In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal ...In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.展开更多
Recently,multimodal multiobjective optimization problems(MMOPs)have received increasing attention.Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible.Although some evolutio...Recently,multimodal multiobjective optimization problems(MMOPs)have received increasing attention.Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible.Although some evolutionary algorithms for them have been proposed,they mainly focus on the convergence rate in the decision space while ignoring solutions diversity.In this paper,we propose a new multiobjective fireworks algorithm for them,which is able to balance exploitation and exploration in the decision space.We first extend a latest single-objective fireworks algorithm to handle MMOPs.Then we make improvements by incorporating an adaptive strategy and special archive guidance into it,where special archives are established for each firework,and two strategies(i.e.,explosion and random strategies)are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives.Finally,we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems.Experimental results show that the proposed algorithm is superior to compared algorithms in solving them.Also,its runtime is less than its peers'.展开更多
In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts mor...In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts more and more attention in recent years.In this paper a new multi-population and diffusion UMDA（MDUMDA） is proposed for dynamic multimodal problems.The multi-population approach is used to locate multiple local optima which are useful to find the global optimal solution quickly to dynamic multimodal problems.The diffusion model is used to increase the diversity in a guided fashion,which makes the neighbor individuals of previous optimal solutions move gradually from the previous optimal solutions and enlarge the search space.This approach uses both the information of current population and the part history information of the optimal solutions.Finally experimental studies on the moving peaks benchmark are carried out to evaluate the proposed algorithm and compare the performance of MDUMDA and multi-population quantum swarm optimization（MQSO） from the literature.The experimental results show that the MDUMDA is effective for the function with moving optimum and can adapt to the dynamic environments rapidly.展开更多
Spatially-structured populations are one approach to increasing genetic diversity in an evolutionary algorithm （EA）. However, they are susceptible to convergence to a single peak in a multimodal fitness landscape. N...Spatially-structured populations are one approach to increasing genetic diversity in an evolutionary algorithm （EA）. However, they are susceptible to convergence to a single peak in a multimodal fitness landscape. Niching methods, such as fitness sharing, allow an EA to maintain multiple solutions in a single population, however they have rarely been used in conjunction with spatially-structured populations. This paper introduces local sharing, a method that applies sharing to the overlapping demes of a spatially-structured population. The combination of these two methods succeeds in maintaining multiple solutions in problems that have previously proved difficult for sharing alone （and vice-versa）.展开更多
基金supported in part by the Science and Technology Project of Yunnan Tobacco Industrial Company under Grant JB2022YL02in part by the Natural Science Foundation of Henan Province of China under Grant 242300421413in part by the Henan Province Science and Technology Research Projects under Grants 242102110334 and 242102110375.
文摘In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.
基金supported in part by the National Natural Science Foundation of China(62071230,62061146002)the Natural Science Foundation of Jiangsu Province(BK20211567)the Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia(FP-147-43)。
文摘Recently,multimodal multiobjective optimization problems(MMOPs)have received increasing attention.Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible.Although some evolutionary algorithms for them have been proposed,they mainly focus on the convergence rate in the decision space while ignoring solutions diversity.In this paper,we propose a new multiobjective fireworks algorithm for them,which is able to balance exploitation and exploration in the decision space.We first extend a latest single-objective fireworks algorithm to handle MMOPs.Then we make improvements by incorporating an adaptive strategy and special archive guidance into it,where special archives are established for each firework,and two strategies(i.e.,explosion and random strategies)are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives.Finally,we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems.Experimental results show that the proposed algorithm is superior to compared algorithms in solving them.Also,its runtime is less than its peers'.
基金supported by the National Natural Science Foundation of China (6087309960775013)
文摘In dynamic environments,it is important to track changing optimal solutions over time.Univariate marginal distribution algorithm（UMDA） which is a class algorithm of estimation of distribution algorithms attracts more and more attention in recent years.In this paper a new multi-population and diffusion UMDA（MDUMDA） is proposed for dynamic multimodal problems.The multi-population approach is used to locate multiple local optima which are useful to find the global optimal solution quickly to dynamic multimodal problems.The diffusion model is used to increase the diversity in a guided fashion,which makes the neighbor individuals of previous optimal solutions move gradually from the previous optimal solutions and enlarge the search space.This approach uses both the information of current population and the part history information of the optimal solutions.Finally experimental studies on the moving peaks benchmark are carried out to evaluate the proposed algorithm and compare the performance of MDUMDA and multi-population quantum swarm optimization（MQSO） from the literature.The experimental results show that the MDUMDA is effective for the function with moving optimum and can adapt to the dynamic environments rapidly.
文摘Spatially-structured populations are one approach to increasing genetic diversity in an evolutionary algorithm （EA）. However, they are susceptible to convergence to a single peak in a multimodal fitness landscape. Niching methods, such as fitness sharing, allow an EA to maintain multiple solutions in a single population, however they have rarely been used in conjunction with spatially-structured populations. This paper introduces local sharing, a method that applies sharing to the overlapping demes of a spatially-structured population. The combination of these two methods succeeds in maintaining multiple solutions in problems that have previously proved difficult for sharing alone （and vice-versa）.
