Island-based Differential Evolution Algorithm for the Discrete-continuous Scheduling with Continuous Resource Discretisation

In the paper, we propose an island-based differential evolution algorithm (IBDEA) for solving the discrete-continuous scheduling problem (DCSP) with continuous resource discretisation - ΘZ. The considered problem originates from DCSP, in which nonpreemtable tasks should be scheduled on parallel identical machines under constraint on discrete resource and requiring, additionally, a renewable continuous resource to minimize the schedule length. The continuous resource in DCSP is divisible continuously and is allocated to tasks from a given interval in amounts unknown in advance. Task processing rate depends on the allocated amount of the continuous resource. To eliminate time consuming optimal continuous resource allocation, an NP-hard problem ΘZ with continuous resource discretisation is introduced and sub-optimally solved by IBDEA. Experimental results show that IBDEA is able to find better solutions than an algorithm realizing only the differential evolution method and was able to improve best-known solutions to the considered problem.