On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem
On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem
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DOI：
10.1109/tevc.2010.2064321
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发表时间：
2011-08
影响因子：
14.3
通讯作者：
O. Schütze;A. Lara;C. Coello
中科院分区：
文献类型：
--
作者：
O. Schütze;A. Lara;C. Coello
在本文中，我们研究了连续多目标优化问题目标数量对进化策略的硬度的影响，这对于多目标优化问题特别感兴趣。更确切地说，我们根据人口的进化（或收敛性）来衡量对帕累托集合集合集合集合的硬度。以前的相关研究主要考虑了人群中非主导的个体的数量，这大大改善了对问题的理解，并导致了可能的补救措施。但是，在某些情况下，这种Ansatz还不够复杂，无法理解所有现象，甚至可能具有误导性。在本文中，我们建议您考虑改善人口状况的概率，以在一定程度上可以通过后裔锥的大小来衡量。例如，我们对一般类单模式测试问题进行了一些定性的考虑，并猜想这些问题通过添加目标而变得更加困难，但是这种差异实际上并不重要，我们通过一些经验研究来支持这一点。此外，我们解决了文献中观察到的目标数量的可伸缩性。也就是说，我们试图根据我们的观察结果提出针对进化策略处理多个目标问题的挑战，并使用它们来解释该领域的最新进展。
In this paper, we study the influence of the number of objectives of a continuous multiobjective optimization problem on its hardness for evolution strategies which is of particular interest for many-objective optimization problems. To be more precise, we measure the hardness in terms of the evolution (or convergence) of the population toward the set of interest, the Pareto set. Previous related studies consider mainly the number of nondominated individuals within a population which greatly improved the understanding of the problem and has led to possible remedies. However, in certain cases this ansatz is not sophisticated enough to understand all phenomena, and can even be misleading. In this paper, we suggest alternatively to consider the probability to improve the situation of the population which can, to a certain extent, be measured by the sizes of the descent cones. As an example, we make some qualitative considerations on a general class of uni-modal test problems and conjecture that these problems get harder by adding an objective, but that this difference is practically not significant, and we support this by some empirical studies. Further, we address the scalability in the number of objectives observed in the literature. That is, we try to extract the challenges for the treatment of many-objective problems for evolution strategies based on our observations and use them to explain recent advances in this field.