Spent potliner treatment process optimization using a MADS algorithm

Audet, Charles; Béchard, Vincent; Chaouki, Jamal

doi:10.1007/s11081-007-9030-2

Cited by 37 publications

(10 citation statements)

References 29 publications

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“…Derivative-free optimization is an area of long history and current rapid growth, fueled by a growing number of applications that range from science problems [4,42,52,143] to medical problems [90,103] to engineering design and facility location problems [2,10,15,48,49,54,57,91,92,98].…”

Section: Introductionmentioning

confidence: 99%

Derivative-free optimization: a review of algorithms and comparison of software implementations

2012

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This paper addresses the solution of bound-constrained optimization problems using algorithms that require only the availability of objective function values but no derivative information. We refer to these algorithms as derivative-free algorithms. Fueled by a growing number of applications in science and engineering, the development of derivativefree optimization algorithms has long been studied, and it has found renewed interest in recent time. Along with many derivative-free algorithms, many software implementations have also appeared. The paper presents a review of derivative-free algorithms, followed by a systematic comparison of 22 related implementations using a test set of 502 problems. The test bed includes convex and nonconvex problems, smooth as well as nonsmooth problems. The algorithms were tested under the same conditions and ranked under several criteria, including their ability to find near-global solutions for nonconvex problems, improve a given starting point, and refine a near-optimal solution. A total of 112,448 problem instances were solved. We find that the ability of all these solvers to obtain good solutions diminishes with increasing problem size. For the problems used in this study, TOMLAB/MULTI-MIN, TOMLAB/GLCCLUSTER, MCS and TOMLAB/LGO are better, on average, than other derivative-free solvers in terms of solution quality within 2,500 function evaluations. These global solvers outperform local solvers even for convex problems. Finally, TOMLAB/OQNLP, NEWUOA, and TOMLAB/MULTIMIN show superior performance in terms of refining a nearoptimal solution.

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Section: Introductionmentioning

confidence: 99%

Derivative-free optimization: a review of algorithms and comparison of software implementations

2012

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“…Compared to the GPS, the MADS is not restricted to a finite number of search directions, and results in a much better local exploration of the space of variables, in particular for the problem with nonlinear constraints (Audet and Dennis Jr 2006). Recently, the MADS has been increasingly used for complex engineering optimization problems, such as chemical processes and fluid structures (Audet et al 2008;Long et al 2014). It should be noted that, other derivative-free local search methods such as Hooke-Jeeves direct search can be selected for hybrid optimization as well.…”

Section: Madsmentioning

confidence: 99%

A Derivative-Free Hybrid Optimization Model for Short-Term Operation of a Multi-Objective Reservoir System Under Uncertainty

Chen

León

Chen

et al. 2018

Water Resour Manage

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Short-term operation of a multi-objective reservoir system under inflow uncertainty has been receiving increasing attention, however, major challenges for the optimization of this system still remain due to the multiple and often conflicting objectives, highly nonlinear constraints and uncertain parameters in which derivative information may not be directly available. Population-based optimization methods do not rely on derivatives while generally have a slow convergence. This study presents a hybrid optimization model for short-term operation of multi-objective reservoirs under uncertainty that is derivative free and has a relatively fast convergence. The model incorporates a local improvement method called Mesh Adaptive Direct Search (MADS) into a population-based method NSGA-II and has no requirement for differentiability, convexity and continuity of the optimization problem. The operation of a multi-objective and multi-reservoir system on the Columbia River under inflow uncertainty is used as a case study. Overall, the hybrid model outperforms optimization models based on either the NSGA-II only or the MADS only. The model is intended for conditions where derivative information of the optimization problem is unavailable, which could have a wide array of applications in water resources systems.

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“…In this seminal paper, Booker et al also applied the Surrogate Management Framework approach to the optimal design of a helicopter rotor blade with thirty-one design variables. More recently, Audet et al [33,34] have provided a generalization of Torczon's pattern search method, which they refer to as Mesh Adaptive Direct Search, and have applied it to optimization of the chemical treatment of discarded potliners to minimize release of toxic waste in the production of aluminum [35]. Mesh Adaptive Direct Search has since been incorporated into the Surrogate Management Framework by Marsden et al in [36].…”

Section: B Trend Optimizationmentioning

confidence: 99%

Fast Generation of Potentials for Self-Assembly of Particles

Toit,

Grubits,

Marsden

et al. 2009

Preprint

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We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce materials with pre-specified structure and properties. We present a heuristic computation-free geometric method, as well as a fast and robust trend optimization method that lead to the formation of high quality honeycomb lattices. The trend optimization method is particularly successful since it is well-suited to efficient optimization of the noisy and expensive objective functions encountered in the self-assembly design problem. We also present anisotropic potentials that robustly lead to the formation of the kagome lattice, a lattice that has not previously been obtained with isotropic potentials.

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Spent potliner treatment process optimization using a MADS algorithm

Cited by 37 publications

References 29 publications

Derivative-free optimization: a review of algorithms and comparison of software implementations

Derivative-free optimization: a review of algorithms and comparison of software implementations

A Derivative-Free Hybrid Optimization Model for Short-Term Operation of a Multi-Objective Reservoir System Under Uncertainty

Fast Generation of Potentials for Self-Assembly of Particles

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