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Random problem generation and the computation of efficient extreme points in multiple objective linear programming

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Abstract

This paper looks at the task of computing efficient extreme points in multiple objective linear programming. Vector maximization software is reviewed and the ADBASE solver for computing all efficient extreme points of a multiple objective linear program is described. To create MOLP test problems, models for random problem generation are discussed. In the computational part of the paper, the numbers of efficient extreme points possessed by MOLPs (including multiple objective transportation problems) of different sizes are reported. In addition, the way the utility values of the efficient extreme points might be distributed over the efficient set for different types of utility functions is investigated. Not surprisingly, results show that it should be easier to find good near-optimal solutions with linear utility functions than with, for instance, Tchebycheff types of utility functions.

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Authors and Affiliations

  1. Faculty of Management Science, University of Georgia, Brooks Hall, 30602-6255, Athens, Georgia, USA

    Ralph E. Steuer

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  1. Ralph E. Steuer
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Dedicated to Professor George B. Dantzig on the occasion of his eightieth birthday.

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Steuer, R.E. Random problem generation and the computation of efficient extreme points in multiple objective linear programming. Comput Optim Applic 3, 333–347 (1994). https://doi.org/10.1007/BF01299208

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  • DOI: https://doi.org/10.1007/BF01299208

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