论文标题
用于计算帕累托前表示的改进的高箱算法
An improved hyperboxing algorithm for calculating a Pareto front representation
论文作者
论文摘要
当解决多个目标函数的优化问题时，我们通常会面临一个或几个目标函数是非凸的情况，或者我们无法轻易显示所涉及的所有功能的凸度。在这种情况下，需要一种用于计算非主导集的表示表示的一般算法。一种合适的方法是由所谓的混音算法组成，该算法的特征是将客观空间拆分为轴平行的高矩形。因此，仅利用非主导性的属性来减少所谓的搜索区域。在文献中，这种算法已经证明，相对于计算的表示点的数量，可以很好地覆盖帕累托前部。但是，对于超过五个目标的问题，该算法的计算成本令人难以置信。在本文中，我们提出了提高算法性能的算法进步，并使其适用于多达九个目标的问题。我们说明了一组测试问题的表现增益和表示的质量。我们还将改进的算法应用于放射疗法计划领域的现实世界问题。
When solving optimization problems with multiple objective functions we are often faced with the situation that one or several objective functions are non-convex or that we can not easily show the convexity of all functions involved. In this case a general algorithm for computing a representation of the nondominated set is required. A suitable approach consists in a so-called hyperboxing algorithm that is characterized by splitting the objective space into axis-parallel hyperrectangles. Thereby, only the property of nondominance is exploited for reducing the so-called search region. In the literature such an algorithm has already shown to provide a very good coverage of the Pareto front relative to the number of representation points calculated. However, the computational cost for the algorithm was prohibitive for problems with more than five objectives. In this paper, we present algorithmic advances that improve the performance of the algorithm and make it applicable to problems with up to nine objectives. We illustrate the performance gain and the quality of the representation for a set of test problems. We also apply the improved algorithm to a real world problem in the field of radiotherapy planning.
