The Multiobjective Discrete Optimization Problem: A Weighted Min-Max Two-Stage Optimization Approach and a Bicriteria Algorithm

We study the multiple objective discrete optimization (MODO) problem and propose two-stage optimization problems as subproblems to be solved to obtain efficient solutions. The mathematical structure of the first level subproblem has similarities to both Tchebycheff type of approaches and a generaliz...

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Bibliographic Details
Published inManagement science Vol. 51; no. 10; pp. 1572 - 1581
Main Authors Say{iota}n, Serpil, Kouvelis, Panos
Format Journal Article
LanguageEnglish
Published Linthicum, MD INFORMS 01.10.2005
Institute for Operations Research and the Management Sciences
SeriesManagement Science
Subjects
Algorithms
Applied sciences
bicriteria knapsack problem
Efficiency decisions
Efficiency objectives
efficient set
Exact sciences and technology
Integers
Knapsack problem
Lexicography
Management science
Mathematical economics
Mathematical vectors
Mathematics
Min-max optimization
multiple objective optimization
Objective functions
Operational research. Management science
Optimal solutions
Optimization
Optimization algorithms
Programming
Studies
min-max optimization
Similarity
efficient set
Multiobjective programming
Similarity solution
Optimization
Knapsack problem
bicriteria knapsack problem
Lexicography
multiple objective optimization
Minimax method
Ordering
Discrete programming
Sampling
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Summary:We study the multiple objective discrete optimization (MODO) problem and propose two-stage optimization problems as subproblems to be solved to obtain efficient solutions. The mathematical structure of the first level subproblem has similarities to both Tchebycheff type of approaches and a generalization of the lexicographic max-ordering problem that are applicable to multiple objective optimization. We present some results that enable us to develop an algorithm to solve the bicriteria discrete optimization problem for the entire efficient set. We also propose a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee. We apply the algorithm to solve the bicriteria knapsack problem. Our computational results on this particular problem demonstrate that our algorithm performs significantly better than an equivalent Tchebycheff counterpart. Moreover, the computational behavior of the sampling version is quite promising.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.1050.0413