A new modeling and solution approach for the number partitioning problem

Alidaee, Bahram; Glover, Fred; Kochenberger, Gary A.; Rego, César

doi:10.1155/jamds.2005.113

Cited by 17 publications

(10 citation statements)

References 11 publications

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“…As noted in recent papers (see for instance (Alidaee et al, 2005(Alidaee et al, , 2006Kochenberger et al, 2005aKochenberger et al, , 2004aKochenberger et al, ,b, 2005b, the model UQP has proven to function efficiently and effectively as a unified framework for modeling and solving a wide variety of combinatorial optimization problems. In the context of other problem classes, we have solved instances of UQP with more than 50,000 variables, which means we could conceivably solve the nonlinear version of MEWCP for graphs with more than 50,000 nodes.…”

Section: Discussionmentioning

confidence: 99%

Solving the maximum edge weight clique problem via unconstrained quadratic programming

Alidaee

Glover²,

Kochenberger

et al. 2007

European Journal of Operational Research

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The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach.

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Section: Discussionmentioning

confidence: 99%

Solving the maximum edge weight clique problem via unconstrained quadratic programming

Alidaee

Glover²,

Kochenberger

et al. 2007

European Journal of Operational Research

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“…Going beyond the usual approach for number partitioning, Alidaee et al [1] proposed the following criterion:…”

Section: Existing Ad Hoc Criteriamentioning

confidence: 99%

“…Besides, it may be shown that the mean difference cannot exceed ffiffi ffi 2 p times the standard deviation. One might argue that a further measure may be obtained if the pairwise differences are squared rather than taken absolutely (this was done by Alidaee et al [1] with their criterion x 0 ). Unfortunately, such a measure is nothing but twice the variance, as already noted by Cossari et al [4], thus it carries no theoretical value.…”

Section: Criteria Derived From Dispersion Measuresmentioning

confidence: 99%

Minimizing workload balancing criteria on identical parallel machines

Cossari

Paletta

et al. 2013

Journal of Industrial and Production Engineering

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This paper considers the problem of scheduling nonpreemptive jobs on identical parallel processors to minimize workload balancing criteria. While workload balancing is an important practical criterion given the need of production systems to efficiently use all of their resources, there is no established measure of performance in the scheduling literature that characterizes total workload balance. In this paper, the normalized standard deviation, the normalized mean deviation, and the normalized mean difference are proposed as criteria that measure the balance of the workloads among the machines associated to a schedule. A local search algorithm, which performs multiple exchanges of jobs among machines, is presented. The results of a wide computational experimentation demonstrate that the proposed algorithm performs well for all the proposed measures.

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“…Our alternative approach is motivated by the fact that in recent years several papers have reported on the attractiveness of nonlinear alternatives to linear models for certain combinatorial optimization problems (see, for instance, [1,[6][7][8][9][10]). In some cases equivalent unconstrained nonlinear models are constructed by absorbing constraints into the objective function and employing infeasibility penalties instead of imposing the constraints explicitly.…”

Section: Introductionmentioning

confidence: 99%

An effective modeling and solution approach for the generalized independent set problem

Kochenberger

Alidaee

Glover

et al. 2006

Optimization Letters

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The generalized independent set (GIS) problem was first introduced by Hochbaum and Pathria (Forest Sci 43(4), [544][545][546][547][548][549][550][551][552][553][554] 1997) and independently explored in greater detail by Hochbaum (Manage Sci 50(6), 2004). This problem, with applications in forest management and a variety of related areas, is a generalization of the classical maximum independent set problem. In this paper we highlight a natural, nonlinear formulation for the problem that is an attractive alternative to the linear model found in the literature. The effectiveness of this alternative formulation is demonstrated by computational experience on test problems of varying size and density, disclosing a dramatic reduction in the time to obtain optimal and near optimal solutions and an ability to solve much larger problems.

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A new modeling and solution approach for the number partitioning problem

Cited by 17 publications

References 11 publications

Solving the maximum edge weight clique problem via unconstrained quadratic programming

Solving the maximum edge weight clique problem via unconstrained quadratic programming

Minimizing workload balancing criteria on identical parallel machines

An effective modeling and solution approach for the generalized independent set problem

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