Abstract
Construct, Merge, Solve & Adapt (CMSA) is a general hybrid metaheuristic for solving combinatorial optimization problems. At each iteration, CMSA (1) constructs feasible solutions to the tackled problem instance in a probabilistic way and (2) solves a reduced problem instance (if possible) to optimality. The construction of feasible solutions is hereby problem-specific, usually involving a fast greedy heuristic. The goal of this paper is to design a problem-agnostic CMSA variant whose exclusive input is an integer linear program (ILP). In order to reduce the complexity of this task, the current study is restricted to binary ILPs. In addition to a basic problem-agnostic CMSA variant, we also present an extended version that makes use of a constraint propagation engine for constructing solutions. The results show that our technique is able to match the upper bounds of the standalone application of CPLEX in the context of rather easy-to-solve instances, while it generally outperforms the standalone application of CPLEX in the context of hard instances. Moreover, the results indicate that the support of the constraint propagation engine is useful in the context of problems for which finding feasible solutions is rather difficult.
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Notes
- 1.
In the context of problems that can be modelled as BIPs, any black-box ILP solver such as, for example, CPLEX can be used for this purpose.
- 2.
The used CP tool can be obtained at https://github.com/h-g-s/cprop.
- 3.
Note that, after fixing a value for \(x_{\pi (j)}\), the value of \(x_{\pi (j+1)}\) might already be fixed due to one of the implications dealt with earlier.
- 4.
Note that all considered BIPs are in standard form, that is, they must be minimized.
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Blum, C., Gambini Santos, H. (2019). Generic CP-Supported CMSA for Binary Integer Linear Programs. In: Blesa Aguilera, M., Blum, C., Gambini Santos, H., Pinacho-Davidson, P., Godoy del Campo, J. (eds) Hybrid Metaheuristics. HM 2019. Lecture Notes in Computer Science(), vol 11299. Springer, Cham. https://doi.org/10.1007/978-3-030-05983-5_1
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