Generating multiple reference vectors for a class of many-objective optimization problems with degenerate Pareto fronts

Yicun Hua,Yuan Cao,Kuangrong Hao,Yaochu Jin

doi:10.1007/s40747-020-00136-5

Abstract

Many-objective optimization problems with degenerate Pareto fronts are hard to solve for most existing many-objective evolutionary algorithms. This is particularly true when the shape of the degenerate Pareto front is very narrow, and there are many dominated solutions near the Pareto front. To solve this particular class of many-objective optimization problems, a new evolutionary algorithm is proposed in this paper. In this algorithm, a set of reference vectors is generated to locate the potential Pareto front and then generate a set of location vectors. With the help of the location vectors, the solutions near the Pareto front are mapped to the hyperplane and clustered to generate more reference vectors pointing to Pareto front. This way, the location vectors are able to efficiently guide the population to converge towards the Pareto front. The effectiveness of the proposed algorithm is examined on two typical test problems with degenerate Pareto fronts, namely DTLZ5 and DTLZ6 with 5–40 objectives. Our experimental results show that the proposed algorithm has a clear advantage in dealing with this class of many-objective optimization problems. In addition, the proposed algorithm has also been successfully applied to optimization of process parameters of polyester fiber filament melt-transportation.

Highlights

Many-objective optimization problems (MaOPs) refer to those multi-objective optimization problems with more thanIn recent years, MaOPs with irregular Pareto fronts have received increasing attention in the field of evolutionary optimization
In our recent work [6], a clustering based multi-objective evolutionary algorithm called CA-MOEA was proposed, which adaptively generates a set of cluster centers in the current population as the reference points to maintain diversity and accelerate convergence for problems with irregular Pareto fronts
A many-objective evolutionary algorithm based on Pareto front location and piecewise mapping clustering is proposed

Summary

Introduction

Many-objective optimization problems (MaOPs) refer to those multi-objective optimization problems with more than. In our recent work [6], a clustering based multi-objective evolutionary algorithm called CA-MOEA was proposed, which adaptively generates a set of cluster centers in the current population as the reference points to maintain diversity and accelerate convergence for problems with irregular Pareto fronts. LC-MaOEA can be seen a decomposition-based evolutionary algorithm, in which the population is guided by four sets of reference vectors, namely, location vectors, axis vectors, mapping-based cluster center vectors and in some cases, Gaussian random vectors These vectors cooperate together to maintain diversity and speed up convergence. We get some location vectors by vector-based effective direction detection method, the number of location vectors in the degenerate Pareto front problem is far from enough to maintain the diversity of the population, so the auxiliary reference vectors is necessary.

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Findings

Conclusion