New Hybrid Optimization Algorithms for Machine Scheduling Problems

• Published in: IEEE transactions on automation science and engineering Vol. 5; no. 2; pp. 337 - 348
• Main Authors: Pan, Y, Shi, L
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.04.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Branch-and-bound; Computation; constraint programming; Dynamic programming; Exact sciences and technology; Experiments; Hardware; hybrid algorithms; Job shop scheduling; Manufacturing; Mathematical models; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Optimization methods; Problem solving; Processor scheduling; Production; Production scheduling; Running; Scheduling; Scheduling algorithm; Scheduling, sequencing; Single machine scheduling; Upper bound; dynamic programming; Branch-and-bound; hybrid algorithms; constraint programming; Branch and bound method; Algorithmics; Dynamic properties; Scheduling; Constrained optimization; Production management; Storage; NP hard problem; Dynamic programming; Single machine; Completion time
• ISSN: 1545-5955; 1558-3783
• DOI: 10.1109/TASE.2007.895005

Dynamic programming, branch-and-bound, and constraint programming are the standard solution principles for finding optimal solutions to machine scheduling problems. We propose a new hybrid optimization framework that integrates all three methodologies. The hybrid framework leads to powerful solution procedures. We demonstrate our approach through the optimal solution of the single-machine total weighted completion time scheduling problem subject to release dates, which is known to be strongly NP-hard. Extensive computational experiments indicate that new hybrid algorithms use orders of magnitude less storage than dynamic programming, and yet can still reap the full benefit of the dynamic programming property inherent to the problem. We are able to solve to optimality all 1900 instances with up to 200 jobs. This more than doubles the size of problems that can be solved optimally by the previous best algorithm running on the latest computing hardware.