An Orthogonal Multi-objective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints

Abstract

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.

An improved multiobjective differential evolution based on Pareto-adaptive -dominance and orthogonal design

“…Leung et al [26] incorporated orthogonal design in GA for numerical optimization problems and found such method was more robust and statistically sound than the classical GAs. OMOEA [27] presented by Zeng et al adopted the orthogonal design method to solve MOPs. In OMOEA, it uses the orthogonal design method to generate a group of sub-niches, every sub-niche evolves at each generation.…”

“…Unfortunately, these objectives are contradictory. Inspired by the ideas from the orthogonal design method successfully used in EAs ( [26,27,31]) and pa-dominance proposed in [32], in this work, we extend our previous work -ODEMO [31] and present an improved DE algorithm to solve MOPs, which integrates established techniques in existing EA's in a single unique algorithm. Our proposed DE algorithm is named pa-ODEMO.…”

A dominance tree and its application in evolutionary multi-objective optimization

“…Due to the transitive property of Pareto dominance [30], some relations (i.e., edges) can be deduced from the existing relations. Taking Fig.…”

A Novel Differential Evolution Algorithm Based on ε-Domination and Orthogonal Design Method for Multiobjective Optimization

“…In order to test the performance of -ODEMO a number of two-and three-objective problems were used, where two-objective test problems (ZDT1, ZDT2, ZDT3, ZDT4 and ZDT6) are introduced in [22], and also have been used in [1,13,14,15,18]. And three-objective test problems (DTLZ1 and DTLZ6) are introduced in [23].…”

“…Leung and Wang [17] incorporated orthogonal design in genetic algorithm for numerical optimization problems and found such method was more robust and statistically sound than the classical GAs. OMOEA [18] and OMOEA-II [19] presented by Sangyou Zeng et al adopted the orthogonal design method to solve the MOPs. Numerical results demonstrated the efficiency of the two tools.…”