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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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
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Abstract	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.
AbstractList	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.
Author	Mavrotas, G. Diakoulaki, D.
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SubjectTerms	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
Title	Multi-criteria branch and bound: A vector maximization algorithm for Mixed 0-1 Multiple Objective Linear Programming
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