A mesh adaptive direct search algorithm for multiobjective optimization
A mesh adaptive direct search algorithm for multiobjective optimization
复制标题
DOI：
10.1016/j.ejor.2009.11.010
复制
发表时间：
2010-08-01
影响因子：
6.4
通讯作者：
Zghal, Walid
中科院分区：
文献类型：
--
作者：
Audet, Charles;Savard, Gilles;Zghal, Walid
本文研究一般约束下非光滑函数的多目标优化问题。首先，我们提出的定义和最优性条件，以及一些单目标配方的MOP，参数化相对于一些参考点的空间中的目标函数。接下来，我们提出了一种新的算法称为MULTIMADS（多目标网格自适应直接搜索）的MOP。MULTIMADS通过求解一系列使用NBI（自然边界相交）框架生成的单目标MOP公式来生成Pareto前沿的近似值。这些单目标问题的解决使用MADS（网格自适应直接搜索）算法约束非光滑优化。Pareto前沿近似满足一些一阶必要的最优性条件的基础上的Clarke演算。MULTIMADS，然后测试从文献中的问题与不同的帕累托前景观和苯乙烯生产过程模拟问题，从化学工程。(C)2009 Elsevier B.V.保留所有权利。
This work studies multiobjective optimization (MOP) of nonsmooth functions subject to general constraints. We first present definitions and optimality conditions as well as some single-objective formulations of MOP, parameterized with respect to some reference point in the space of objective functions. Next, we propose a new algorithm called MULTIMADS (multiobjective mesh adaptive direct search) for MOP. MULTIMADS generates an approximation of the Pareto front by solving a series of single-objective formulations of MOP generated using the NBI (natural boundary intersection) framework. These single-objective problems are solved using the MADS (mesh adaptive direct search) algorithm for constrained nonsmooth optimization. The Pareto front approximation is shown to satisfy some first-order necessary optimality conditions based on the Clarke calculus. MULTIMADS is then tested on problems from the literature with different Pareto front landscapes and on a styrene production process simulation problem from chemical engineering. (C) 2009 Elsevier B.V. All rights reserved.