In this paper, we tackle the Energy-Flexible FlowShop Scheduling (EnFFS) problem, a multi-objective optimisation problem focused on the minimisation of both the overall completion time and the global energy consumption 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 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 a 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 compare it with a state-of-the-art Constraint Programming solver. We present some results obtained against both a EnFFS benchmark recently proposed in the literature, and a set of new challenging instances of increasing size.
