Reference point specification in MOEA/D for multi-objective and many-objective problems
Reference point specification in MOEA/D for multi-objective and many-objective problems
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DOI：
10.1109/smc.2016.7844861
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
H. Ishibuchi;Ken Doi;Y. Nojima
中科院分区：
文献类型：
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作者：
H. Ishibuchi;Ken Doi;Y. Nojima
近年来，基于分解的多目标进化算法（MOEA/D）框架下提出了许多进化多目标优化算法。这些算法的特征在于使用均匀分布的归一化权重向量，从该权重向量生成一组均匀分布的参考线。他们的基本思想是沿着沿着每条参考线搜索一个Pareto最优解。虽然它们在诸如适应度评估、对每个参考线的解分配和解替换的各个方面不同，但是它们共享相同的基本思想（即，沿着沿着每条参考线搜索帕累托最优解）。权重向量规范的重要性已在文献中强调。然而，虽然参考点作为所有参考线的起点发挥着重要作用，但尚未详细审查参考点的具体规定。参考点通常由每个目标在所检查的解决方案上的最佳值组成，这是理想点的近似值。然而，这种近似在早期代中并不好，在早期代中，真正的理想点可能比每个目标在所检查的解决方案上的最佳值好得多（即使它在后代中非常好）。基于这些讨论，我们提出了一个参考点规格方法。
Recently a number of evolutionary multi-objective optimization (EMO) algorithms have been proposed using the framework of MOEA/D (multi-objective evolutionary algorithm based on decomposition). Those algorithms are characterized by the use of uniformly distributed normalized weight vectors from which a set of uniformly distributed reference lines is generated. Their basic idea is to search for a Pareto optimal solution along each reference line. While they are different in various aspects such as fitness evaluation, solution assignment to each reference line, and solution replacement, they share the same basic idea (i.e., to search for a Pareto optimal solution along each reference line). The importance of weight vector specification has been emphasized in the literature. However, the specification of a reference point has not been examined in detail whereas it plays an important role as a starting point of all reference lines. The reference point usually consists of the best value of each objective over the examined solutions, which is an approximation of the ideal point. However, this approximation is not good in early generations where the true ideal point may be much better than the best value of each objective over the examined solutions (even if it is very good in later generations). Based on these discussions, we propose a reference point specification method.