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Mathematical programming based heuristics for the 0–1 MIP: a survey

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Abstract

The 0–1 mixed integer programming problem is used for modeling many combinatorial problems, ranging from logical design to scheduling and routing as well as encompassing graph theory models for resource allocation and financial planning. This paper provides a survey of heuristics based on mathematical programming for solving 0–1 mixed integer programs (MIP). More precisely, we focus on the stand-alone heuristics for 0–1 MIP as well as those heuristics that use linear programming techniques or solve a series of linear programming models or reduced problems, deduced from the initial one, in order to produce a high quality solution of a considered problem. Our emphasis will be on how mathematical programming techniques can be used for approximate problem solving, rather than on comparing performances of heuristics.

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Acknowledgements

This work is supported by the ELSAT2020 project which is co-financed by the European Union with the European Regional Development Fund, the French state and the Hauts de France Region Council. We are indebted to Fred Glover for his help in improving English of this paper, and also owe our gratitude to reviewers whose comments have helped to improve the paper’s exposition.

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  1. LAMIH UMR CNRS 8201 - Université de Valenciennes, 59313, Valenciennes Cedex 9, France

    Saïd Hanafi & Raca Todosijević

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  1. Saïd Hanafi
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  2. Raca Todosijević
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Correspondence to Saïd Hanafi.

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Hanafi, S., Todosijević, R. Mathematical programming based heuristics for the 0–1 MIP: a survey. J Heuristics 23, 165–206 (2017). https://doi.org/10.1007/s10732-017-9336-y

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