Game Theoretic Multi-Agent Systems Scheduler for Parallel Machines

Abstract

This paper considers the scheduling of n independent jobs on m non-identical machines using the ideas from game theory and multi-agent systems. The values of n and m are fixed at 30 and 6 respectively giving a schedule space with a dimension of approximately 1023 schedules. The agents are used to represent the jobs and they select machines on which the jobs should be processed, resulting into schedules. The schedules that are generated are evaluated using the makespan which is the total time taken for all the jobs to be processed. The makespan of the schedules that are generated vary when the agents that represent the jobs change the way they make their selection decisions. The agent selection policies that are investigated in this paper include pure random choice, potential game strategy and dispersion game strategy. The results that are obtained show that the random choice strategy and the potential game strategy generate the empirical best schedules by chance. The dispersion game strategy however is shown to converge very quickly to a stable schedule type whose best makespan value is between 3.1 to 3.4 times larger than the empirical best schedule. The main contributions in this paper include generating schedules in a concrete schedule space using ideas from game theory and multi-agent systems and the results that are obtained.