Structure vs. Efficiency of the Cross-Entropy Based Population Learning Algorithm for Discrete-Continuous Scheduling with Continuous Resource Discretisation

Abstract

In the chapter, we consider the population learning algorithm (PLA2), earlier designed by the authors, and study how the interconnection topology and heterogeneity of the constituent modules influence its efficiency. PLA2 is a population- based approach which takes advantage of the features common to the social education system rather than to the evolutionary processes. The problem of scheduling nonpreemtable tasks on parallel identical machines under constraint on discrete resource and requiring, additionally, renewable continuous resource to minimize the schedule length is chosen as the problem to cope with. A continuous resource is divisible continuously and is allocated to tasks from given intervals 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 sub-optimally solved by PLA2. The PLA2’s island design can be easily transferred to an agent system with cooperating agents.