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A new approach to integrating mixed integer programming and constraint logicprogramming

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Abstract

This paper represents an integration of Mixed Integer Programming (MIP) and ConstraintLogic Programming (CLP) which, like MIP, tightens bounds rather than adding constraintsduring search. The integrated system combines components of the CLP system ECLiPSe[7] and the MIP system CPLEX [5], in which constraints can be handled by either one orboth components. Our approach is introduced in three stages. Firstly, we present an automatictransformation which maps CLP programs onto such CLP programs that any disjunction iseliminated in favour of auxiliary binary variables. Secondly, we present improvements ofthis mapping by using a committed choice operator and translations of pre‐defined non‐linearconstraints. Thirdly, we introduce a new hybrid algorithm which reduces the solutionspace of the problem progressively by calling finite domain propagation of ECLiPSe aswell as dual simplex of CPLEX. The advantages of this integration are illustrated by efficientlysolving difficult optimisation problems like the Hoist Scheduling Problem [23]and the Progressive Party Problem [27].

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Authors
  1. R. Rodosek
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  2. M.G. Wallace
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  3. M.T. Hajian
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Rodosek, R., Wallace, M. & Hajian, M. A new approach to integrating mixed integer programming and constraint logicprogramming. Annals of Operations Research 86, 63–87 (1999). https://doi.org/10.1023/A:1018904229454

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