Hybrid Black Hole Algorithm for Bi-Criteria Job Scheduling on Parallel Machines

Nature-inspired algorithms are recently being appreciated for solving complex optimization and engineering problems. Black hole algorithm is one of the recent nature-inspired algorithms that have obtained inspiration from black hole theory of universe. In this paper, four formulations of multi-objective black hole algorithm have been developed by using combination of weighted objectives, use of secondary storage for managing possible solutions and use of Genetic Algorithm (GA). These formulations are further applied for scheduling jobs on parallel machines while optimizing bi-criteria namely maximum tardiness and weighted flow time. It has been empirically verified that GA based multi-objective Black Hole algorithms leads to better results as compared to their counterparts. Also the use of combination of secondary storage and GA further improves the resulting job sequence. The proposed algorithms are further compared to some of the existing algorithms, and empirically found to be better. The results have been validated by numerical illustrations and statistical tests. Index Terms—Auxiliary archive, Black Hole algorithm, Genetic algorithm, Job scheduling, Nature-inspired algorithm, Tardiness, Weighted flow time.

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