Abstract
The evolutionary algorithms for many-objective optimization based on reference-point decomposition are widely concerned since they generally maintain good performance on many optimization problems, however, most of these algorithms show insufficient versatility on optimization problems with various types of Pareto fronts. To address this issue, we propose an evolutionary algorithm for manyobjective optimization based on indicator and vector-angle decomposition, termed IVAD. In the proposed algorithm, the objective vectors of current population, as a set of reference vectors, are used to dynamically partition the whole objective space. And the max-min-vector-angle selection strategy, by calculating the vector angles between each pair of solutions, is constructed to select well-diversity solutions. Furthermore, to enhance the balance between convergence and diversity, the elite replacement, based on I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ε+</sub> indicator and vector angle, is proposed for each cluster that the selected individuals belong to. The proposed algorithm is compared with state-of-the-art many-objective evolutionary algorithms based on reference-point and vectorangle decomposition on three test suites with up to 15 objectives. Experimental results demonstrate that the proposed IVAD obtains more competitive performance on many-objective optimization problems with various types of Pareto fronts, and enhances the ability to balance convergence and diversity.
Highlights
In the real world, e.g., cloud computing [1], energyefficient scheduling [2] and cloud service [3], it is often necessary to consider multi-objective optimization problems (MOPs)
We compare IVAD with advanced many-objective evolutionary algorithms (MaOEAs) based on reference-vector decomposition, e.g., RPEA [13], NSGAIII [27], RVEA [29] and MOEADDU [30], which have been demonstrated to be effective when dealing with many-objective optimization problems (MaOPs)
IVAD is compared with MaOEAs based on vector-angle decomposition, e.g., VaEA [34] and MaOEACSS [35], which play a key role in maintaining population diversity on different distribution of Pareto front (PF)
Summary
E.g., cloud computing [1], energyefficient scheduling [2] and cloud service [3], it is often necessary to consider multi-objective optimization problems (MOPs). The first type is based on reference-point decomposition, presetting a set of uniformly distributed reference points (reference vectors) on the hyperplane or hypersphere [26] [27] Their performance strongly depends on Pareto fronts shapes of many-objective problems [28]. A two-archive algorithm (Two Arch2) [39] is constructed by combing good characteristics of indicator and dominance relation to improve the ability to search many-objective space These MaOEAs based on reference-point decomposition have shown potential performance in solving MaOPs. some relevant studies point out that they show insufficient versatility on MaOPs with various types of Pareto fronts [28] [31].
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