A prediction strategy based on special points and multiregion knee points for evolutionary dynamic multiobjective optimi
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A prediction strategy based on special points and multiregion knee points for evolutionary dynamic multiobjective optimization Lixin Wei1,2 · Zeyin Guo1,2 · Rui Fan1,2 · Hao Sun1,2 · Zhiwei Zhao3
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Dynamic multiobjective optimization problems exist widely in the real word and require the optimization algorithms to track the Pareto front (PF) over time. A prediction strategy based on special points and multi-region knee points (MRKPs) is proposed for solving dynamic multiobjective optimization problems. Whenever a change is detected, the prediction strategy reacts effectively to the change by generating four subpopulations based on four strategies. The first subpopulation is created by selecting the representative individuals using a special point strategy. The second subpopulation consists of a solution set using a multiregion knee point strategy. The third subpopulation is introduced to the nondominated set by a convergence strategy. The fourth subpopulation comprises diverse individuals from an adaptive diversity maintenance strategy. The four subpopulations merge into a new population to accurately predict the location and distribution of the PF after an environmental change. MRKP is compared with four popular evolutionary algorithms on standard instances with different changing dynamics. Finally, MRKP provides better results than other competitors in terms of Inverted Generational Distance and Hypervolume metrics. The results reveal that MRKP can quickly adapt to changing environments and provide good tracking ability when dealing with dynamic multiobjective optimization problems. Keywords Evolutionary algorithm · Dynamic multiobjective optimization · Special point · Knee point
1 Introduction Many real-world optimization problems must be solved in dynamic or uncertain environments. These kinds of problems are usually called dynamic multiobjective optimization problems (DMOPs) [1], which are characterized by some changes that may occur in the Pareto set (PS) or PF, object functions, problem instances, or constraints. Instances of DMOPs include dynamic scheduling [2, 3], machine learning [4], trajectory planning [5], metal rolling control [6, 7], engineering applications [8], and scientific research [9–11].
Lixin Wei
[email protected] 1
Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei, China
2
Engineering Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment, Yanshan University, Qinhuangdao, 066004, Hebei, China
3
Department of Computer Science and Technology, Tangshan University, Hebei, 063000, China
Multiobjective optimization problems [12–15] involve finding a set of tradeoff solutions by optimizing conflicting objectives simultaneously. When a multiobjective optimization problem involves time-dependent components, it can be regarded as a DMOP [16]. The goal of a traditional static evolutionary algorithm is to make a population gradually co
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