Population learning with differential evolution for the discrete-continuous scheduling with continuous resource discretisation

In the paper, we consider a population learning algorithm denoted (PLA3), with the differential evolution method for solving the discrete-continuous scheduling problem (DCSP) with continuous resource discretisation - Θ_z. 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 Θ_z with continuous resource discretisation is introduced and suboptimally solved by PLA3. Experimental results show that PLA3 was able to improve best-known solutions and excels its predecessor PLA2 in solving the considered problem.