一类新型动态多目标鲁棒进化优化方法

A Novel Dynamic Multi-objective Robust Evolutionary Optimization Method

传统动态多目标优化问题(Dynamic multi-objective optimization problems,DMOPs)的求解方法,通常需要在新环境下,通过重新激发寻优过程,获得适应该环境的Pareto最优解.这可能导致较高的计算代价和资源成本,甚至无法在有限时间内执行该优化解.由此,提出一类寻找动态鲁棒Pareto最优解集的进化优化方法.动态鲁棒Pareto解集是指某一时刻下的Pareto较优解可以以一定稳定性阈值,逼近未来多个连续动态环境下的真实前沿,从而直接作为这些环境下的Pareto解集,以减小计算代价.为合理度量Pareto解的环境适应性,给出了时间鲁棒性和性能鲁棒性定义,并将其转化为两类鲁棒优化模型.引入基于分解的多目标进化优化方法和无惩罚约束处理方法,构建了动态多目标分解鲁棒进化优化方法.特别是基于移动平均预测模型实现了未来动态环境下适应值的多维时间序列预测.基于提出的两类新型性能评价测度,针对8个典型动态测试函数的仿真实验,结果表明该方法得到满足决策者精度要求,且具有较长平均生存时间的动态鲁棒Pareto最优解.

Traditional methods solving dynamic multi-objective optimization problems （DMOPs） often trigger the evolution process again to find the Pareto-optimal solutions as soon as new environment appears. This may lead to larger computation and resources costs, even unable to perform the optimum solution in the limited time. Therefore, a novel evolutionary optimization method is proposed looking for dynamic robust Pareto-optimal solution sets, which are the Pareto-optimal solutions for certain enviromnent. They can approximate to the true Pareto fronts in following consecutive dynamic environments along a certain satisfaction threshold, and directly be used as Pareto solutions of these environments so as to reduce the computation cost. Two metrics including time robustness and performance robustness are presented to measure the environmental adaptability of Pareto-optimal solutions. Subsequently, they are transformed into two kinds of robust optimization models. Multi-objective evolutionary algorithm based on decomposition and penalty-parameter less constraint handling method are introduced to form the decomposition-based dynamic multi-objective robust evolutionary optimization method. Especially, a moving average prediction model is adopted to realize multi-dimensional time series prediction of these solutions. In term of eight benchmark functions and two novel metrics, the simulation results indicate that the proposed method can obtain the robust Pareto-optimal solutions meeting the need of decision makers with more average survive time.