A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density
A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density
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DOI：
10.1109/tevc.2010.2098411
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发表时间：
2012-04
影响因子：
14.3
通讯作者：
C. Chow;S. Y. Yuen
中科院分区：
文献类型：
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作者：
C. Chow;S. Y. Yuen
大多数现有的多目标进化算法（MOEAs）假设Pareto最优解/Pareto最优目标向量存在于所获得的Pareto最优集（PS）/Pareto最优前沿（PF）的邻域中。显然，这一假设不能很好地工作的多目标问题（MOP），其真正的PF和真正的PS的形式是多段-真正断开MOP（TYD-MOP）。此外，这些MOEA通常涉及三个以上的控制参数，其中一些甚至涉及九个控制参数。其性能相对于参数设置的稳定性通常是未知的。本文提出了一种多目标密度驱动进化算法（MODdEA），它可以处理TYD-MOP。MODdEA通过二进制空间划分（BSP）树存储所有评估的解决方案。受益于BSP方案，自然地获得了由存档的快速解密度估计。MODdEA使用这个估计的密度与非支配秩一起概率地选择交配个体，这以无参数的方式放松了PF上的邻域假设。此外，提出了扩展算术交叉和多样化变异两种遗传算子，增强了算法的探索性搜索能力。MODdEA检查两个测试问题集。第一个测试集由六个TYD-MOP组成;第二个测试集由17个基准MOP组成，这些基准MOP通常由现有MOEA进行检查。与14个测试MOEA相比，MODdEA对TYD-MOP具有上级性能，并且对真实PF和PS是一个单一连接段的MOP具有竞争力。
Most existing multiobjective evolutionary algorithms (MOEAs) assume the existence of Pareto-optimal solutions/Pareto-optimal objective vectors in a neighborhood of an obtained Pareto-optimal set (PS)/Pareto-optimal front (PF). Obviously, this assumption does not work well on the multiobjective problem (MOP) whose true PF and true PS are in the form of multiple segments-truly disconnected MOP (TYD-MOP). Moreover, these MOEAs commonly involve more than three control parameters; and some of them even involve nine control parameters. The stabilities of their performance against parameter settings are generally unknown. In this paper, we propose a MOEA, namely multiobjective density driven evolutionary algorithm (MODdEA), which can handle TYD-MOP. MODdEA stores all evaluated solutions by a binary space partitioning (BSP) tree. Benefiting from the BSP scheme, a fast solution density estimation by the archive is naturally obtained. MODdEA uses this estimated density together with the nondominated rank to probabilistically select mating individuals, which relaxes the neighborhood assumption on PF in a parameter-less manner. Moreover, two genetic operators, extended arithmetic crossover and diversified mutation, are proposed to enhance the explorative search ability of the algorithm. MODdEA is examined on two test problem sets. The first test set consists of six TYD-MOPs; the second test set consists of 17 benchmark MOPs which are commonly examined by the existing MOEAs. Comparing to 14 test MOEAs, MODdEA has superior performance on TYD-MOP and is competitive on MOP whose true PF and PS are one single connected segment.