A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

Changzhi Wu,Qiang Long,Xiangyu Wang,Jueyou Li,Lin Jiang

doi:10.1155/2015/349781

Abstract

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. But, normally, there are some trade-offs between the elitism and diversity. For some multiobjective problems, elitism and diversity are conflicting with each other. Therefore, solutions obtained by applying MOGAs have to be balanced with respect to elitism and diversity. In this paper, we propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust.

Highlights

In this paper, we consider the following multiobjective optimization problem:(MOP) Minimize F (x) (1)Subject to x ∈ X, where F(x) = (f1(x), f2(x), . . . , fp(x))T is a multiobjective function ub} ⊂ Rn, X set, and lb and ub are = {x lower∈ Rn : lb ≤ x ≤ bound and upper bound, respectively
Most of the optimization problems appearing in the real-world application have multiple objectives; they can be modeled as multiobjective optimization problems
The worst performance of OOMOGA appears in solving the test Problem 7; the IGD evaluation is 0.1267, which is worse than all the other solvers

Summary

A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. We propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust

Introduction

Preliminaries

A New Multiobjective Genetic Algorithm

Elitism metric 5

Numerical Experiments

Conclusion