Nested Partitions Method for Global Optimization

Shi, Leyuan; Ólafsson, Sigurđur

doi:10.1287/opre.48.3.390.12436

Cited by 329 publications

(149 citation statements)

References 18 publications

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“…Most known approaches are based on some form of random search, with the added difficulty of having to estimate the cost function at every step. Such algorithms have been recently proposed by Yan and Mukai [12], Gong et al [13], Shi and Olafsson [14]. Another recent contribution to this area involves the ordinal optimization approach presented in [15].…”

Section: Introductionmentioning

confidence: 99%

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Gokbayrak

Cassandras

2001

Journal of Optimization Theory and Applications

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We consider stochastic discrete optimization problems where the decision variables are non-negative integers. We propose and analyze an on-line control scheme which transforms the problem into a "surrogate" continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both actual and surrogate system states. It is shown that the solution of the original problem is recovered as an element of the discrete state neighborhood of the optimal surrogate state. For the special case of separable cost functions, we show that this methodology becomes particularly efficient. Finally, convergence of the proposed algorithm is established under standard technical conditions and numerical results are included in the paper to illustrate the fast convergence properties of this approach.

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Section: Introductionmentioning

confidence: 99%

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Gokbayrak

Cassandras

2001

Journal of Optimization Theory and Applications

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“…genetic algorithms [18]) or set-based (e.g. nested partitions [19]) and can tackle both combinatorial (MH a ) and continuous optimization (MH b ). They were originally developed to address deterministic problems, even though the algorithm itself may be stochastic.…”

Section: Metaheuristics (Mh)mentioning

confidence: 99%

Hybrid simulation–optimization methods: A taxonomy and discussion

Figueira¹,

Almada-Lobo²

2014

Simulation Modelling Practice and Theory

205

104

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The possibilities of combining simulation and optimization are vast and the appropriate design highly depends on the problem characteristics. Therefore, it is very important to have a good overview of the different approaches. The taxonomies and classifications proposed in the literature do not cover the complete range of methods and overlook some important criteria. We provide a taxonomy that aims at giving an overview of the full spectrum of current simulation-optimization approaches. Our study may guide researchers who want to use one of the existing methods, give insights into the cross-fertilization of the ideas applied in those methods and create a standard for a better communication in the scientific community. Future reviews can use the taxonomy here described to classify both general approaches and methods for specific application fields.

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“…Examples of well-known metaheuristics, as an approximate approach, are simulated annealing [10], annealing adaptive search [11], cross entropy [12], genetic algorithms [13] and nested partitions [14]. Moreover, many hybrid approaches that combine both the exact and approximate algorithms have been studied to exploit the benefits of each [15].…”

Section: Introductionmentioning

confidence: 99%

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

Kohn

Zabinsky

2013

Entropy

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Large-scale binary integer programs occur frequently in many real-world applications. For some binary integer problems, finding an optimal solution or even a feasible solution is computationally expensive. In this paper, we develop a discrete meta-control procedure to approximately solve large-scale binary integer programs efficiently. The key idea is to map the vector of n binary decision variables into a scalar function defined over a time interval [0, n] and construct a linear quadratic tracking (LQT) problem that can be solved efficiently. We prove that an LQT formulation has an optimal binary solution, analogous to a classical bang-bang control in continuous time. Our LQT approach can provide advantages in reducing computation while generating a good approximate solution. Numerical examples are presented to demonstrate the usefulness of the proposed method.

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Nested Partitions Method for Global Optimization

Cited by 329 publications

References 18 publications

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Hybrid simulation–optimization methods: A taxonomy and discussion

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

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