Effects of discrete objective functions with different granularities on the search behavior of EMO algorithms
Effects of discrete objective functions with different granularities on the search behavior of EMO algorithms
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DOI：
10.1145/2330163.2330232
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
H. Ishibuchi;M. Yamane;Y. Nojima
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文献类型：
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作者：
H. Ishibuchi;M. Yamane;Y. Nojima
组合优化中的目标函数是离散的。离散目标函数的可能值的数目在不同的问题中是完全不同的。离散目标函数的优化通常是非常困难的。在多目标优化的情况下，不同的目标函数具有不同数量的可能值。这意味着目标空间的每个轴都有不同的粒度。有些轴的粒度很细，有些则很粗。本文通过计算实验研究了不同粒度的离散目标函数对进化多目标优化算法搜索行为的影响。实验结果表明，粒度较粗的离散目标函数会降低EMO算法沿该目标的搜索速度。一个有趣的观察结果是，在一个目标上的减速通常会导致在其他目标上的搜索速度加快。我们还研究了向每个离散目标函数添加小随机噪声的效果，以增加可能的目标值的数量。
Objective functions in combinatorial optimization are discrete. The number of possible values of a discrete objective function is totally different from problem to problem. Optimization of a discrete objective function is often very difficult. In the case of multiobjective optimization, a different objective function has a different number of possible values. This means that each axis of the objective space has a different granularity. Some axes may have fine granularities while others are coarse. In this paper, we examine the effect of discrete objective functions with different granularities on the search behavior of EMO (evolutionary multiobjective optimization) algorithms through computational experiments. Experimental results show that a discrete objective function with a coarse granularity slows down the search of EMO algorithms along that objective. An interesting observation is that such a slow-down along one objective often leads to the speed-up of the search along other objectives. We also examine the effect of adding a small random noise to each discrete objective function in order to increase the number of possible objective values.