论文标题
帕累托前近似的信任区域方法
A Trust Region Method for Pareto Front Approximation
论文作者
论文摘要
在本文中，我们考虑了黑框多目标优化问题，其中所有目标函数均未分析。在多目标优化中，重要的是在帕累托前部产生一组均匀分布的离散解决方案以构建良好的近似值。在Black-Box Biobigentive优化中，可以通过Pareto Front的订购特性评估解决方案之间的距离。这些距离允许能够评估所有溶液点的分布，因此保持解决方案分布的均匀性并不难。但是，超过两个目标的问题没有订购财产，因此注意到这些问题需要其他技术来衡量解决方案分布的覆盖范围并保持均匀性。在本文中，我们提出了一种基于信任区域方法的算法，用于黑盒多目标优化中的Pareto前近似值。在算法中，我们通过采用密度函数并探索该点附近的区域，从而在非主导点集中选择一个参考点。这即使对于具有两个以上目标函数的问题，解决方案分布的统一性也可以确保。我们还证明，算法的迭代点会收敛到帕累托关键点。最后，我们提出数值结果，表明该算法生成了近似于帕累托前部的良好分布的解决方案，即使在三个目标函数的问题的情况下也是如此。
In this paper, we consider black-box multiobjective optimization problems in which all objective functions are not given analytically. In multiobjective optimization, it is important to produce a set of uniformly distributed discrete solutions over the Pareto front to build a good approximation. In black-box biobjective optimization, one can evaluate distances between solutions with the ordering property of the Pareto front. These distances allow to be able to evaluate distribution of all solution points, so it is not difficult to maintain uniformity of solutions distribution. However, problems with more than two objectives do not have ordering property, so it is noted that these problems require other techniques to measure the coverage and maintain uniformity of solutions distribution. In this paper, we propose an algorithm based on a trust region method for the Pareto front approximation in black-box multiobjective optimization. In the algorithm, we select a reference point in the set of non-dominated points by employing the density function and explore area around this point. This ensures uniformity of solutions distribution even for problems with more than two objective functions. We also prove that the iteration points of the algorithm converge to Pareto critical points. Finally, we present numerical results suggesting that the algorithm generates the set of well-distributed solutions approximating the Pareto front, even in the case for the problems with three objective functions.
