A Cross-Entropy Based Algorithm for Combinatorial Optimization Problems

Cross Entropy has been recently applied to combinatorial optimization problems with promising results. This paper proposes a new cross-entropy based algorithm for monotonic integer programming problems with knapsack-type constraints. We show how the metaheuristic method can be adapted to tackle constrained problems, provided that some basic mathematical properties are enforced. Furthermore, some insight on the convergence of the method is provided. Finally, the algorithm is tested on a number of problems drawn from the reliability realm. The proposed algorithm has been extensively tested both on problems from the literature and on randomly generated large scale instances. Computational results prove the effectiveness as well as the robustness of the algorithm on different classes of problems. A Cross-Entropy Based Algorithm for Combinatorial Optimization Problems M. Caserta a,∗, M. Cabo Nodar a aInstituto Tecnologico de Monterrey, Calle del Puente, 222, Col. Ejidos de Huipulco, Del. Tlalpan, México DF, 14380, México. Abstract Cross Entropy has been recently applied to combinatorial optimization problems with promising results. This paper proposes a new cross-entropy based algorithm for monotonic integer programming problems with knapsack-type constraints. We show how the metaheuristic method can be adapted to tackle constrained problems, provided that some basic mathematical properties are enforced. Furthermore, some insight on the convergence of the method is provided. Finally, the algorithm is tested on a number of problems drawn from the reliability realm. The proposed algorithm has been extensively tested both on problems from the literature and on randomly generated large scale instances. Computational results prove the effectiveness as well as the robustness of the algorithm on different classes of problems.Cross Entropy has been recently applied to combinatorial optimization problems with promising results. This paper proposes a new cross-entropy based algorithm for monotonic integer programming problems with knapsack-type constraints. We show how the metaheuristic method can be adapted to tackle constrained problems, provided that some basic mathematical properties are enforced. Furthermore, some insight on the convergence of the method is provided. Finally, the algorithm is tested on a number of problems drawn from the reliability realm. The proposed algorithm has been extensively tested both on problems from the literature and on randomly generated large scale instances. Computational results prove the effectiveness as well as the robustness of the algorithm on different classes of problems.