Harmony search algorithm with dynamic subpopulations for scheduling identical parallel machines

In this paper, we study the identical parallel machines scheduling problem for minimizing the makespan. A novel harmony search (HS) algorithm with dynamic subpopulations is proposed to tackle this problem. First, an encoding scheme based on random key representation and list schedule rule is developed, which constructs a mapping scheme between the real-valued harmony vectors and job assignments. Second, the whole harmony memory is divided into many small-sized subpopulations. Each subpopulation performs evolution independently and exchanges information with the other subpopulations periodically by using a regrouping schedule. Moreover, a novel improvisation process is applied to generate new harmonies by making use of the information of the local best harmony in each subpopulation. Simulation results demonstrate that the proposed HS algorithm is more effective when compared with the other two heuristics.