Boosters: A Derivative-Free Algorithm Based on Radial Basis Functions

Oeuvray, Rodrigue; Bierlaire, Michel

doi:10.1080/02286203.2009.11442507

Cited by 36 publications

(17 citation statements)

References 12 publications

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“…Spline models have also been used, although their use within an SO framework has focused on univariate or bivariate functions, and as Barton and Meckesheimer (2006) mention: "unfortunately, the most popular and effective multivariate spline methods are based on interpolating splines, which have little applicability for SO". Radial basis functions (Oeuvray andBierlaire 2009, Wild et al 2008) and Kriging surrogates (Kleijnen et al 2010, Booker et al 1999) have also been proposed.…”

Section: Literature Reviewmentioning

confidence: 99%

A Simulation-Based Optimization Framework for Urban Transportation Problems

Osorio

Bierlaire

2013

Operations Research

168

112

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This paper proposes a simulation-based optimization (SO) method that enables the efficient use of complex stochastic urban traffic simulators to address various transportation problems. It presents a metamodel that integrates information from a simulator with an analytical queueing network model. The proposed metamodel combines a general-purpose component (a quadratic polynomial), which provides a detailed local approximation, with a physical component (the analytical queueing network model), which provides tractable analytical and global information. This combination leads to an SO framework that is computationally efficient and suitable for complex problems with very tight computational budgets.We integrate this metamodel within a derivative-free trust region algorithm. We evaluate the performance of this method considering a traffic signal control problem for the Swiss city of Lausanne, different demand scenarios and tight computational budgets. The method leads to well-performing signal plans. It leads to reduced, as well as more reliable, average travel times.Key words : Simulation-based optimization, Traffic control, Metamodel, Queueing IntroductionMicroscopic urban traffic simulators embed the most detailed traffic models. They represent individual vehicles and can account for vehicle-specific technologies/attributes. They represent individual travelers and embed detailed disaggregate behavioral models that describe how these travelers make travel decisions (e.g. departure time choice, mode choice, route choice, how travelers respond to real-time traffic information, how they decide to change lanes). They also provide a detailed representation of the underlying 1 Osorio and Bierlaire: A simulation-based optimization framework for urban transportation problems 2 Article submitted to Operations Research; manuscript no. (Please, provide the mansucript number!) supply network (e.g. variable message signs, public transport priorities). Thus, these traffic simulators can describe in detail the interactions between vehicle performance (e.g. instantaneous energy consumption, emissions), traveler behavior and the underlying transportation infrastructure, and yield a detailed description of traffic dynamics in urban networks.These simulators can provide accurate network performance estimates in the context of what-if analysis or sensitivity analysis. They are therefore often used to evaluate a set of predetermined transportation strategies (e.g., traffic management or network design strategies). Nevertheless, using them to derive appropriate strategies, i.e., to perform simulation-based optimization (SO), is an intricate task.We focus on transportation problems of the following form:The objective function f is usually the expected value of a stochastic network performance measure, F . The probability distribution function of F depends on the deterministic decision or control vector x and on deterministic exogenous parameters p. The feasible space Ω consists of a set of general (e.g., nonconvex) constraints that lin...

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Section: Literature Reviewmentioning

confidence: 99%

A Simulation-Based Optimization Framework for Urban Transportation Problems

Osorio

Bierlaire

2013

Operations Research

168

112

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“…As part of his 2005 dissertation, Oeuvray developed a derivative-free trust-region algorithm employing a cubic RBF model with a linear tail. His algorithm, BOOST-ERS, was motivated by problems in the area of medical image registration and was subsequently modified to include gradient information when available [13]. Convergence theory was borrowed from the literature available at the time [4].…”

Section: Rbfs For Optimizationmentioning

confidence: 99%

“…By using this new function value to update the model, an iterative process develops. Over the last ten years, such derivative-free trust-region algorithms have become increasingly popular (see for example [5,13,14,15]). However, they are often tailored to minimize the underlying computational complexity, as in [15], or to yield global convergence, as in [5].…”

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confidence: 99%

“…In developing this new way of managing the set of interpolation points, we have simultaneously generalized the results of Oeuvray and Bierlaire [13] to include a richer set of RBF models and created an algorithm which is particularly efficient in the computationally expensive setting. While we have recently established a global convergence result in [22], the focus of this paper is on implementation details and the success of ORBIT in practice.…”

mentioning

confidence: 99%

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ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

Wild

Regis²,

Shoemaker

2008

SIAM J. Sci. Comput.

206

152

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Abstract. We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow OR-BIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points are sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points. We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also very encouraging and support ORBIT's effectiveness on blackbox functions for which no special mathematical structure is known or available.

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“…The form is that we use the mathematical model coming from the quantitative analysis to get the key, then based on which we make qualitative inference [7,8]. At the same time, according to the relationship structure set mapping which gets from qualitative inference, we establish mathematical model through all kinds of set mapping space hypothesis.…”

Section: B Simulation Model Of Traffic Congestion Degreementioning

confidence: 99%

Analysis Method of Traffic Congestion Degree Based on Spatio-Temporal Simulation

He¹

2012

IJACSA

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Abstract-The purpose of this research is to design and implement a road traffic congestion and traffic patterns simulation (TPS) model and integrate it with extension-information model (EIM). The problems of road traffic simulation and control are studied according to the method of extension information model, and from the spatio-temporal analysis point of view. The rules of the traffic simulation from existence to evolution are analyzed using theories. Based on this study, the concept of traffic system entropy is introduced, and resulted in the establishment of a fundamental frame work for the road traffic simulation system based on extension spatio-temporal information system. Moreover, a practicable methodology is presented.

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Boosters: A Derivative-Free Algorithm Based on Radial Basis Functions

Cited by 36 publications

References 12 publications

A Simulation-Based Optimization Framework for Urban Transportation Problems

A Simulation-Based Optimization Framework for Urban Transportation Problems

ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

Analysis Method of Traffic Congestion Degree Based on Spatio-Temporal Simulation

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