A Multi-objective Large Neighborhood Search Methodology for Scheduling Problems with Energy Costs

In this paper, we tackle the Energy-Flexible Flow Shop Scheduling (EnFFS) problem, a multi-objective optimization problem focused on the minimization of both the overall completion time C and the global energy consumption E of the solutions. The tackled problem is an extension of the Flexible Flow-Shop Scheduling problem where each activity in a job has a set of possible execution modes with different trade-off between energy consumed and processing time. Moreover, global energy consumption E may also depend on the possibility to switch-off the machines during the idle periods. The goal of this work is to widen the knowledge about performance capabilities, in particular the ability of efficiently finding high quality approximations of the solution Pareto front. To this aim, we explore the development of innovative meta-heuristic algorithms for solving the proposed multi-objective scheduling problem. In particular, we consider stochastic local search (SLS) algorithms, introducing a Multi-Objective Large Neighbourhood Search (MO-LNS) framework in line with the large neighbourhood search approaches proposed in literature, and present some preliminary results obtained against a EnFFS benchmark recently proposed in the literature, showing some initial but appreciable improvements. Moreover, four new instances are presented and experimented upon, which will be hopefully used by the community as a novel benchmark on which to test new multi-objective optimisation research contributions.