In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and red...In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.展开更多
To realize Industry 5.0,manufacturers face various optimization problems that seldom appear in isolation.Evolutionary MultiTasking(EMT)is an effective method to solve multiple related problems by extracting and utiliz...To realize Industry 5.0,manufacturers face various optimization problems that seldom appear in isolation.Evolutionary MultiTasking(EMT)is an effective method to solve multiple related problems by extracting and utilizing common knowledge.Knowledge transfer is the key to the effectiveness of EMT.Existing EMT methods mainly focus on designing effective intertask learning methods and ignore the fact that provided knowledge's appropriateness also has a significant effect on EMT's performance.There is plentiful knowledge in assistant tasks,and knowledge transfer may not work well and even lead to a negative effect if useless knowledge is selected to guide target tasks.EMT is thus confronted with a challenge to find appropriate knowledge.This work proposes an efficient knowledge classification-assisted EMT framework to identify and select valuable knowledge from assistant tasks.During the evolution process,better-performing candidates are supposed to have advantages in exploitation.Therefore,assistant individuals that are similar to better-performing target individuals are used to provide positive knowledge.Specifically,the target sub-population is divided into different levels and then a classifier is trained to divide assistant sub-population.Considering that target and assistant sub-populations have different characteristics,we use domain adaptation to reduce their distribution discrepancies.In this way,the trained classifier can classify assistant individuals more accurately,and truly useful knowledge can be selected for target tasks.The superior performance of our proposed framework over state-of-the-art algorithms is verified via a series of benchmark problems.展开更多
Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-obj...Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.展开更多
Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they prop...Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.展开更多
Evolutionary multitasking optimization(EMTO) can obtain beneficial knowledge for the target task from the auxiliary task to improve its performance, which has received extensive attention in scientific research and en...Evolutionary multitasking optimization(EMTO) can obtain beneficial knowledge for the target task from the auxiliary task to improve its performance, which has received extensive attention in scientific research and engineering problems. Nevertheless, faced with the widespread large-scale multi-objective optimization problems(LSMOPs), the existing EMTO literature barely involves the research of LSMOPs. More importantly, these EMTO algorithms often get trapped in local optima when dealing with LSMOPs, resulting in a slow convergence speed, which is worthy of our attention. To this end, this paper proposes an EMTO algorithm dedicated to solving LSMOPs. On the one hand, given the intricate nature of LSMOPs, we propose a knowledge domination-based knowledge transfer mechanism that can flexibly transfer knowledge from multiple knowledge representations, i.e., the information distribution and distribution distance of the task population. On the other hand, we design an elite vector-guided search strategy. Specifically, the generative adversarial network(GAN) model should first be trained within the divided populations. Then, the well-trained model is used to generate a high-quality individual for the target individual. After that, the high-quality individual is combined with the top-performing individual in the current population to find the elite vector corresponding to the target individual. Finally, the elite vector is applied to guide the target individual to accelerate convergence towards the global optimum in the high-dimensional decision space. We conduct comprehensive experimental investigations on two artificial LSMOPs suites and six real-world LSMOPs to validate the efficiency and robustness of the proposed algorithm,through comparative analysis with state-of-the-art peer algorithms.展开更多
Evolutionary multi-task optimization(EMTO)presents an efficient way to solve multiple tasks simultaneously.However,difficulties they face in curbing the performance degradation caused by unmatched knowledge transfer a...Evolutionary multi-task optimization(EMTO)presents an efficient way to solve multiple tasks simultaneously.However,difficulties they face in curbing the performance degradation caused by unmatched knowledge transfer and inefficient evolutionary strategies become more severe as the number of iterations increases.Motivated by this,a novel self-adjusting dualmode evolutionary framework,which integrates variable classification evolution and knowledge dynamic transfer strategies,is designed to compensate for this deficiency.First,a dual-mode evolutionary framework is designed to meet the needs of evolution in different states.Then,a self-adjusting strategy based on spatial-temporal information is adopted to guide the selection of evolutionary modes.Second,a classification mechanism for decision variables is proposed to achieve the grouping of variables with different attributes.Then,the evolutionary algorithm with a multi-operator mechanism is employed to conduct classified evolution of decision variables.Third,an evolutionary strategy based on multi-source knowledge sharing is presented to realize the cross-domain transfer of knowledge.Then,a dynamic weighting strategy is developed for efficient utilization of knowledge.Finally,by conducting experiments and comparing the designed method with several existing algorithms,the empirical results confirm that it significantly outperforms its peers in tackling benchmark instances.展开更多
Because of its strong ability to solve problems,evolutionary multitask optimization(EMTO)algorithms have been widely studied recently.Evolutionary algorithms have the advantage of fast searching for the optimal soluti...Because of its strong ability to solve problems,evolutionary multitask optimization(EMTO)algorithms have been widely studied recently.Evolutionary algorithms have the advantage of fast searching for the optimal solution,but it is easy to fall into local optimum and difficult to generalize.Combining evolutionary multitask algorithms with evolutionary optimization algorithms can be an effective method for solving these problems.Through the implicit parallelism of tasks themselves and the knowledge transfer between tasks,more promising individual algorithms can be generated in the evolution process,which can jump out of the local optimum.How to better combine the two has also been studied more and more.This paper explores the existing evolutionary multitasking theory and improvement scheme in detail.Then,it summarizes the application of EMTO in different scenarios.Finally,according to the existing research,the future research trends and potential exploration directions are revealed.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61972040the Science and Technology Research and Development Project funded by China Railway Material Trade Group Luban Company.
文摘In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.
基金supported in part by the National Natural Science Foundation of China(51775385)the Natural Science Foundation of Shanghai(23ZR1466000)+2 种基金the Shanghai Industrial Collaborative Science and Technology Innovation Project(2021-cyxt2-kj10)the Innovation Program of Shanghai Municipal Education Commission(202101070007E00098)Tongxiang Institute of Artificial General Intelligence(TAGI2-A-2024-0006).
文摘To realize Industry 5.0,manufacturers face various optimization problems that seldom appear in isolation.Evolutionary MultiTasking(EMT)is an effective method to solve multiple related problems by extracting and utilizing common knowledge.Knowledge transfer is the key to the effectiveness of EMT.Existing EMT methods mainly focus on designing effective intertask learning methods and ignore the fact that provided knowledge's appropriateness also has a significant effect on EMT's performance.There is plentiful knowledge in assistant tasks,and knowledge transfer may not work well and even lead to a negative effect if useless knowledge is selected to guide target tasks.EMT is thus confronted with a challenge to find appropriate knowledge.This work proposes an efficient knowledge classification-assisted EMT framework to identify and select valuable knowledge from assistant tasks.During the evolution process,better-performing candidates are supposed to have advantages in exploitation.Therefore,assistant individuals that are similar to better-performing target individuals are used to provide positive knowledge.Specifically,the target sub-population is divided into different levels and then a classifier is trained to divide assistant sub-population.Considering that target and assistant sub-populations have different characteristics,we use domain adaptation to reduce their distribution discrepancies.In this way,the trained classifier can classify assistant individuals more accurately,and truly useful knowledge can be selected for target tasks.The superior performance of our proposed framework over state-of-the-art algorithms is verified via a series of benchmark problems.
基金supported in part by the National Natural Science Fund for Outstanding Young Scholars of China (61922072)the National Natural Science Foundation of China (62176238, 61806179, 61876169, 61976237)+2 种基金China Postdoctoral Science Foundation (2020M682347)the Training Program of Young Backbone Teachers in Colleges and Universities in Henan Province (2020GGJS006)Henan Provincial Young Talents Lifting Project (2021HYTP007)。
文摘Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.
基金supported in part by the National Key Research and Development Program of China(2022YFD2001200)the National Natural Science Foundation of China(62176238,61976237,62206251,62106230)+3 种基金China Postdoctoral Science Foundation(2021T140616,2021M692920)the Natural Science Foundation of Henan Province(222300420088)the Program for Science&Technology Innovation Talents in Universities of Henan Province(23HASTIT023)the Program for Science&Technology Innovation Teams in Universities of Henan Province(23IRTSTHN010).
文摘Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
基金supported in part by the National Natural Science Foundation of China(62506083, 62476096)Guangdong Provincial Construction Project of Teaching Quality and Teaching Reform Engineering in Undergraduate Universities ([2024] No. 30)
文摘Evolutionary multitasking optimization(EMTO) can obtain beneficial knowledge for the target task from the auxiliary task to improve its performance, which has received extensive attention in scientific research and engineering problems. Nevertheless, faced with the widespread large-scale multi-objective optimization problems(LSMOPs), the existing EMTO literature barely involves the research of LSMOPs. More importantly, these EMTO algorithms often get trapped in local optima when dealing with LSMOPs, resulting in a slow convergence speed, which is worthy of our attention. To this end, this paper proposes an EMTO algorithm dedicated to solving LSMOPs. On the one hand, given the intricate nature of LSMOPs, we propose a knowledge domination-based knowledge transfer mechanism that can flexibly transfer knowledge from multiple knowledge representations, i.e., the information distribution and distribution distance of the task population. On the other hand, we design an elite vector-guided search strategy. Specifically, the generative adversarial network(GAN) model should first be trained within the divided populations. Then, the well-trained model is used to generate a high-quality individual for the target individual. After that, the high-quality individual is combined with the top-performing individual in the current population to find the elite vector corresponding to the target individual. Finally, the elite vector is applied to guide the target individual to accelerate convergence towards the global optimum in the high-dimensional decision space. We conduct comprehensive experimental investigations on two artificial LSMOPs suites and six real-world LSMOPs to validate the efficiency and robustness of the proposed algorithm,through comparative analysis with state-of-the-art peer algorithms.
基金supported in part by the Plan of Key Scientific Research Projects of Colleges and Universities in Henan Province(25A413005,24A120005)the National Science and Technology Major Project(2021ZD0112302)the National Natural Science Foundation of China(62222301,61890930-5,62021003).
文摘Evolutionary multi-task optimization(EMTO)presents an efficient way to solve multiple tasks simultaneously.However,difficulties they face in curbing the performance degradation caused by unmatched knowledge transfer and inefficient evolutionary strategies become more severe as the number of iterations increases.Motivated by this,a novel self-adjusting dualmode evolutionary framework,which integrates variable classification evolution and knowledge dynamic transfer strategies,is designed to compensate for this deficiency.First,a dual-mode evolutionary framework is designed to meet the needs of evolution in different states.Then,a self-adjusting strategy based on spatial-temporal information is adopted to guide the selection of evolutionary modes.Second,a classification mechanism for decision variables is proposed to achieve the grouping of variables with different attributes.Then,the evolutionary algorithm with a multi-operator mechanism is employed to conduct classified evolution of decision variables.Third,an evolutionary strategy based on multi-source knowledge sharing is presented to realize the cross-domain transfer of knowledge.Then,a dynamic weighting strategy is developed for efficient utilization of knowledge.Finally,by conducting experiments and comparing the designed method with several existing algorithms,the empirical results confirm that it significantly outperforms its peers in tackling benchmark instances.
基金Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2022JM-327 and in part by the CAAI-Huawei MindSpore Academic Open Fund.
文摘Because of its strong ability to solve problems,evolutionary multitask optimization(EMTO)algorithms have been widely studied recently.Evolutionary algorithms have the advantage of fast searching for the optimal solution,but it is easy to fall into local optimum and difficult to generalize.Combining evolutionary multitask algorithms with evolutionary optimization algorithms can be an effective method for solving these problems.Through the implicit parallelism of tasks themselves and the knowledge transfer between tasks,more promising individual algorithms can be generated in the evolution process,which can jump out of the local optimum.How to better combine the two has also been studied more and more.This paper explores the existing evolutionary multitasking theory and improvement scheme in detail.Then,it summarizes the application of EMTO in different scenarios.Finally,according to the existing research,the future research trends and potential exploration directions are revealed.
