This paper presents a neurodynamic approach for a class of convex-concave minimax problems. First, variational inequalities are given, serving as the necessary and sufficient conditions for the desired saddle point of the underlying objective function. Next, based on the variational inequalities, a neurodynamic approach is designed for the minimax problems. Taking advantage of a proper Lyapunov function, the stability of the state solution of the proposed neurodynamic approach is guaranteed. Furthermore, the proposed neurodynamic approach is able to solve the non-quadratic convex-concave minimax problem exponentially. Compared with the existing researches for the quadratic minimax problem, the proposed neurodynamic approach has wider scope of applications to some extent. Finally, a numerical experiment is provided to show the effectiveness of the proposed neurodynamic approach.
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Pub Date : 2022-10-14DOI: 10.1109/ICIST55546.2022.9926808
Yiyi Jiang, Zhi-hui Zhan, Jinchao Zhang
Evolutionary multi-task optimization (EMTO) is a recently emerging topic in the research area of evolutionary computation, aiming at solving multiple different optimization tasks simultaneously. Recently, with the development of EMTO, many multi-task optimization problem (MTOP) benchmark test suites have been proposed. However, these MTOP test suites are not sufficiently challenging. That is, the tasks in these MTOPs always have the same dimensionality and the aligned dimensions of the tasks can have related physical meanings or similar optimal values. To address these disadvantages of existing MTOP test suites, we propose a new and more challenging compositive MTOP (cMTOP) test suite. There are ten cMTOP instances in this test suite and each instance contains two tasks. These cMTOP instances are more challenging with three properties. First, the tasks in each cMTOP have different numbers of dimensions. Second, to make the aligned dimensions of two tasks have irrelated physical meanings, each task is a composition function composed of several basic functions. Third, each task in cMTOP is shifted and rotated to make the aligned dimensions of the two tasks have different optimal values. Based on these properties, the proposed cMTOP test suite is more challenging and can better evaluate the performance of EMTO algorithms. Finally, we analyze the performance of several state-of-the-art EMTO algorithms on this new and challenging cMTOP test suite.
{"title":"A New and More Challenging Compositive Multi-Task Optimization Problem Test Suite","authors":"Yiyi Jiang, Zhi-hui Zhan, Jinchao Zhang","doi":"10.1109/ICIST55546.2022.9926808","DOIUrl":"https://doi.org/10.1109/ICIST55546.2022.9926808","url":null,"abstract":"Evolutionary multi-task optimization (EMTO) is a recently emerging topic in the research area of evolutionary computation, aiming at solving multiple different optimization tasks simultaneously. Recently, with the development of EMTO, many multi-task optimization problem (MTOP) benchmark test suites have been proposed. However, these MTOP test suites are not sufficiently challenging. That is, the tasks in these MTOPs always have the same dimensionality and the aligned dimensions of the tasks can have related physical meanings or similar optimal values. To address these disadvantages of existing MTOP test suites, we propose a new and more challenging compositive MTOP (cMTOP) test suite. There are ten cMTOP instances in this test suite and each instance contains two tasks. These cMTOP instances are more challenging with three properties. First, the tasks in each cMTOP have different numbers of dimensions. Second, to make the aligned dimensions of two tasks have irrelated physical meanings, each task is a composition function composed of several basic functions. Third, each task in cMTOP is shifted and rotated to make the aligned dimensions of the two tasks have different optimal values. Based on these properties, the proposed cMTOP test suite is more challenging and can better evaluate the performance of EMTO algorithms. Finally, we analyze the performance of several state-of-the-art EMTO algorithms on this new and challenging cMTOP test suite.","PeriodicalId":211213,"journal":{"name":"2022 12th International Conference on Information Science and Technology (ICIST)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114935280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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