On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

Sherali, Hanif D.; Desai, Jitamitra

doi:10.1007/0-387-25570-2_5

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…Several alternative schemes of implementing this concept by replacing the vector x (1) in (9) by higher-order polynomial terms have been proposed by Sherali and Desai (2005), and ongoing investigations exhibit a promise of enhancing the solvability of many challenging problems using this idea.…”

Section: Enhancing Rlt Via Semidefinite Cutsmentioning

confidence: 99%

RLT: A unified approach for discrete and continuous nonconvex optimization

Sherali

2006

Ann Oper Res

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Section: Enhancing Rlt Via Semidefinite Cutsmentioning

confidence: 99%

RLT: A unified approach for discrete and continuous nonconvex optimization

Sherali

2006

Ann Oper Res

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“…For instance, Banerjee and Ierapetritou (2002) use high-dimensional model representations to approximate the black box, Kofler (2007) uses nonlinear covariance models, Pelikan et al (2001) apply Bayesian network models, Driessen et al (2006) optimize a linear model in a trust region. Response surface methodology-based on paradigms such as neural networks, kriging and radial basis functions-has been a popular choice for the optimization of expensive black boxes in chemical engineering (Davis and Ierapetritou, 2007), global optimization (Jones et al, 1998;Regis and Shoemaker, 2005;Sherali and Desai, 2005;Huang et al, 2006;Holmström et al, 2007;Holmström, 2008) and simulation-optimization (Daughety and Turnquist, 1981;Humphrey and Wilson, 2000;Keys and Rees, 2004;Rosen and Harmonosky, 2005;Wang, 2005;Alkhamis and Ahmed, 2006;Barton and Meckesheimer, 2006;Kleijnen, 2008;Angün et al, 2009;Yalçinkaya and Bayhan, 2009).…”

Section: Introductionmentioning

confidence: 98%

The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach

Laguna

Molina

Franco

et al. 2010

Journal of the Operational Research Society

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There is renewed interest in the development of effective and efficient methods for optimizing models of which the optimizer has no structural knowledge. This is what in the literature is referred to as optimization of black boxes. In particular, we address the challenge of optimizing expensive black boxes, that is, those that require a significant computational effort to be evaluated. We describe the use of rough set theory within a scatter search framework, with the goal of identifying high-quality solutions with a limited number of objective function evaluations. The rough set strategies that we developed take advantage of the information provided by the best and diverse solutions found during the search, in order to define areas of the solution space that are promising for search intensification. We test our procedure on a set of 92 nonlinear multimodal functions of varied complexity and size and compare the results with a state-of-the-art procedure based on particle swarm optimization.

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Reformulation‐Linearization Technique for MIPs

Sherali

2011

Wiley Encyclopedia of Operations Research and Management Science

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The reformulation‐linearization technique (RLT) for mixed‐integer programs is an automatic model enhancement approach that generates a hierarchy of relaxations spanning the spectrum from the continuous linear programming (LP) relaxation to the convex hull of feasible solutions. This process is applicable to both 0‐1 as well as general discrete programs, and can be further augmented through the use of classes of semidefinite cuts. Often, the first‐level relaxation itself provides a sufficiently tight model reformulation that significantly improves problem solvability. The RLT procedure also offers a unifying framework for solving continuous nonconvex factorable optimization problems to global optimality.

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On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

Cited by 5 publications

References 41 publications

RLT: A unified approach for discrete and continuous nonconvex optimization

RLT: A unified approach for discrete and continuous nonconvex optimization

The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach

Reformulation‐Linearization Technique for MIPs

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