A differential evolution algorithm for discrete-continuous scheduling

In this paper, we propose a uniform approach to solving a discrete-continuous scheduling problem (DCSP). DCSP is an NP-hard problem, which is a special case of the resource-constrained project scheduling problem (RCPSP). Special cases of DCSP arise in practical situations such as battery charging, minimizing energy consumption of ICT systems, or refueling a fleet of boats. To solve DCSP, its two component sub-problems must be solved: (i) sequencing tasks on machines and (ii) allocating a continuous resource to tasks in such a way as to optimize a given criterion. Problem (ii) is formulated as a convex mathematical programming problem with linear constraints that can be solved with an appropriate solver, which can be time-consuming. So far, approaches of different types have been used to solve these two sub-problems, but we propose to solve problems (i) and (ii) using the same method - differential evolution. This approach is simpler in practice than the existing ones, because it does not require inventing special methods, which makes it much easier and reduces the time to design an algorithm to solve DCSP. Computational experiment has shown that our proposed approach is highly competitive in terms of execution time to existing solutions and could be the preferred choice due to its simpler implementation.