A Double Learning Models-Based Multi-Objective Estimation of Distribution Algorithm

Qiaoyong Jiang,Yanyan Lin,Han Liu

doi:10.1109/access.2019.2945818

Abstract

The recently developed regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) and inverse models-based multi-objective evolutionary algorithm (IM-MOEA) have been shown to be two effective methods for solving some complex multi-objective optimization problems (MOPs). However, RM-MEDA and IM-MOEA are still challenged when solving MOPs with many local Pareto fronts, and usually generate poor solutions when the population has no obvious regularity. In order to overcome these limits, an ensemble of RM-MEDA and IM-MOEA, denoted as RM-IM-EDA, is proposed in this paper. This ensemble is based on a dynamic mixture of the sampling in the decision space by the regularity-based learning model and the sampling in the objective space using the inverse learning models. In addition, a sequence-based deterministic initialization method is introduced to identify the properties of fitness landscape. The objective behind this scheme is to reduce the probability of sinking into the local Pareto optimum. For the comparison purposes, the proposed RM-IM-EDA is tested on 32 benchmark problems. Experiment results statistically affirm the efficiency of the proposed approach to obtain better results compared with each individual algorithm and other four state-of-the-art MEDAs.

Highlights

Multi -objective optimization problems (MOPs), which refer to multiple conflicting objectives to be optimized simultaneously, can be briefly stated as follows: min F(x) = (f1(x), f2(x), · · ·, fm(x)), s.t.x = (x1, x2, · · ·, xD) ∈ (1)where x = (x1, x2, · · ·, xD) is a decision vector in decision space = Di=1[xi, xi] ⊆ D, D is the number of decision variables, and Li and Ui denote the lower and upper boundaries of the ith decision variable xi, respectively
If a solution x∗ cannot be dominated by any other solutions in, the x∗ is known as Pareto optimal, and the union of all x∗ is termed the Pareto set (PS), while the image of PS in the objective space, namely, the union of F(x∗), is called the Pareto front (PF)
We propose an ensemble of regularity model-based multi-objective estimation of distribution algorithm (RM-multiobjective estimation of distribution algorithms (MEDAs)) and inverse models-based multi-objective evolutionary algorithm (IM-multi-objective evolutionary algorithms (MOEAs)) (RM-IM-EDA), which is expected to exploit the advantage of sampling from the two probabilistic learning models, and achieve better performance than each individual algorithm

Summary

INTRODUCTION

In order to find an approximation of the PF (or PS), a lot of multi-objective evolutionary algorithms (MOEAs) have been proposed during the past two decades They can be briefly categorized into Pareto dominance-based [1], decomposition-based [2], and performance indicator-based MOEAs [3]. The improvements of IM-MOEA: In IM-MOEA, a group of predefined uniformly distribution reference vectors are employed to partition the objective space into several sub-regions Such a partition may not be very efficient for MOPs with irregular PFs because some reference vectors are associated with an insufficient number or even no solutions.

RM-MEDA

IM-MOEA

CONCLUSION