There have been few researches on solving multimodal multiobjective optimization problems, whereas they arc commonly seen in real-world applications but difficult for the existing evolutionary optimizers. In this pape...
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There have been few researches on solving multimodal multiobjective optimization problems, whereas they arc commonly seen in real-world applications but difficult for the existing evolutionary optimizers. In this paper, we propose a novel multimodalmultiobjective evolutionary algorithm using two-archive and recombination strategies. In the proposed algorithm, the properties of decision variables and the relationships among them arc analyzed at first to guide the evolutionary search. Then, a general framework using two archives, i.e., the convergence and the diversity archives, is adopted to cooperatively solve these problems. Moreover, the diversity archive simultaneously employs a clustering strategy to guarantee diversity in the objective space and a niche-based clearing strategy to promote the same in the decision space. At the end of evolution process, solutions in the convergence and the diversity archives are recombined to obtain a large number of multiple Pareto optimal solutions. In addition, a set of benchmark test functions and a performance metric are designed for multimodal multiobjective optimization. The proposed algorithm is empirically compared with two state-of-the-art evolutionary algorithms on these test functions. The comparative results demonstrate that the overall performance of the proposed algorithm is significantly superior to the competing algorithms.
In real-world scenes involving multimodal multiobjective optimization, there may exist different Pareto optimal sets (PSs) for the same Pareto front (PF), and some PFs even need to reserve all PSs, including local and...
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In real-world scenes involving multimodal multiobjective optimization, there may exist different Pareto optimal sets (PSs) for the same Pareto front (PF), and some PFs even need to reserve all PSs, including local and global PSs. Most existing multimodal multiobjective optimization algorithms often distinguish solutions according to their diversity and convergence performances in the objective space. However, they pay little attention to the potential of solutions in the decision space. To solve this issue, a novel multimodalmultiobjective memetic algorithm based on a local detection mechanism and a clustering-based selection strategy is proposed in this paper. To reserve more global and local PSs in the decision space, a density-based clustering method is adopted in the local detection mechanism, assisting in collecting solutions in the local clusters. Furthermore, in the clustering-based selection strategy, two different clustering methods are applied to different situations according to the ratio of the local optimal solutions. Extensive experimental results and performance comparisons with state-of-the-art algorithms show the superiority of our proposed algorithm.
When performing feature selection on most data sets, there is a general situation that some different feature subsets have the same number of selected features and classification error rate. This indicates that featur...
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ISBN:
(数字)9781665467087
ISBN:
(纸本)9781665467087
When performing feature selection on most data sets, there is a general situation that some different feature subsets have the same number of selected features and classification error rate. This indicates that feature selection in some data sets is a multimodal multiobjective optimization (1VEVIO) problem. Most of the current studies on feature selection ignore the 1VIVIO problems. Therefore, this paper proposes a feature selection method based on a multimodalmultiobjective genetic algorithm (MMOGA) to solve the problem. This algorithm is mainly improved in three aspects. First, a special initialization strategy based on symmetric uncertainty is designed to improve the fitness of the initial population. Second, this paper adds a niche strategy to the genetic algorithm to search for multimodal solutions. Unlike traditional niche methods that has a central individual, this algorithm also considers the distances between individuals in the niche. Third, to effectively utilize excellent individuals for evolution, this algorithm uses a method based on the Pareto set of the niche to generate offspring. Finally, by comparing with other algorithms, the effectiveness of the MMOGA in feature selection is verified. This algorithm can successfully find equivalent feature subsets on different datasets.
Recently, multimodal multiobjective optimization has started to attract a lot of attention. Its task is to find multiple Pareto optimal solution sets in the decision space, which are equivalent in the objective space....
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ISBN:
(纸本)9781728121536
Recently, multimodal multiobjective optimization has started to attract a lot of attention. Its task is to find multiple Pareto optimal solution sets in the decision space, which are equivalent in the objective space. In some applications, it is important to find multiple global and local Pareto optimal solution sets in the decision space, which have similar quality in the objective space. In evolutionary computation, a wide variety of test problems with various characteristics are needed for fair comparison of different algorithms. However, we have only a small number of test problems for multimodal multiobjective optimization. In this paper, we propose a scalable multimodalmultiobjective test problem with respect to the five parameters: (i) the number of objectives, (ii) the number of decision variables, (iii) the number of equivalent Pareto optimal solution sets in the decision space, (iv) the number of local Pareto fronts, and (v) the number of local Pareto optimal solution sets in the decision space for each local Pareto front. Our proposal is the first scalable test problem with respect to all of these five parameters.
multimodalmultiobjective problems (MMOPs) exist in scientific research and practical projects, and their Pareto solution sets correspond to the same Pareto front. Existing evolutionary algorithms often fall into loca...
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multimodalmultiobjective problems (MMOPs) exist in scientific research and practical projects, and their Pareto solution sets correspond to the same Pareto front. Existing evolutionary algorithms often fall into local optima when solving such problems, which usually leads to insufficient search solutions and their uneven distribution in the Pareto front. In this work, an improved membrane algorithm is proposed for solving MMOPs, which is based on the framework of P system. More specifically, the proposed algorithm employs three elements from P system: object, reaction rule, and membrane structure. The object is implemented by real number coding and represents a candidate solution to the optimization problem to be solved. The function of the reaction rule of the proposed algorithm is similar to the evolution operation of the evolutionary algorithm. It can evolve the object to obtain a better candidate solution set. The membrane structure is the evolutionary logic of the proposed algorithm. It consists of several membranes, each of which is an independent evolutionary unit. This structure is used to maintain the diversity of objects, so that it provides multiple Pareto sets as output. The effectiveness verification study was carried out in simulation experiments. The simulation results show that compared with other experimental algorithms, the proposed algorithm has a competitive advantage in solving all 22 multimodal benchmark test problems in CEC2019.
The main aim of feature subset selection is to find the minimum number of required features to perform classification without affecting the accuracy. It is one of the useful real-world applications for different types...
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The main aim of feature subset selection is to find the minimum number of required features to perform classification without affecting the accuracy. It is one of the useful real-world applications for different types of classification datasets. Different feature subsets may achieve similar classification accuracy, which can help the user to select the optimal features. There are two main objectives involved in selecting a feature subset: minimizing the number of features and maximizing the accuracy. However, most of the existing studies do not consider multiple feature subsets of the same size. In this paper, we have proposed an algorithm for multimodal multiobjective optimization based on differential evolution with respect to the feature subset selection problem. We have proposed the probability initialization method to identify the selected features with equal distribution in the search space. We have also proposed a niching technique to explore the search space and exploit the nearby solutions. Further, we have proposed a convergence archive to locate and store the optimal feature subsets. Exhaustive experimentation has been conducted on different datasets with varying characteristics to identify multiple feature subsets. We have also proposed an evaluation metric for the quantitative comparison of the proposed algorithm with the existing algorithms. Results have also been compared with existing algorithms in the objective space and in terms of classification accuracy, which shows the effectiveness of the proposed algorithm.(c) 2023 Elsevier B.V. All rights reserved.
Current multimodal multiobjective optimization (MMO) has mostly focused on locating multiple equivalent global Pareto optimal sets (PSs) or local PSs in the decision space, rarely considering finding both simultaneous...
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Current multimodal multiobjective optimization (MMO) has mostly focused on locating multiple equivalent global Pareto optimal sets (PSs) or local PSs in the decision space, rarely considering finding both simultaneously. To address this issue, this paper explores a crowded individual activation multiobjective differential evolution algorithm based on subpopulation region solution selection, named CAMODE_SR. In CAMODE_SR, a subpopulation region solution selection mechanism is developed to search for more uniformly distributed global and local Pareto optimal solutions. Specifically, two types of specific neighborhood radii are designed depending on the location information of the Pareto optimal solutions discovered during evolution. The two types of radii construct specific neighborhoods for the global and local optimal solutions to maintain the solutions with better diversity. To improve the exploitation capacity of the population, a crowded individual activation mechanism is proposed by developing an activation function associated with iteration. The activation function activates the crowded individuals in local regions to exploit more superior solutions near global optimal solutions. The proposed CAMODE_SR achieves a good tradeoff between the performance of locating both global and local PSs. Extensive experiments on the CEC 2020 MMO benchmark functions demonstrate that the proposed CAMODE_SR is significantly superior to nine state-of-the-art MMEAs in tackling multimodal multiobjective optimization problems with global and local PSs.
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