replacing individuals in the offspring set. According to the method, different optimization strategies are adopted to evolve and optimize different populations, the adaptability of the algorithm is enhanced, and resource waste is reduced.

Description

Technical Field

[0001] This invention belongs to the field of evolutionary computation and multi-task optimization technology, specifically involving a constrained multi-task optimization method and system based on task collaboration and resource adaptation, which is particularly suitable for scenarios such as industrial scheduling, power system optimal power flow calculation and logistics path planning where there are high-dimensional constraints and multiple optimization objectives. Background Technology

[0002] Evolutionary algorithms (EAs) address problems by simulating the evolution of populations in nature. They are widely used in engineering, computer science, energy, and other fields. Since optimization problems typically do not arise in isolation, an optimization paradigm called evolutionary multi-task optimization (MTO) has emerged. In real-world scenarios, many optimization problems are interconnected, and a large number of tasks involve constraints. Constrained multi-task optimization (CMTO) better describes and handles these complex problems, providing an effective method for solving practical multi-objective optimization problems and improving the effectiveness and practicality of algorithms in real-world applications.

[0003] In handling constrained multi-task optimization problems (CMTOPs), there are many different constraint handling techniques, and these techniques lead to varying ranges of offspring retained in the population. Examples include feasibility-first (FP) rules, epsilon-constraint (EC) techniques, multi-objective methods, and methods utilizing the correlation between constraints and objective functions. While these forward learning methods can achieve excellent results on some problems, they may exhibit learning errors on others. No single constraint handling technique (CHT) can outperform all others on all problems. In other words, because different constrained optimization problems (COPs) have different characteristics, different constraint handling techniques may perform differently in specific problem constraints. Therefore, integrating multiple constraint handling techniques can be applied to a wider range of constrained optimization problems.

[0004] While the existing constrained multi-task algorithm CEDA-MP can ensure the feasibility of the solution, it often wastes computational resources in multi-objective scheduling scenarios such as optimal power flow (OPF) in power systems because it does not distinguish the size of the feasible region of each task. For example, in the IEEE 30-bus system, when load node voltage constraints and unit output constraints exist simultaneously, the traditional algorithm requires 100,000 function evaluations to converge, while the present invention, through a task adaptive strategy, only requires 60,000 evaluations to achieve the same accuracy, reducing fuel costs by 12.3% and the number of voltage limit violations by 85%.

[0005] Furthermore, for tasks with a large feasible region, constraint relaxation or unconstrained techniques are more suitable; for tasks with a small feasible region, constraint priority techniques may be more effective. Therefore, based on the characteristics of different tasks and solution spaces, by combining the roulette wheel selection method with a feedback reward mechanism, the task can adaptively select an appropriate optimization strategy. Summary of the Invention

[0006] This invention addresses the problems of low resource utilization, slow convergence speed, and susceptibility to local optima in existing technologies. It proposes a Constrained Multi-Task Optimization (CMTO-ICRA) method for specific industrial scenarios. By establishing two populations for each task and dynamically selecting constraint handling strategies, it achieves efficient allocation of computational resources and rapid acquisition of the global optimum. This method combines constraint handling with multi-task processing methods and introduces a resource allocation strategy for multi-task algorithms using multiple populations. One population employs a feasibility-first strategy, while the other uses a domain adaptation method with constraint relaxation for evolution. In each generation of the evolutionary process, an evolutionary population is selected based on parameters. After evolution, the other population is used to generate offspring, randomly replacing some offspring from the current population to ensure that superior individuals from the other population are not lost, thus achieving the dual goals of resource allocation and information utilization.

[0007] According to one aspect of this specification, a constrained multi-task optimization method based on task collaboration and resource adaptation is provided, comprising:

[0008] Two populations are established for each task;

[0009] One population is evolved using a feasibility-first strategy, while the other population is evolved using a domain adaptation strategy based on constraint relaxation.

[0010] After each evolutionary cycle, individuals of a predetermined proportion are selected from two populations with the same task to evolve, and the offspring produced by the evolution are included in the offspring set.

[0011] During the evolution of each population, the offspring produced by evolution are evaluated through environmental selection, and the roulette wheel algorithm is used to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations, thus obtaining the optimal solution;

[0012] Based on the population corresponding to different tasks, individuals of a preset proportion are selected for mating, and the resulting offspring are used to randomly replace individuals in the offspring set.

[0013] Furthermore, the evolutionary offspring produced through environmental selection are evaluated, including:

[0014] Calculate the population success rate and the success rate of offspring being superior to their parents based on the offspring produced by evolution;

[0015] The Recombination Mating Probability (RMP) is adjusted based on the population success rate and the success rate of offspring being superior to that of parents.

[0016] Furthermore, methods for calculating population success rate and the success rate of offspring outperforming their parents include:

[0017] The success rate of the population is calculated as follows: traverse each individual in the population and compare the objective function value of the individual with the objective function value of the offspring of the same task. If the objective function value of the individual is better, then s = s + 1, where N is the number of individuals in the population and sr = N / s.

[0018] The success rate of offspring being superior to parents is calculated as follows: the number of offspring generated through information transfer is denoted as TNP, the number of offspring that are superior to parents is denoted as ts, and then tsr = TNP / ts.

[0019] Furthermore, a roulette wheel algorithm is used to adaptively allocate resources based on the evaluation results, including:

[0020] Adjustments are made based on historical performance data, and a task index k is selected for multi-task optimization;

[0021] The task selection probability matrix is ​​initialized or updated by comparing the current number of function evaluations with the maximum number of function evaluations.

[0022] If f <f max If the task selection probability is uniformly initialized, then the task selection probability will be updated using the history matrix H. After the update, the roulette wheel selection algorithm will be called to select the task index k.

[0023] Compare offspring with their parents to calculate and p, the and p is used to update the task selection probability.

[0024] Furthermore, the method also includes further optimization of the population evolution process using a constraint-relaxation-based domain adaptation strategy, specifically:

[0025] The strategy is optimized to make the recombination and mating probability adaptive, and the value of the recombination and mating probability is increased or decreased based on the feedback of the results.

[0026] A separate RMP is assigned to each subtask in the population, and two parameters γ and c are introduced, where γ is used to determine whether an improvement has been achieved, and c is used to control the magnitude of RMP adjustment.

[0027] Furthermore, the method also includes dynamically adjusting the recombination and mating probability matrix during multi-task optimization:

[0028] First, expand the recombination mating probability matrix to match the current generation g. If the selected evolutionary population index ch_k=1, then calculate the replacement rate.

[0029] Based on the relationship between the replacement rate and the threshold, a decision is made on whether to adjust the recombination and mating probability: if the replacement rate is lower than the threshold, the transfer and replacement rate is calculated using the transfer flag vector and the replacement flag vector, and the recombination and mating probability is increased or decreased accordingly.

[0030] Furthermore, the method also includes an RMP addition formula:

[0031]

[0032]

[0033]

[0034] in, Let represent the (recombination mating probability) value of task t in the Gen generation, C is the adjustment parameter, and the value of temp represents the success rate tsr of the offspring being superior to the parent generation.

[0035] According to one aspect of this specification, a constrained multi-task optimization system based on task collaboration and resource adaptation is provided, comprising:

[0036] The population creation module is used to create two populations for each task.

[0037] The population evolution module is used to evolve one population using a feasibility-first strategy and another population using a domain adaptation strategy based on constraint relaxation.

[0038] The offspring generation module is used to select a preset proportion of individuals from two populations with the same task for evolution after each evolution cycle, and the offspring generated by the evolution are included in the offspring set.

[0039] The resource adaptation module is used to evaluate the offspring produced by evolution through environmental selection when each population is evolving, and to use the roulette wheel algorithm to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations and the optimal solution is obtained.

[0040] The task collaboration module is used to select a preset proportion of individuals for mating based on the population corresponding to different tasks, and the resulting offspring are used to randomly replace individuals in the offspring set.

[0041] According to one aspect of this specification, an electronic device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the constrained multi-task optimization method based on task collaboration and resource adaptation, the electronic device being deployed in a power grid dispatch center or a cloud dispatch platform.

[0042] According to one aspect of this specification, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the constrained multi-task optimization method based on task cooperation and resource adaptation, wherein the storage medium is used to store power grid load data, population evolution records, and final optimization instructions.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] 1. This invention enhances the adaptability of the algorithm and reduces resource waste by employing different optimization strategies to evolve and optimize different stages of different tasks.

[0045] 2. This invention solves the problem of negative migration caused by information exchange between populations under a constraint relaxation strategy by introducing an adaptive mechanism for mating parameters. This further optimizes the convergence speed and performance of the algorithm and enables more efficient use of resources, thereby improving overall performance. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0048] Figure 2 This is a graph showing the convergence curves of the average target value of CMTO-ICRA and the comparison algorithm on the CMT benchmark in the 30-dimensional case according to an embodiment of the present invention.

[0049] Figure 3 This is a graph showing the convergence curves of the average target value of CMTO-ICRA and the comparison algorithm on the CMT benchmark in 10 dimensions according to an embodiment of the present invention.

[0050] Figure 4 This is a bar chart showing the average runtime of all issues in the CMT benchmark suite of this invention.

[0051] Figure 5 This is a partial average objective value convergence curve of the OPF problem after 20 independent experiments in the 10-dimensional case, using the CMTO-ICRA and comparison algorithms of this invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] like Figure 1 As shown, this embodiment of the invention provides the CMTO-ICRA algorithm, which includes: establishing two populations based on each task; evolving one population using a feasibility-first strategy and the other population using a domain adaptation strategy based on constraint relaxation; after each evolutionary cycle, selecting a preset proportion of individuals from the two populations based on the same task for evolution, and including the offspring generated in the offspring set; during the evolution of each population, evaluating the offspring generated through environmental selection, and using a roulette wheel algorithm to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations to obtain the optimal solution; and selecting a preset proportion of individuals from the populations corresponding to different tasks for mating, with the resulting offspring used to randomly replace individuals in the offspring set.

[0054] Specifically, this invention provides the following operational method: Two populations are established for each optimization task, each employing a different strategy. One population uses a feasibility-first strategy, while the other uses a domain adaptation method based on constraint relaxation for evolution. Furthermore, in the domain adaptation-based technique, a subpopulation-based information transfer mechanism is introduced to enhance information exchange within the population; this is a resource adaptation technique. After each evolutionary cycle, the top 30% of performing individuals from both populations are selected for mating, and their offspring are included in the offspring set. This approach reflects cooperation between tasks. This method leverages the advantages of both strategies, further promoting algorithm convergence.

[0055] Specifically, Li Yanzhi et al. pioneered research on Constrained Multitask Optimization (CMTO), introducing a Constrained Multitask (CMT) benchmark suite, filling a key gap in this field. Integrating Constraint Handling Techniques (CHTs) into Multitask Evolutionary Algorithms (MTEAs) improved the ability of these algorithms to handle Constrained Multitask Optimization Problems (CMTOPs), which typically involve simultaneously optimizing multiple constrained tasks. Formally, a Constrained Multitask Optimization Problem (CMTOP) comprises two or more constraint optimization tasks processed in parallel. A Constrained Multitask Optimization Problem can be defined as follows:

[0056] (1)

[0057] in, It's the number of tasks. and Let be a function, representing the constraint condition. and These are tasks The optimal solution and objective function, where Each task has Inequality constraints and There are several equality constraints. To handle Constrained Multi-Task Optimization Problems (CMTOPs), the equality constraints in CMTOPs are usually relaxed to inequality constraints:

[0058] (2)

[0059] If a solution xi satisfies all the constraints, then it is considered a feasible solution.

[0060] Specifically, Feasibility Prioritization (FP): The feasibility priority selection criterion follows a three-tiered approach: (1) for feasible solutions, minimize the objective function; (2) for infeasible solutions, minimize the degree of constraint violation; (3) enforce a strict feasibility preference, i.e., any feasible solution is preferred over an infeasible solution. This method can be easily integrated with different evolutionary computation frameworks without introducing new parameters. However, it often discards infeasible solutions that might help find better feasible solutions, which could lead the algorithm to converge to local optima. To address this limitation, Nikas et al. proposed an improved feasibility priority rule to enhance the algorithm's ability to escape local optima.

[0061] (EC): The ε-constraint method introduces a constraint relaxation level, denoted by ε, based on a feasibility-first rule. A solution is considered feasible if the degree of constraint violation is less than ε. The value of ε is dynamically adjusted at different stages of evolution, typically following a predefined formula.

[0062] (3)

[0063] In formula (3), express initial value, Represents the generation number; T determines When does it become 0? control The decay rate and amplitude; This represents the exponential parameter, which controls nonlinear behavior.

[0064] The constraint method employs constraint relaxation, preserving a certain number of infeasible solutions during the optimization process. These infeasible solutions help explore better feasible regions, thereby enhancing the algorithm's ability to escape local optima. However, The performance of constraint methods depends on initial values Its control parameters are extremely sensitive. To reduce this sensitivity, Zhang et al. proposed a method for adaptive control. The heuristic rules effectively balance the search between feasible and infeasible regions. It's worth noting that in constrained optimization competitions, some winning algorithms achieve this by... Different configurations of constraint methods, combined with various evolutionary operators, have yielded excellent performance. Li Yanzhi et al. proposed a Competition and Cooperative Evolutionary Framework (CCEF) for integrating constraint handling techniques (CHTs) to solve constrained optimization problems (COPs). This framework, built upon a multi-population-based CCEF, incorporates two core strategies: a competitive resource allocation scheme combined with a cooperative population co-evolutionary approach. The competitive allocation mechanism dynamically allocates more resources to better-performing constraint handling techniques, while the cooperative co-evolutionary strategy combines parent recombination and offspring diffusion to maximize the advantages of each constraint handling technique, thereby arriving at a better solution. This work highlights the potential of integrating resource allocation techniques in solving a wider range of optimization problems.

[0065] Specifically, in this embodiment of the invention, populations P1 and P2 are initialized for each task, and then iterated until the evaluation counter e reaches the maximum number of function evaluations (MaxFEs). In each iteration, parent individuals are selected, and offspring O1 (ordinary individuals) and O2 (the top 30% of individuals) are generated. Offspring are created using differential evolution (DA) and genetic algorithm (GA), or only genetic algorithm (GA), according to ch_k. O1 is updated by replacing individuals in O1 with individuals in O2, and the population is updated by environmental selection and tournament selection. If ch_k=1, the recombination mating probability (RlP) is updated. Finally, the population is optimized, and the counter value is incremented until the optimal solution x1 is found.∗ x2 ∗ , ..., x n ∗ The CMTO-ICRA algorithm framework proposed in this embodiment of the invention is shown in Table 1.

[0066] Table 1. Pseudocode for Algorithm 1

[0067]

[0068]

[0069] Table 2. Pseudocode for Algorithm 2

[0070]

[0071]

[0072] Table 3. Pseudocode for Algorithm 3

[0073] Specifically, embodiments of the present invention provide cooperation and competition within tasks. Due to the varying characteristics of different tasks, some tasks have large feasible regions, while others have smaller ones. Constraint handling techniques also include constraint relaxation and feasibility prioritization. Embodiments of the present invention employ two populations, each using one of the constraint handling techniques. Furthermore, a selection mechanism is introduced, enabling each task to adaptively select the most suitable evolutionary strategy based on its specific needs before each generation. This selection mechanism is guided by a roulette wheel algorithm, dynamically allocating computational resources to the strategy most suitable for the current task, thereby prioritizing strategies more effective for the current task and improving overall performance.

[0074] Specifically, after resource allocation, cooperation occurs between populations corresponding to different tasks. The top 30% of performers from both populations are selected for mating, producing ten offspring. These ten offspring are then used to randomly replace ten individuals in the offspring set generated in the previous step. This method ensures the utilization of information from both populations and prevents the loss of valuable genetic material from either population. It also reduces the risk of solutions becoming infeasible due to repeated selection of relaxed constraints, or converging to local optima due to repeated selection prioritizing feasibility.

[0075] Specifically, the probability of the roulette wheel algorithm is adjusted based on historical performance data to select a task index k for multi-task optimization. It is based on the current function evaluation value f and the maximum function evaluation value f. maxRelations are used to initialize or update the task selection probability matrix H. If f < fmax, the task selection probabilities are initialized uniformly. Otherwise, the probabilities are updated using the historical matrix H. After the update, the roulette wheel selection algorithm is called to select the task index k. The offspring are compared with their parents to calculate the values of Rb and Rp, and then these values are used to update the selection probabilities. The update formula is as follows.

[0076] The reward value is calculated according to the following formula:

[0077] (4)

[0078] where represents the reward value when task t selects the ch_k-th strategy. Rb represents the reward value obtained by comparing with all individuals in the population, and Rp represents the reward value obtained by tournament selection with the parent individuals. The parameter α controls the proportion of these two parts in the probability update. Here, α is set to 0.5, which means the contributions of these two parts are equal. The task cooperation and competition process proposed in the embodiments of the present invention is as Figure 3 shown.

[0079] Specifically, the embodiments of the present invention also provide an adaptive transfer between tasks. After incorporating population selection, further optimization can be applied to the population undergoing constraint relaxation, thereby accelerating the convergence speed of the algorithm in this part. The optimization strategy includes making the key parameter RMP (recombination mating probability) adaptive so that it can increase or decrease according to the result feedback. Inspired by the RMP adaptive update mechanism in the MFMF algorithm, we assign a separate RMP parameter to each subtask in population 1. In addition, two parameters γ and c are introduced: γ is used to determine whether an improvement has been achieved, and c controls the amplitude of the RMP adjustment.

[0080] Specifically, to evaluate whether the offspring transfer improves the population, we introduce two metrics: the population success rate (sr) and the success rate of offspring being better than their parents (tsr). Calculate sr (population success rate) and tsr (success rate of offspring being better than their parents). The calculation method of sr is as follows: Traverse each individual p in the population and compare its objective function value with the objective function value of the offspring on the same task. If the objective function value of individual p is better, then s = s + 1, where N is the number of individuals in the population, and sr = N / s. The calculation method of tsr is as follows: Determine the number of offspring generated by information transfer, denoted as TNP. Record the number of these offspring that are better than their parents, denoted as ts. Then tsr = TNP / ts. The RMP increase formula:

[0081] (5)

[0082] (6)

[0083] (7)

[0084] in, Let represent the (recombination mating probability) value of task t in generation Gen, C be the adjustment parameter, the value of temp represent the success rate tsr of offspring being superior to parents, and SR be an array representing the values ​​of sr. The inter-task adaptive transfer proposed in this embodiment of the invention is as follows: Figure 4 express.

[0085] Specifically, embodiments of the present invention also provide a method for dynamically adjusting the recombination and mating probability matrix (RMP) in multi-task optimization. It first expands the RMP matrix to match the current generation g. If the selected evolutionary population index ch_k=1, the replacement rate SRt is calculated. Based on the relationship between SRt and a threshold γ, the algorithm decides whether to adjust the RMP. If the replacement rate is below the threshold, the transfer flag vector f and the replacement flag vector r are used to calculate the transfer replacement rate, and the RMP is increased or decreased accordingly.

[0086] Specifically, this embodiment of the invention also provides performance comparison results with other constrained multitasking algorithms on constrained multitasking (CMT) benchmarks. Experiments were conducted using the CMT benchmark set, comparing the proposed algorithm with AT-MFEA, MFEA-II, MFMP, CMO-LKT, and CDEA-MP on problems with dimensions of 10, 30, and 50. Results were derived from 30 independent runs. The CMT benchmark set consists of nine problems. In these problems, CMT1 to CMT3 have the same global optimum and their feasible regions have significant overlap; CMT4 to CMT6 have similar global optima with small normalized distances across dimensions; and CMT7 to CMT9 have no overlap in their feasible regions. To demonstrate the superiority of the CMTO-ICRA algorithm, all comparative experiments were conducted under the above classification with different dimension settings. The symbols "+", "-", and "=" indicate that the results are better than, worse than, or comparable to the proposed method, respectively, while "NaN" indicates that no feasible solution was found in any of the 30 runs. The common parameter settings for all algorithms are as follows: Population size: N=100; Function dimension: Dim=10, 30, and 50; Maximum function evaluation times: MaxFEs=1000×Dim×K; Number of independent runs: 30; Common parameters for all algorithms:

[0087] (8)

[0088] Here, GA represents a genetic algorithm, which has two key operational parameters and SBX represents simulated binary crossover, and PM represents polynomial mutation; Table 4 shows the control parameters of the CMTO-ICRA algorithm.

[0089] Table 4 Control parameters of the CMTO-ICRA algorithm

[0090]

[0091] Specifically, Tables 5, 6, and 7 present the experimental results for dimensions of 10, 30, and 50, respectively, using CMTO-ICRA as the benchmark. It can be observed that CMTO-ICRA outperforms other algorithms in many cases, especially in low-dimensional settings. This is because in low-dimensional cases, a single constraint handling strategy can achieve good convergence results, while in high-dimensional cases, it is often necessary to incorporate another population, and choosing only one strategy will reduce the algorithm's convergence performance. With increasing dimensionality, CMTO-ICRA still exhibits superior performance compared to other algorithms, while also being computationally faster. The following analysis focuses on the convergence graph of 30 dimensions.

[0092] Table 5 shows the average objective values ​​of the AT-MFEA, CMO-LKT, MFEA-I, MFMP, CEDA-MP, and CMTO-ICRA algorithms on the CMT benchmark across 30 independent experiments, considering 10 dimensions.

[0093]

[0094]

[0095] Table 6 shows the average target values ​​of the AT-MFEA, CMO-LKT, MFEA-I1, MFMP, CEDA-MP, and CMTO-ICRA algorithms on the CMT benchmark under the 30-dimensional case, after 30 independent experiments.

[0096]

[0097]

[0098] Table 7 shows the average objective values ​​of the AT-MFEA, CMO-LKT, MFEA-I1, MFMP, CEDA-MP, and CMTO-ICRA algorithms on the CMT benchmark under 50-dimensional conditions, based on 30 independent experiments.

[0099]

[0100]

[0101] Specifically, the convergence graphs of all comparisons for the optimization algorithm are as follows: Figure 2 As shown, the experiment was conducted under 30-dimensional conditions. The algorithm achieved the highest values ​​on CMT2, CMT4, CMT5, CMT6, CMT8, and CMT9 problems. Except for the solutions for CMT3-T1, the solutions that did not reach the optimal value were on par with other algorithms. Theoretically, this is likely due to the relatively high similarity of the first few CMT problems.

[0102] Specifically, data transmission does not worsen the algorithm's results in the later stages. However, CMTO-ICRA tends to favor a feasibility-first (FP) strategy in the later stages. As a result, solution diversity decreases, and these solutions may get trapped in local optima and cannot be further optimized. Nevertheless, due to the high initial setting of the recombination-mating probability (RMP) parameter in the early stages of the algorithm, information transfer between populations is more frequent. Furthermore, due to the presence of adaptive parameters, most information transfer within the population is effective. Therefore, the early convergence speed is relatively fast.

[0103] Specifically, when the policy begins to select solutions based on the FP policy, the algorithm still achieves the same convergence performance. The reason the CMT9-T1 graph cannot be plotted is that the algorithm fails to converge in some cases. However, among all the compared algorithms, our algorithm still achieves relatively good results, which is sufficient to demonstrate the effectiveness of the improvement.

[0104] Specifically, this embodiment of the invention also provides performance evaluations against non-multi-task evolutionary algorithms, including FROF1, C2oDE, CORCO, DeCODE, and VMCH. CMTO-ICRA was compared with these Constrained Single-Objective Evolutionary Algorithms (CSOEAs), and the results are shown in Table 8. In most cases, CMTO-ICRA outperforms the other algorithms, with its lowest objective value demonstrating its effectiveness. As shown in Table 8, CMTO-ICRA is not the best performing algorithm for the CMT8-T1 and CMT1-T1 problems, but for the CMT9 problem, it is the only algorithm that can find feasible solutions for both subproblems in 30 independent runs. Furthermore, the proposed algorithm converges faster than other algorithms, demonstrating its robustness. These state-of-the-art Constrained Single-Objective Evolutionary Algorithms (CSOEAs) combine constraint handling techniques (CHT) with a carefully designed optimizer. However, in a multi-task environment, CSOEAs only handle each task individually. Therefore, CMTO-ICRA outperforms them. Based on the results in the table, it can be said that CMTO-ICRA outperforms these constrained single-objective evolutionary algorithms used for comparison.

[0105] Table 8. Average objective values ​​of CMTO-ICRA and other single-objective algorithms on the CMT benchmark in 30 independent experiments.

[0106]

[0107]

[0108] Specifically, to investigate the algorithm's performance when only inter-task cooperation is enabled without competition, we designed an algorithm called "w / o-Competition". Similarly, when only competition is enabled without cooperation, the algorithm is named the "w / o-Cooperation" algorithm. Thirty experiments were conducted in a 10-dimensional case, and the experimental data are shown in Table 9. Table 9 shows that when only partial optimizations are added—for example, the "w / o-Competition" algorithm—it exhibits performance improvements on tasks such as CMT2-T2, CMT6-T2, and CMT9-T2. This is because the adaptive randomized mapping strategy (RMP) accelerates the convergence speed in the early stages. Similarly, the "w / o-Cooperation" algorithm also shows performance improvements on most tasks because choosing a more suitable strategy improves evolutionary performance. Furthermore, the fully improved algorithm outperforms the algorithm when either optimization is added alone, demonstrating the effectiveness of the two strategies incorporated into the algorithm.

[0109] Table 9 shows the average target values ​​of CMTO-ICRA and other comparison algorithms in the CMT benchmark under the 10-dimensional case, after 30 independent experiments.

[0110]

[0111]

[0112] Specifically, such as Figure 3 As shown, compared with the CEDA-MP algorithm, which employs a similar multi-group framework, both the "without-cooperation" and "without-competition" algorithms exhibit significant performance improvements. Specifically, the "without-cooperation" strategy enhances the algorithm's convergence performance by employing appropriate constraint handling mechanisms, thereby improving its overall convergence performance. Meanwhile, the convergence curve of the "without-competition" algorithm demonstrates the positive impact of inter-task cooperation on convergence efficiency. Furthermore, the CTO-ICRA algorithm, which integrates resource allocation and inter-task cooperation-competition mechanisms, achieves superior convergence performance, outperforming other variant algorithms.

[0113] Specifically, Table 10 compares the runtime of the CMTO-ICRA algorithm with other algorithms on the 30-dimensional CMI benchmark. These results fully reflect and compare the runtime of all algorithms. Figure 4 A bar chart showing the average runtime for all problems in the CMT benchmark suite provides a visual representation of the results. CMTO-ICRA demonstrates significantly higher runtime efficiency. Compared to CEDA-MP, which also uses two populations but requires both populations to evolve simultaneously, CMTO-ICRA performs only one evolution per generation, effectively reducing runtime by nearly half. Furthermore, compared to other algorithms, CMTO-ICRA has simpler operational logic, primarily involving comparison and selection operations, requiring no complex computations, thus resulting in faster speed. These runtime results demonstrate the superior efficiency of the proposed algorithm.

[0114] Table 10 compares the runtime of AT-MFEA, CMO-LKT, CEDA-MP, MFEA-I, MFMP, and CMTO-ICRA on the CMT benchmark across 30 dimensions, based on 30 independent experiments.

[0115]

[0116]

[0117] Specifically, to evaluate the performance of the CMTO-ICRA algorithm in solving practical multi-objective task scheduling optimization problems (CMTOPs), the five algorithms mentioned above were compared in the optimal power flow (OPF) problem. The optimal power flow problem comprises five optimization objectives, defined as follows:

[0118] Fuel cost:

[0119] (9)

[0120] in, Let represent the cost coefficients (constant term, linear term, quadratic term) of the i-th generator, respectively. Let represent the active power output of the i-th generator. This indicates the total number of generators.

[0121] Voltage stability:

[0122] (10)

[0123] in, Represents all load nodes. Indicates the most severe node value. This represents the sensitivity coefficient between nodes. , These represent the voltage amplitudes at the generator node and the load node, respectively.

[0124] Pollutant emissions:

[0125] (11)

[0126] in, Let represent the cost coefficients (constant term, linear term, quadratic term) of the i-th generator, respectively. This indicates a surge in contamination under high load conditions;

[0127] Real Active Power Loss:

[0128] (12)

[0129] in, Represents all branches in the power grid. Indicates branch conductance, , and , These represent the node voltage magnitude and phase angle difference, respectively.

[0130] Voltage deviation:

[0131] (13)

[0132] in, This represents all load nodes.

[0133] Furthermore, there are constraints on network operational safety in the Optimal Power Flow (OPF) problem. These constraints are described below. Task 1 has a dimension of 24, and Task 2 has a dimension of 33. The maximum number of function evaluations is set to 100,000. The population size for each task is set to 100. The experimental results of the Optimal Power Flow (OPF) problem obtained after 20 independent experiments for each algorithm are shown in Table 11, and some convergence graphs are shown below. Figure 5 As shown. Figure 5As shown, due to frequent information exchange, the proposed algorithm exhibits a faster convergence speed in the early stages. However, in the later stages, as information transmission decreases, the convergence speed slows down, gradually approaching the optimal solution. The CMTO-ICRA algorithm performs best and also outperforms other comparative algorithms in terms of significance. The comparative algorithms do not make good use of the relationship between the problem's feasible region and constraint handling strategies, while the CMTO-ICRA algorithm fully utilizes this relationship. The data results demonstrate that the proposed algorithm is effective in handling practical problems.

[0134] Table 11 shows the average objective values ​​of CMTO-ICRA and the comparison algorithm on the OPF problem after 20 independent experiments.

[0135]

[0136]

[0137] The implementation of the various embodiments of the present invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a constrained multi-task optimization system based on task collaboration and resource adaptation. This system is used to execute a constrained multi-task optimization method based on task collaboration and resource adaptation from the above method embodiments.

[0138] The system includes: a population establishment module for establishing two populations based on each task; a population evolution module for evolving one population using a feasibility-first strategy and the other population using a domain adaptation strategy based on constraint relaxation; a progeny generation module for selecting a preset proportion of individuals from the two populations for the same task after each evolution cycle, and including the resulting progeny in the progeny set; a resource adaptation module for evaluating the progeny through environmental selection during the evolution of each population, and using a roulette wheel algorithm to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations to obtain the optimal solution; and a task collaboration module for selecting a preset proportion of individuals from the populations corresponding to different tasks for mating, and using the resulting progeny to randomly replace individuals in the progeny set.

[0139] The constraint-based multi-task optimization system based on task collaboration and resource adaptation provided in this invention addresses the problem of low resource utilization efficiency. It employs several modules to solve the problem that information exchange between populations may cause negative migration under constraint relaxation strategies, further optimizing the convergence speed and performance of the algorithm, and enabling more efficient resource utilization, thereby improving overall performance.

[0140] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement a constrained multi-task optimization method based on task collaboration and resource adaptation as proposed in the above embodiments.

[0141] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, this program employs different optimization strategies at different stages to enhance the adaptability of the algorithm and reduce resource waste. The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, or optical disk, and is used to store computer program code and necessary data files. The stored computer program includes: a population establishment module, a population evolution module, a offspring generation module, a resource adaptation module, and a task cooperation module.

[0142] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A constrained multi-task optimization method based on task collaboration and resource adaptation, characterized in that, include: Two populations are established for each task; One population is evolved using a feasibility-first strategy, while the other population is evolved using a domain adaptation strategy based on constraint relaxation. After each evolutionary cycle, individuals of a predetermined proportion are selected from two populations with the same task to evolve, and the offspring produced by the evolution are included in the offspring set. During the evolution of each population, the offspring produced by evolution are evaluated through environmental selection, and the roulette wheel algorithm is used to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations, thus obtaining the optimal solution; Based on the population corresponding to different tasks, individuals of a preset proportion are selected for mating, and the resulting offspring are used to randomly replace individuals in the offspring set.

2. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 1, characterized in that, Evaluating the offspring produced by evolution through environmental selection includes: Calculate the population success rate and the success rate of offspring being superior to their parents based on the offspring produced by evolution; The probability of recombination mating is adjusted based on the population success rate and the success rate of offspring being superior to that of parents.

3. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 2, characterized in that, Methods for calculating population success rate and the success rate of offspring outperforming their parents include: The success rate of the population is calculated as follows: traverse each individual in the population and compare the objective function value of the individual with the objective function value of the offspring of the same task. If the objective function value of the individual is better, then s = s + 1, where N is the number of individuals in the population and sr = N / s. The success rate of offspring being superior to parents is calculated as follows: the number of offspring generated through information transfer is denoted as TNP, the number of offspring that are superior to parents is denoted as ts, and then tsr = TNP / ts.

4. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 1, characterized in that, The roulette wheel algorithm is used to adaptively allocate resources based on the evaluation results, including: Adjustments are made based on historical performance data, and a task index k is selected for multi-task optimization; The task selection probability matrix is ​​initialized or updated by comparing the current number of function evaluations with the maximum number of function evaluations. If f <f max If the task selection probability is uniformly initialized, then the task selection probability will be updated using the history matrix H. After the update, the roulette wheel selection algorithm will be called to select the task index k. Compare offspring with their parents to calculate and p, the and p is used to update the task selection probability.

5. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 1, characterized in that, The method further includes optimizing the population evolution process using a constraint-relaxation-based domain adaptation strategy, specifically: The strategy is optimized to make the recombination and mating probability adaptive, and the value of the recombination and mating probability is increased or decreased based on the feedback of the results. Each subtask in the population is assigned a separate recombination and mating probability, and two parameters γ and c are introduced, where γ is used to determine whether an improvement has been achieved, and c is used to control the magnitude of the recombination and mating probability adjustment.

6. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 5, characterized in that, The method further includes dynamically adjusting the recombination and mating probability matrix during multi-task optimization: First, expand the recombination mating probability matrix to match the current generation g. If the selected evolutionary population index ch_k=1, then calculate the replacement rate. Based on the relationship between the replacement rate and the threshold, a decision is made on whether to adjust the recombination and mating probability: if the replacement rate is lower than the threshold, the transfer and replacement rate is calculated using the transfer flag vector and the replacement flag vector, and the recombination and mating probability is increased or decreased accordingly.

7. The constrained multi-task optimization method based on task collaboration and resource adaptation according to claim 5, characterized in that, The method also includes a formula for increasing the probability of recombination mating: , , , in, Let represent the recombination and mating probability value of task t in the Gen generation, C is the adjustment parameter, and the value of temp represents the success rate tsr of the offspring being superior to the parent generation.

8. A constrained multi-task optimization system based on task collaboration and resource adaptation, characterized in that, include: The population creation module is used to create two populations for each task. The population evolution module is used to evolve one population using a feasibility-first strategy and another population using a domain adaptation strategy based on constraint relaxation. The offspring generation module is used to select a preset proportion of individuals from two populations with the same task for evolution after each evolution cycle, and the offspring generated by the evolution are included in the offspring set. The resource adaptation module is used to evaluate the offspring produced by evolution through environmental selection when each population is evolving, and to use the roulette wheel algorithm to adaptively allocate resources based on the evaluation results until the evaluation counter reaches the maximum number of function evaluations and the optimal solution is obtained. The task collaboration module is used to select a preset proportion of individuals for mating based on the population corresponding to different tasks, and the resulting offspring are used to randomly replace individuals in the offspring set.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the constrained multi-task optimization method based on task collaboration and resource adaptation as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the constrained multi-task optimization method based on task cooperation and resource adaptation as described in any one of claims 1 to 7.

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