Improving logic-based Benders’ algorithms for solving min-max regret problems

This paper addresses a class of problems under interval data uncertainty, composed min-max regret generalisations classical 0-1 optimisation with costs. These are called robust-hard when their counterparts already NP-hard. The state-of-the-art exact algorithms for in general work by solving corresponding mixed integer linear programming formulation Benders’ decomposition fashion. Each the possibly exponentially many cuts is separated on fly through resolution an instance problem counterpart. Since these separation subproblems may be NP-hard, not all them can easily modelled means Linear Programming (LP), unless P = NP. In this work, we formally describe logic-based framework and assess impact three warm-start procedures. procedures providing promising initial primal bounds linearly relaxed model LP-based heuristic. Extensive computational experiments two challenging indicate that highly improve quality obtained within limited execution time. Moreover, simplicity effectiveness speed-up makes reproducible option dealing general, especially more subclass