Approximating the nondominated set of an MOLP by approximately solving its dual problem
type: Item
instance of: scholarly article
title: Approximating the nondominated set of an MOLP by approximately solving its dual problem
zbMATH Open document ID: 1184.90161
author: Lizhen Shao
author: Matthias Ehrgott
published in: Mathematical Methods of Operations Research
publication date: 2009-01-30T00:00:00Z
review text: The authors propose an algorithm to solve the dual multiobjective linear program approximately. By using a coupling function, they calculate a corresponding polyhedral set in the objective space of the primal multiobjective linear program. The approximate solution set can be proved to be an approximation of the weakly nondomimated set of the primal problem. This approximate method is applied to solve the bean intensity optimization problem of radiatherapy treatment planning.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5500940
zbMATH Keywords: Multiobjective linear programming
zbMATH Keywords: Geometric duality
zbMATH Keywords: \(\epsilon \)-nondominated set
zbMATH Keywords: Radiotheraphy treatment planning
MaRDI profile type: Publication
full work available at URL: s00186-007-0194-5
OpenAlex ID: W2030295088
cites work: Hybrid approach for solving multiple-objective linear programs in outcome space
cites work: An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem
cites work: On-line and off-line vertex enumeration by adjacency lists
cites work: Q5692464
cites work: A dual variant of Benson's ``outer approximation algorithm'' for multiple objective linear programming
cites work: State Constraints in Convex Control Problems of Bolza
cites work: Approximation methods in multiobjective programming
cites work: Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning
cites work: Q4317868
DOI: 10.1007/S00186-007-0194-5
Recommended article: Approximating nondominated sets in continuous multiobjective optimization problems
Recommended article: Approximating the noninferior set in multiobjective linear programming problems
Recommended article: Computing non-dominated solutions in MOLFP
Recommended article: Q5074081
Recommended article: An approximation to the nondominated set of a multiobjective linear fractional programming problem
Recommended article: Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems
Recommended article: Q3821956
Recommended article: Q4613616
Recommended article: Approximate Saddle Point and Duality for Multiobjective n-Set Optimization
Recommended article: Approximating a solution set of nonlinear inequalities
description: scientific article; zbMATH DE number 5500940