Generic CP-Supported CMSA for Binary Integer Linear Programs
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.
- 1.Achterberg, T.: Constraint Integer Programming. Ph.D. thesis (2007)Google Scholar
- 4.Blum, C.: Construct, merge, solve and adapt: application to unbalanced minimum common string partition. In: Blesa, M.J., Blum, C., Cangelosi, A., Cutello, V., Di Nuovo, A., Pavone, M., Talbi, E.-G. (eds.) HM 2016. LNCS, vol. 9668, pp. 17–31. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39636-1_2CrossRefGoogle Scholar
- 7.Ernst, A.T., Singh, G.: Lagrangian particle swarm optimization for a resource constrained machine scheduling problem. In: 2012 IEEE Congress on Evolutionary Computation, pp. 1–8 (2012)Google Scholar
- 10.Fourer, R., Gay, D., Kernighan, B.: AMPL, vol. 117. Boyd & Fraser Danvers (1993)Google Scholar
- 15.Lizárraga, E., Blesa, M.J., Blum, C.: Construct, merge, solve and adapt versus large neighborhood search for solving the multi-dimensional knapsack problem: which one works better when? In: Hu, B., López-Ibáñez, M. (eds.) EvoCOP 2017. LNCS, vol. 10197, pp. 60–74. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-55453-2_5CrossRefGoogle Scholar
- 17.Sandholm, T., Shields, R.: Nogood learning for mixed integer programming. Technical report (2006)Google Scholar