解约束多目标优化问题的一种鲁棒的进化算法

A Robust Evolutionary Algorithm for Constrained Multi-Objective Optimization Problems

将约束条件与目标函数融合在一起 ,对有约束的多目标优化问题 (MOP)建立了一种新的偏序关系 ,引入了约束占优的定义 ,并证明了在新的偏序关系意义下的Pareto最优集就是满足约束条件的Pareto最优集 ,从而在对种群中的个体进行评估或排序时 ,并不需要特别去关心个体是否可行 ,避免了罚函数选择参数的困难 尝试应用有限Markov链的有关理论证明了此进化算法的收敛性 用较复杂的Benchmark函数进行了大量的数值实验 ,测试结果表明新算法在解集分布的均匀性。

In this paper, a new partial order relation is defined by combining constrained conditions and the objective functions, and a definition of constrained domination between two solutions is suggested, which is an extension to the definition of domination The consistency between Pareto optimal set obtained by means of the new definition and the Pareto optimal set satisfying the constrained conditions has been proved So when the individuals are evaluated or ranked, it isn't needed to care about whether the individuals are feasible, therefore implementing a penalty parameterless constraint handling approach By using the theory of finite Markov chain, the convergence properties of this algorithm are proved Several benchmark MO optimization problems are taken to test this algorithm The numerical experiments show that the proposed approach provides good performance in terms of convergence and diversity of solutions