在很多实际应用问题中,不确定性的存在对于优化问题的最优解的性能会产生影响.在求解不确定环境下的优化问题时,往往需要考虑解的鲁棒性.最优解的鲁棒性定义通常要考虑其局部邻域内所有解的表现.在多目标优化背景下,如何逼近鲁棒最优帕累托前沿也是一件非常有挑战性的工作.已有的鲁棒多目标进化算法能够比较好地处理低维鲁棒多目标优化问题,即问题的决策变量维数不超过10,但对于高维鲁棒多目标优化问题的表现往往不好.提出了一种结合自编码器以及协同进化方法的多目标进化算法(Decomposition-based Multiobjective Evolutionary Algorithm Assisted by Autoencoder and Cooperative Coevolution,MOEA/D-AECC),用来解决可降维的高维鲁棒多目标优化问题.该算法利用两个不同种群分别优化原始多目标优化问题以及对应的鲁棒多目标优化问题.为提高算法处理高维问题的能力,该算法利用自编码器模型对高维数据进行降维,从而提取出高维数据的低维特征.通过重构这些低维特征来学习可靠的下降方向,之后沿着可靠的下降方向采样产生新解.最后,通过实验测试了 MOEA/D-AECC算法在一组可降维的高维鲁棒多目标优化问题上的表现.实验结果表明,MOEA/D-AECC算法的寻优显著优于其他几种代表性的鲁棒多目标进化算法.
A Robust Multi-objective Evolutionary Algorithm Assisted by Autoencoder
In many practical application problems,the existence of uncertainty has an impact on the performance of the optimal solution to an optimization problem.When solving optimiza-tion problems in uncertain environments,it is often necessary to consider the robustness of the solution.The definition of robustness of an optimal solution usually considers the performance of all solutions in its local neighborhood.In the context of multiobjective optimization,it is a very challenging task to approximate the robust Pareto fronts.Existing robust multi-objective evolutionary algorithms(MOEA)can handle low-dimensional robust multi-objective optimiza-tion problems(MOPs),i.e.,the dimensionality of the decision variables is less than 10,but often perform poorly for high-dimensional robust MOPs.In this paper,we propose an MOEA,called MOEA/D-AECC(Decomposition-based Multiobjective Evolutionary Algorithm Assisted by Autoencoder and Cooperative Coevolution,MOEA/D-AECC),which combines autoencoder as well as co-evolutionary methods,for solving high-dimensional robust MOPs with low eff-ective dimension.The algorithm utilizes two different populations to optimize the original MOPs and the corresponding robust MOPs,respectively.To improve the ability to handle high-dimensional problems,the algorithm utilizes an autoencoder for dimensionality reduction in order to extract the low-dimensional features of the high-dimensional data.The descent directions are learned by reconstructing these low-dimensional features,then new solutions are generated by sampling along these descent directions.Finally,the performance of MOEA/D-AECC is tested on a set of high-dimensional robust MOPs with low effective dimensions in this paper.The experimental results show that the performance of MOEA/D-AECC is significantly better than several other representative robust MOEA.
万方数据
维普
