Enhancing large neighbourhood search heuristics for Benders’ decomposition

A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search heuristics is limited to finding solutions to the BD master problem. Given the lack of general frameworks for BD, only ad hoc approaches have been developed to enhance the ability of BD to find high quality primal feasible solutions through the use of large neighbourhood search heuristics. The general BD framework of SCIP has been extended with a trust region based heuristic and a general enhancement for large neighbourhood search heuristics. The general enhancement employs BD to solve the auxiliary problems of all large neighbourhood search heuristics to improve the quality of the identified solutions. The computational results demonstrate that the trust region heuristic and a general large neighbourhood search enhancement technique accelerate the improvement in the primal bound when applying BD.

A modified adaptive large neighbourhood search for a vehicle routing problem with flexible time window

Vehicle routing problems are widely available in real world application. In this paper, we tackle the resolution of a specific variant of the problem called in the literature vehicle routing problem with flexible time windows (VRPFlexTW), when the solution has to obey several other constraints, such as the consideration of travel, service, and waiting time together with time-window restrictions. There are proposed two modified versions of the Multi-objective Adaptive Large Neighbourhood Search (MOALNS). The MOALNS approach and its different components are described. Also it is listed a computational comparison between the MOALNS versions and the Ant colony optimiser (ACO) on a few instances of the VRPFlexTW.