Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a cond...

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Bibliographic Details
Published in:Naval research logistics Vol. 65; no. 3; pp. 203 - 217
Main Authors: Tohidi, G., Hassasi, H.
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.04.2018
Wiley Subscription Services, Inc
Subjects:
adjacency
affine independence
Algorithms
Computation
Convexity
efficient face
Linear programming
multiobjective linear programming
Multiple objective analysis
Search methods
top‐down search strategy
ISSN:0894-069X, 1520-6750
Online Access:Get full text
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Summary:It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.
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ISSN:0894-069X
1520-6750
DOI:10.1002/nav.21805