免疫克隆多目标优化算法求解约束优化问题

Immune Clonal Multi-Objective Optimization Algorithm for Constrained Optimization

针对现有的约束处理技术的一些不足之处,提出一种用于求解约束优化问题的算法——免疫克隆多目标优化算法(immune clonal multi-objective optimization algorithm,简称ICMOA).算法的主要特点是通过将约束条件转化为一个目标,从而将问题转化为两个目标的多目标优化问题.引入多目标优化中的Pareto-支配的概念,每一个个体根据其被支配的程度进行克隆、变异及选择等操作.克隆操作实现了全局择优,有利于得到高质量的解;变异操作提高算法的局部搜索能力,有利于所得解的多样性;选择操作有利于算法向着最优搜索,而且加快了收敛速度.基于抗体群的随机状态转移过程,证明该算法具有全局收敛性.通过对13个标准测试问题的测试,并与已有算法进行比较。结果表明,该算法在收敛速度和求解精度上均具有一定的优势.

In this paper, the disadvantages of some existing algorithms in handling constrained objective problems （COPs） are analyzed and an algorithm used for COPs--immune clonal multi-objective optimization algorithm （ICMOA） is proposed. This algorithm treats constrained optimization as a multi-objective optimization with two objectives. One objective is the original objective function and the other is obtained by the constraints. The concept of the Pareto-dominance in multi-objective optimization is introduced and each individual is implemented clone, mutation, selection and other operations based on the degree of its Pareto-dominance. The clone operation implements the searching for optimal solution in the global region and is available for getting a high quality solution. The mutation operation improves the searching for optimal solution in the local region and assures the diversity of the solutions. The selection operation guarantees the convergence to the optimal solution and improves the convergence speed. Based on the theorem of Markov chain, the global convergence of the new algorithm is proved. Compared with the existing algorithms, simulation results on 13 benchmark test problems show that the new algorithm has some advantages in convergence speed and precision.