Evolutionary many-objective optimization algorithm based on angle and clustering
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Evolutionary many-objective optimization algorithm based on angle and clustering Zhijian Xiong1,2 · Jingming Yang1 · Ziyu Hu1 · Zhiwei Zhao2
· Xiaojing Wang3
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In evolutionary multi-objective optimization, maintaining a well balance of convergence and diversity is particularly important for the performance of evolutionary algorithms. Considering the convergence and diversity at the same time, a many-objective optimization algorithm combining angle-based selection strategy and clustering strategy is proposed. In the former strategy, the whole population is divided into several partitions to ensure the diversity of the population, and superior individuals are selected to ensure the convergence of the population. The latter strategy, the individual vector angle is used to reflect the similarity and the individuals are divided into some clusters, which helps to describe the population distribution. The performance of this algorithm is compared with five state-of-the-art evolutionary manyobjective optimization algorithms on a variety of benchmark test problems with 5, 10 and 15 objectives. The results suggest that the algorithm can slightly better competitive performance. Keywords Clustering · Angle · Many-objective optimization · Evolutionary algorithms
1 Introduction Multi-objective optimization problems (MOPs) are commonly seen in real world applications [26], such as electrical engineering, industrial scheduling [23, 25], and information retrieval systems [4]. These problems aim to simultaneously optimize more than two often conflicting objectives. Unlike single-objective optimization, the goal of solving an multi-objective optimization problem (MOP) is to find a set of trade-off solutions known as Pareto front (PF) in the objective space. Over the past two decades, a lot of evolutionary Multiobjective optimization algorithms (MOEAs) have been Zhiwei Zhao
[email protected] Zhijian Xiong [email protected] 1
School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, People’s Republic of China
2
Department of Computer Science and Technology, Tangshan University, Tangshan 063000, People’s Republic of China
3
Information Department, Kailuan General Hospital, Tangshan 063000, People’s Republic of China
proposed to solve MOPs. These MOEAs can find a set of Pareto optimal solutions in a single run. According to their selection mechanism, MOEAs can be roughly divided into three categories. These are briefly introduced next: •
Pareto-based approaches: Pareto-dominance approaches are the most popular class of approaches, which include NSGA-II [16], PAES [29] and PESA-II [13], MOEA3D [24], MOEA-EHI [22]. In these approaches, some better Pareto rank solutions are selected according to dominance-based selection criteria. In addition, a diversity-related strategy will be adopted to achieve an even distribution of the Pareto optimal solutions. Such approaches have shown very effective performance in tackling MOPs with tw
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