基于正交设计的多目标演化算法

A Multi-Objective Evolutionary Algorithm Based on Orthogonal Design

提出一种基于正交设计的多目标演化算法以求解多目标优化问题(MOPs).它的特点在于:(1)用基于正交数组的均匀搜索代替经典EA的随机性搜索,既保证了解分布的均匀性,又保证了收敛的快速性;(2)用统计优化方法繁殖后代,不仅提高了解的精度,而且加快了收敛速度;(3)实验结果表明,对于双目标的MOPs,新算法在解集分布的均匀性、多样性与解精确性及算法收敛速度等方面均优于SPEA;(4)用于求解一个带约束多目标优化工程设计问题,它得到了最好的结果———Pareto最优解,在此之前,此问题的Pareto最优解是未知的.

A multi-objective evolutionary algorithm (MOEA), called orthogonal multi-objective evolutionary algorithm (OMOEA), is proposed in this paper. The idea of OMOEA is that an original niche (decision space) evolves first, and splits into a group of subniches according to the output niche-population of the evolution; then every subniche iterates the above operations so as to enhance the precision of the solutions. The main component of the new technique is the niche evolution procedure which uses a generalized design method for MOPs to locate a non-dominated set like the orthogonal design and uses the statistical optimal method for SOPs to locate optimal solution. Employed orthogonal design method and statistical method, the OMOEA can converge fast and yield evenly distributed solutions with high precision. The numerical results show that above algorithm performs better than SPEA and other MOEAs for MOPs with two objectives. For an engineering MOP with five objectives and seven constraints, the new technique finds the precise Pareto-optimal solutions which is unknown before.