A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization

During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other success...

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Published in:	IEEE transactions on cybernetics Vol. 52; no. 5; pp. 3696 - 3709
Main Authors:	Kumar, Abhishek, Das, Swagatam, Mallipeddi, Rammohan
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.05.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Adaptation Benchmark testing Business competition Constrained optimization Covariance matrices Covariance matrix covariance matrix adaptation evolution strategy (CMA-ES) Cybernetics Decision feedback equalizers Evolutionary algorithms Evolutionary computation Global optimization Maintenance engineering multiobjective optimization (MOO) Multiple objective analysis Optimization Pareto optimization Power flow Ranking reference vector-based ranking (RVRanking) strategy Strategy
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.
AbstractList	During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems. During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.
Author	Kumar, Abhishek Das, Swagatam Mallipeddi, Rammohan
Author_xml	– sequence: 1 givenname: Abhishek orcidid: 0000-0003-1940-0234 surname: Kumar fullname: Kumar, Abhishek email: abhishek.kumar.eee13@iitbhu.ac.in organization: Department of Electrical Engineering, Indian Institute of Technology Varanasi, Varanasi, India – sequence: 2 givenname: Swagatam orcidid: 0000-0001-6843-4508 surname: Das fullname: Das, Swagatam email: swagatam.das@isical.ac.in organization: Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India – sequence: 3 givenname: Rammohan orcidid: 0000-0001-9071-1145 surname: Mallipeddi fullname: Mallipeddi, Rammohan email: mallipeddi@knu.ac.kr organization: Department of Artificial Intelligence, College of IT Engineering, Kyungpook National University, Daegu, South Korea
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SubjectTerms	Adaptation Benchmark testing Business competition Constrained optimization Covariance matrices Covariance matrix covariance matrix adaptation evolution strategy (CMA-ES) Cybernetics Decision feedback equalizers Evolutionary algorithms Evolutionary computation Global optimization Maintenance engineering multiobjective optimization (MOO) Multiple objective analysis Optimization Pareto optimization Power flow Ranking reference vector-based ranking (RVRanking) strategy Strategy
Title	A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization
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