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Experiments in mixed-integer linear programming using pseudo-costs

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Abstract

This paper discusses heuristic “branch and bound” methods for solving mixed integer linear programming problems. The research presented on here is the follow on to that recorded in [3].

After a resumé of the concept of pseudo-costs and estimations, new heuristic rules for generating a tree which make use of pseudo-costs and estimations are presented. Experiments have shown that models having a low percentage of integer variables behave in a radically different way from models with a high percentage of integer variables. The new heuristic rules seem to apply generally to the first type of model.

Later, other heuristic rules are presented that are used with models having a high percentage of integer variables and with models having a special structure (models including special ordered sets.)

The rules introduced here have been implemented in the IBM Mathematical Programming System Extended/370. They are used to solve large mixed integer linear programming models.

Numerical results that permit comparisons to be made among the different rules are provided and discussed.

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Authors and Affiliations

  1. Program Product Center, IBM-France, Paris, France

    J. -M. Gauthier & G. Ribière

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  1. J. -M. Gauthier
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  2. G. Ribière
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Gauthier, J.M., Ribière, G. Experiments in mixed-integer linear programming using pseudo-costs. Mathematical Programming 12, 26–47 (1977). https://doi.org/10.1007/BF01593767

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  • DOI: https://doi.org/10.1007/BF01593767

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