An Adaptative Reference Vector Based Evolutionary Algorithm for Many-Objective Optimization

Junhua Li,Guoyu Chen,Ming Li,Hao Chen

doi:10.1109/access.2019.2923422

Abstract

Recent studies have shown difficulties in balancing convergence and diversity for many-objective optimization problems with various types of Pareto fronts. This paper proposes an adaptive reference vector based evolutionary algorithm for many-objective optimization, termed as ARVEA. The ARVEA develops a reference vector adaptation method, which can adapt different types of Pareto fronts by adjusting the distribution of reference vectors. Besides, this algorithm adopts Pareto dominance as the first selection criterion, and the achievement scalarizing function (ASF) is introduced as the secondary selection criterion. The empirical results demonstrate that the proposed ARVEA has good performance for solving problems with various types of Pareto fronts, surpassing several state-of-the-art evolutionary algorithms designed for many-objective optimization.

Highlights

In the real word, it is very common to encounter problems involving more than one conflicting objectives
EXPERIMENTAL RESULTS the proposed ARVEA is first compared with five many-objective evolutionary algorithms (MaOEAs) designed for solving many-objective optimization problems (MaOPs) namely, NSGA-III [22], RVEA [21], MOMBI-II [34], VaEA [35] and multi-objective evolutionary algorithms (MOEAs)/D-AWA [33]
DTLZ1–7 are problems with scalable number of objectives, which are widely used to test the performance of MaOEAs on multi-objective optimization problems (MOPs) and MaOPs, IDTLZ1 and IDTLZ2 are the problems of inverted DTLZ1 and DTLZ2, respectively

Summary

INTRODUCTION

It is very common to encounter problems involving more than one conflicting objectives. The RVEA introduces a set of uniformly distributed reference vectors to partition objective space into a number of subspaces, such that the candidate solutions can efficiently converge to the optimum of each SOP without considering the conflicts between different objectives This algorithm further investigates the method of decomposition, and the method demonstrates that it can well balance convergence and diversity. The remaining space of A is filled up by solutions from A\A one by one until A reaches its maximal size of min |R| , A , where at each time the candidate solution p having the maximum value of minq∈A dis(F(p), F(q)) in A\A is copied to A , with dis(F(p), F(q)) denoting the Euclidean distance between solution p and q in objective space In this way, archive always obtain a set of nondominated solutions with good distribution, it can effectively reflect the PF and assist in adapting reference vectors. 3) ELITISM SELECTION In each subpopulation, the solution having the minimal ASF value is selected as the elitist, and copied to the population of generation Q (line 18 to 22 in Algorithm 3)

COMPUTATIONAL COMPLEXITY OF ARVEA

EXPERIMENTAL RESULTS

CONCLUSION