论文标题
在直接多搜索中使用一阶信息进行多目标优化
Using first-order information in Direct Multisearch for multiobjective optimization
论文作者
论文摘要
导数是单目标优化的重要工具。实际上，通常认为基于衍生的方法比无衍生的优化方法具有更好的性能。在这项工作中，我们将表明，当目标是计算给给定问题的完整帕累托正面的近似值时，同样的情况不适用于基于多目标衍生的优化。将针对基于衍生的多物镜优化问题的Direct MultiSearch（DMS）（DMS）（DMS）的竞争力（DMS）的竞争力。然后，我们将评估向DMS框架添加一阶信息的潜在丰富。衍生物将用于修剪在算法的轮询步骤中考虑的正跨度集，强调了符合附近可行区域几何形状的上升方向可以具有的作用。 DMS的两种变体都与基于最新衍生的算法具有竞争力。此外，对于合理的功能评估预算，新变体不仅与基于衍生的求解器竞争，而且还与DMS的原始实施相关。
Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of a given problem. The competitiveness of Direct MultiSearch (DMS), a robust and efficient derivative-free optimization algorithm, will be stated for derivative-based multiobjective optimization problems. We will then assess the potential enrichment of adding first-order information to the DMS framework. Derivatives will be used to prune the positive spanning sets considered at the poll step of the algorithm, highlighting the role that ascent directions, that conform to the geometry of the nearby feasible region, can have. Both variants of DMS show to be competitive against a state-of-art derivative-based algorithm. Moreover, for reasonable small budgets of function evaluations, the new variant is not only competitive with the derivative-based solver but also with the original implementation of DMS.
