An Efficient Scenario Penalization Matheuristic for a Stochastic Scheduling Problem

We propose a new scenario penalization matheuristic for a stochastic scheduling problem based on both mathematical programming models and local search methods. The application considered is an NP-hard problem expressed as a risk minimization model involving quantiles related to value at risk which is formulated as a non-linear binary optimization problem with linear constraints. The proposed matheuritic involves a parameterization of the objective function that is progressively modified to generate feasible solutions which are improved by local search procedure. This matheuristic is related to the ghost image process approach by Glover (Comput Oper Res 21(8):801–822, 1994) which is a highly general framework for heuristic search optimization. This approach won the first prize in the senior category of the EURO/ROADEF 2020 challenge. Experimental results are presented which demonstrate the effectiveness of our approach on large instances provided by the French electricity transmission network RTE.