Adaptive lexicographical optimization with vague goals in green fuzzy flexible job shop scheduling

Abstract Nowadays, the need to reduce the industry’s energy demands means that green concerns must be incorporated as performance indicators. In scheduling, this translates into decision makers willing to sacrifice, to a certain point, production-related criteria, such as meeting delivery deadlines, in favour of reducing energy consumption. The exact degree of compromise can be difficult to set a priori; instead, the expert may only be able to provide some vague production goals that need to be achieved before dealing with energy savings. The decision maker’s task is further complicated in many real-world problems due to the presence of uncertainty in some of the parameters. In this paper, we tackle a flexible job shop scheduling problem with uncertain task durations, minimising the total weighted tardiness while also considering the total energy consumption. In this setting, when there is a clear hierarchy between multiple objectives, a lexicographical goal programming approach seems natural but has the caveat of needing well-defined target values a priori. Therefore, we propose a new hierarchical multiobjective adaptive strategy to work in a lexicographic goal programming setting where only vaguely defined goals are provided. This strategy is then embedded in a memetic algorithm. Extensive experimentation shows that the proposed adaptive strategy is more suitable for the problem at hand than a purely lexicographic and a traditional lexicographic goal programming strategy, and it constitutes an excellent complement to Pareto-based methods.