Enhancing large neighbourhood search heuristics for Benders\u2019 decomposition

Abstract

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.