Multiobjective differential evolution algorithm based on decomposition for a type of multiobjective bilevel programming problems

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 multiobje...

Full description

Saved in:
Bibliographic Details
Published in:Knowledge-based systems Vol. 107; pp. 271 - 288
Main Authors: Li, Hong, Zhang, Qingfu, Chen, Qin, Zhang, Li, Jiao, Yong-Chang
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2016
Subjects:
Decomposition
Evolutionary algorithms
Mathematical analysis
Mathematical models
MOEA/D
Multiobjective bilevel programming problem
Multiple objective
Nonlinear programming
NSGA-II
Optimization
Pareto optimality
Programming
Tchebycheff approach
Weighted sum approach
Pareto optimality
NSGA-II
Multiobjective bilevel programming problem
Weighted sum approach
MOEA/D
Tchebycheff approach
ISSN:0950-7051, 1872-7409
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0950-7051
1872-7409
DOI:10.1016/j.knosys.2016.06.018