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New observations are made about two lower bound schemes for single-machine min-sum scheduling problems. We find that the strongest bound of those provided by transportation problem relaxations can be computed by solving a linear program. We show the equivalence of this strongest bound and the bound provided by the LP relaxation of the time-indexed integer(More)
We recently developed a new randomized optimization framework, the Nested Partitions (NP) method. This approach uses partitioning, random sampling, promising index, and backtracking to create a Markov chain that has global optima as its absorbing states. This new method combines global search and local search (heuristic) procedures in a nature way and it is(More)
We present an efficient search method for job-shop scheduling problems. Our technique is based on an innovative way of relaxing and subsequently reimposing the capacity constraints on some critical operations. We integrate this technique into a fast tabu search algorithm. Our computational results on benchmark problems show that this approach is very(More)
While the process of IMRT planning involves optimization of the dose distribution, the procedure for selecting the beam inputs for this process continues to be largely trial-and-error. We have developed an integer programming (IP) optimization method to optimize beam orientation using mean organ-at-risk (MOD) data from single-beam plans. Two test cases were(More)
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(More)
Coupling beam angle optimization with dose optimization in intensity-modulated radiation therapy (IMRT) increases the size and complexity of an already large-scale combinatorial optimization problem. We have developed a novel algorithm, nested partitions (NP), that is capable of finding suitable beam angle sets by guiding the dose optimization process. NP(More)
Partition-based random search (PRS) provides a class of effective algorithms for global optimization. In each iteration of a PRS algorithm, the solution space is partitioned into subsets which are randomly sampled and evaluated. One subset is then determined to be the promising subset for further partitioning. In this paper, we propose the problem of(More)