Multi-criteria branch and bound: A vector maximization algorithm for Mixed 0-1 Multiple Objective Linear Programming

The paper describes the Multi-Criteria Branch and Bound (MCBB) algorithm, a vector maximization algorithm capable of deriving all efficient extreme points, for small- and medium-sized Mixed 0-1 Multiple Objective Linear Programming (Mixed 0-1 MOLP). Particular emphasis is given to computational aspe...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 171; no. 1; pp. 53 - 71
Main Authors: Mavrotas, G., Diakoulaki, D.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.12.2005
Elsevier
Subjects:
Branch and bound
Calculus of variations and optimal control
Exact sciences and technology
Mathematical analysis
Mathematics
Mixed integer programming
Multiple objective programming
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Sciences and techniques of general use
Branch and bound
Mixed integer programming
Multiple objective programming
Integer programming
Numerical analysis
Maximization
Algorithm performance
Mixed programming
Applied mathematics
Decision making
Multiobjective programming
Linear programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:The paper describes the Multi-Criteria Branch and Bound (MCBB) algorithm, a vector maximization algorithm capable of deriving all efficient extreme points, for small- and medium-sized Mixed 0-1 Multiple Objective Linear Programming (Mixed 0-1 MOLP). Particular emphasis is given to computational aspects aiming principally at accelerating the solution procedure. For facilitating the decision maker’s search toward the most preferred efficient solution, the notion of efficient combinations of the binary variables is further exploited. It is also shown that the MCBB algorithm can be used in single objective problems (Mixed Integer LP problems) in order to determine all alternative optima, as well as in Mixed Integer MOLP problems and Pure 0-1 MOLP problems that frequently arise in practice. A computational experiment is included in the paper in order to illustrate the performance of the algorithm.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.01.038