Incumbent solutions in branch-and-bound algorithms: Setting the record straight

Ragsdale, Cliff T.; Shapiro, Gerald

doi:10.1016/0305-0548(95)00037-2

Cited by 2 publications

(2 citation statements)

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“…symmetry in the problem imposed a significant burden on the solver that could not be alleviated by even incorporating f ≤ f * at the root node of the B&B process. Furthermore, it is observed that enforcing such tight upper bound constraints induced limited computational speed-ups and sometimes had adverse computational effects, which resonates with the findings of Ragsdale and Shapiro (1996; as further echoed by Proll (2007) in the context of the blockmodel problem). Likewise, Table 4 reports the computational performance of DTP ("sym = 5"), DTP-S, and DTP µ -S to which we have appended the constraint f ≤ f * .…”

Section: Models With Bounded Objective Functionssupporting

confidence: 54%

“…For the noise dosage and the wagon load-balancing problems, the formulations COP µ -S and COP-S strongly dominated COP ("sym = 5", f ≤ f * ), which suggests that jointly employing the two symmetry-defeating paradigms (objective perturbations and hierarchical constraints) provides a far more decisive factor in enhancing problem solvability than relying on the CPLEX-enabled symmetrydefeating feature, even when the objective function is subjected to a very tight bound. In fact, imposing such strong upper bound constraints yielded limited computational improvements and often had adverse effects on the solver for the applications we investigated, which echoes the findings of Ragsdale and Shapiro (1996) and Proll (2007).…”

Section: Conclusion and Directions For Future Researchmentioning

confidence: 56%

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Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

Ghoniem¹,

Sherali

2011

IIE Transactions

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This article introduces the concept of defeating symmetry in combinatorial optimization via objective perturbations based on, and combined with, symmetry-defeating constraints. Under this novel reformulation, the original objective function is suitably perturbed using a weighted sum of expressions derived from hierarchical symmetry-defeating constraints in a manner that preserves optimality and judiciously guides and curtails the branch-and-bound enumeration process. Computational results are presented for a noise dosage problem, a doubles tennis scheduling problem, and a wagon load-balancing problem to demonstrate the efficacy of using this strategy in concert with traditional hierarchical symmetry-defeating constraints. The proposed methodology is shown to significantly outperform the use of hierarchical constraints or objective perturbations in isolation, as well as the automatic symmetry-defeating feature that is enabled by CPLEX, version 11.2.

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Section: Models With Bounded Objective Functionssupporting

confidence: 54%

Section: Conclusion and Directions For Future Researchmentioning

confidence: 56%

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

Ghoniem¹,

Sherali

2011

IIE Transactions

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ILP approaches to the blockmodel problem

Proll

2007

European Journal of Operational Research

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Blockmodelling is a method for identifying structural similarities or equivalences between elements which has applications in a variety of contexts, including multiattribute performance assessment. One criterion for forming blocks results in a difficult nonlinear integer programme. We give several integer linear programming formulations of this problem and provide comparative computational results. We show that methods of reducing symmetry proposed by Sherali and Smith are not effective in this case and propose an iterative approach in which the size of the problem is reduced.

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Incumbent solutions in branch-and-bound algorithms: Setting the record straight

Cited by 2 publications

References 3 publications

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

ILP approaches to the blockmodel problem

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