Multiobjective differential evolution algorithm based on decomposition for a type of multiobjective bilevel programming problems
Multiobjective differential evolution algorithm based on decomposition for a type of multiobjective bilevel programming problems
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一类多目标双层规划问题的基于分解的多目标差分进化算法
DOI：
10.1016/j.knosys.2016.06.018
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发表时间：
2016-09-01
影响因子：
8.8
通讯作者：
Jiao, Yong-Chang
中科院分区：
文献类型：
--
作者：
Li, Hong;Zhang, Qingfu;Jiao, Yong-Chang
研究了上层为多目标下层为单目标的多目标双层规划问题。通过对下层优化采用Karush-Kuhn-Tucker（KKT）最优性条件，将原多目标双层优化问题转化为带互补约束的多目标单层优化问题.为了处理互补约束，现有的平滑技术与平衡约束的数学规划。这样，一个多目标单级非线性规划问题被形式化。针对这一多目标单层优化问题，分别采用基于加权和法和切比雪夫法的标量化方法，提出了一种基于分解的约束多目标差分进化算法。一些说明性的数值例子，包括线性和非线性版本的MOBLPP与多个目标在上层进行测试，以显示所提出的方法的有效性。此外，NSGA-II是用来解决这个多目标的单级优化模型。比较结果之间的加权和方法，切比雪夫方法，和NSGA-II。(C)2016爱思唯尔B.V.保留所有权利。
This paper considers the multiobjective bilevel programming problem (MOBLPP) with multiple objective functions at the upper level and a single objective function at the lower level. By adopting the Karush-Kuhn-Tucker (KKT) optimality conditions to the lower level optimization, the original multiobjective bilevel problem can be transformed into a multiobjective single-level optimization problem involving the complementarity constraints. In order to handle the complementarity constraints, an existing smoothing technique for mathematical programs with equilibrium constraints is applied. Thus, a multiobjective single-level nonlinear programming problem is formalized. For solving this multiobjective single-level optimization problem; the scalarization approaches based on weighted sum approach and Tchebycheff approach are used respectively, and a constrained multiobjective differential evolution algorithm based on decomposition is presented. Some illustrative numerical examples including linear and nonlinear versions of MOBLPPs with multiple objectives at the upper level are tested to show the effectiveness of the proposed approach. Besides, NSGA-II is utilized to solve this multiobjective single-level optimization model. The comparative results among weighted sum approach, Tchebycheff approach, and NSGA-II are provided. (C) 2016 Elsevier B.V. All rights reserved.