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A novel Hopfield neural network approach for minimizing total weighted tardiness of jobs scheduled on identical machines. (English) Zbl 1311.90120
Summary: This paper explores fast, polynomial time heuristic approximate solutions to the NP-hard problem of scheduling jobs on N identical machines. The jobs are independent and are allowed to be stopped and restarted on another machine at a later time. They have well-defined deadlines, and relative priorities quantified by nonnegative real weights. The objective is to find schedules which minimize the total weighted tardiness of all jobs. We show how this problem can be mapped into quadratic form and present a polynomial time heuristic solution based on the Hopfield neural network approach. It is demonstrated, through the results of extensive numerical simulations, that this solution outperforms other popular heuristic methods. The proposed heuristic is both theoretically and empirically shown to be scalable to large problem sizes (over 100 jobs to be scheduled), which makes it applicable to grid computing scheduling, arising in fields such as computational biology, chemistry and finance.
MSC:
90C27 Combinatorial optimization
90C59 Approximation methods and heuristics in mathematical programming
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90C20 Quadratic programming
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