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New hybrid optimization algorithms for machine scheduling problems
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DOI：10.1109/TASE.2007.895005.png)
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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 A(P-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. Note to Practitioners-In practice, production scheduling is a crucial task at the majority of modern manufacturing firms. It has direct impact on the efficiency of the firms' day-to-day operations. This paper addresses the issue of optimization algorithm design for scheduling problems. With a set of algorithmic building blocks at our disposal, we could form solution procedures that follow standard frameworks, or we could instead obtain more efficient hybrid algorithms that bring about the best of all worlds by reaping the synergy of different frameworks. Our computational results demonstrate unequivocally the power of the latter approach.
Keyword:
branch-and-bound
constraint programming
dynamic programming
hybrid algorithms
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