Hybrid Nested Partitions and Mathematical Programming Approach and Its Applications

Large-scale discrete optimization problems are difficult to solve, especially when different kinds of real constraints are considered. Conventionally, standard mathematical programming is a general approach for discrete optimization, but may suffer from the unacceptable long solution time in applications. On the other hand, some heuristics/metaheuristics methods are more powerful in finding approximate solutions efficiently, but mostly are problem and constraint dependent. In this paper, we develop a new hybrid nested partitions and mathematical programming approach, which creates compliance between mathematical programming and the heuristics/metaheuristics methods. Potentially applicable to many different types of problems, the hybrid approach can provide approximate solutions efficiently, and in the meantime can easily handle different kinds of constraints. The applications of the hybrid approach to the local pickup and delivery problem (LPDP) and the discrete facility location problem (DFLP) are presented in this paper.