Algorithms for hybrid MILP/CP models for a class of optimization problems

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Algorithms for hybrid MILP/CP models for a class of optimization problems (2001)

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by Vipul Jain , Ignacio E. Grossmann

Venue:	INFORMS Journal on Computing
Citations:	98 - 12 self

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@ARTICLE{Jain01algorithmsfor,
    author = {Vipul Jain and Ignacio E. Grossmann},
    title = {Algorithms for hybrid MILP/CP models for a class of optimization problems},
    journal = {INFORMS Journal on Computing},
    year = {2001},
    volume = {13},
    pages = {2001}
}

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Abstract

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

Keyphrases

hybrid milp cp model optimization problem least-cost schedule computational performance van hentenryck mixed integer linear programming several set reduced set combined milp-cp opl model complementary strength dissimilar parallel machine hybrid model cpu time equivalence relation non-zero objective function coefficient cp variable application example lp cp-based branch-and-bound algorithm decomposition method feasibility cp problem constraint programming relaxed milp milp constraint cp constraint milp cp due date binary variable magnitude reduction

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