Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Fowler, Kathleen; Reese, Jill P.; Kees, Christopher E.; Dennis, J. E.; Kelley, C. T.; Miller, Cass T.; Audet, Charles; Booker, Andrew J.; Couture, G.; Darwin, R.W.; Farthing, Matthew W.; Finkel, D.; Gablonsky, J. M.; Gray, Genetha Anne.; Kolda, Tamara G.

doi:10.1016/j.advwatres.2008.01.010

Cited by 88 publications

(47 citation statements)

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“…Since the time of that comparison, the number of available derivative-free optimization solvers has more than quadrupled. Other comparisons, such as [11,33,38,48,53,65,67,97,138], are restricted to a few solvers related to the algorithms proposed in these papers. In addition, these comparisons consider small sets of test problems.…”

Section: Introductionmentioning

confidence: 99%

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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 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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“…Moreover, imposing a wider range of hydrological or conjunctive use constraints, e.g., limiting values of hydraulic head at pumping wells near critical features of the domain, should be enforced to better understand the underlying models. Previous work (Fowler et al, 2004(Fowler et al, , 2008 highlighted the influence these types of constraints have on optimization landscapes, leading to non-convexities and discontinuous feasible regions and further supporting the use of evolutionary algorithms as a global search tool.…”

Section: Discussionmentioning

confidence: 99%

“…The result shows small plateaus in the optimization landscapes and large regions with minimal changes in water usage. These properties create local minima that can trap gradient based methods or stencil based methods when a sufficiently small increment is used (Fowler et al, 2004(Fowler et al, , 2008. Fig.…”

Section: Optimization Landscapesmentioning

confidence: 99%

A decision making framework with MODFLOW-FMP2 via optimization: Determining trade-offs in crop selection

Fowler

Jenkins

Ostrove

et al. 2015

Environmental Modelling & Software

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a b s t r a c tFarmers in regions experiencing water stress or drought conditions can struggle to balance their crop portfolios. Periods of low precipitation often lead to increased, unsustainable reliance on groundwatersupplied irrigation. As a result, regional water management agencies place limits on the amount of water which can be obtained from groundwater, requiring farmers to reduce acreage for more water-intensive crops or remove them from the portfolio entirely. Real-time decisions must be made by the farmer to ensure viability of their farming operation and reduce the impacts associated with limited water resources. Evolutionary algorithms, coupled with accurate, flexible, realistic simulation tools, are ideal mechanisms to allow farmers to assess scenarios with regard to multiple, competing objectives. In order to effective, however, one must be able to select among a variety of simulation tools and optimization algorithms. Many simulation tools allow no access to the source code, and many optimization algorithms are now packaged as part of a suite of tools available to a user. In this work, we describe a framework for integrating these different software components using only their associated input and output streams. We analyze our strategy by coupling a multi-objective genetic algorithm available in the DAKOTA optimization suite (developed and distributed by Sandia National Laboratory) with the MODFLOW-FMP2 simulation tool (developed and distributed by the United States Geological Survey). MODFLOW-FMP2 has been used extensively to model hydrological and farming processes in agriculture-dominated regions, allowing us to represent both farming and conservation interests. We evaluate our integration by considering a case study related to planting decisions facing farmers experiencing water stress. We present numerical results for three competing objectives associated with stakeholders in a given region (i.e., profitability, meeting demand targets, and water conservation). The data obtained from the optimization are robust with respect to algorithmic parameter choices, validating the ability of the associated evolutionary algorithm to perform well without expert guidance. This is integral to our approach, as a motivation for this work is providing decision-making tools. In addition, the results from this study demonstrate that output from the chosen evolutionary algorithm provides a suite of feasible planting scenarios, giving farmers and policy makers the ability to compromise solutions based on realistic simulation data.

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“…The second point is interesting in many real-life applications in which a good solution algorithm for a particular problem is sought, e.g., in [10] (all for black box problems). The third point targets general benchmarks of solver software.…”

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The optimization test environment

et al. 2013

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Testing is a crucial part of software development in general, and hence also in mathematical programming. Unfortunately, it is often a time consuming and little exciting activity. This naturally motivated us to increase the eciency in testing solvers for optimization problems and to automatize as much of the procedure as possible.Keywords: test environment, optimization, solver benchmarking, solver comparisonThe testing procedure typically consists of three basic tasks: a) organize test problem sets, also called test libraries; b) solve selected test problems with selected solvers; c) analyze, check and compare the results. The Test Environment is a graphical user interface (GUI) that enables to manage the tasks a) and b) interactively, and task c) automatically.The Test Environment is particularly designed for users who seek to 1. adjust solver parameters, or 2. compare solvers on single problems, or 3. evaluate solvers on suitable test sets.The rst point considers a situation in which the user wants to improve parameters of a particular solver manually, see, e.g., [5]. The second point is interesting in many real-life applications in which a good solution algorithm for a particular problem is sought, e.g., in [10] (all for black box problems). The third point targets general benchmarks of solver software. It often requires a selection of subsets of large test problem sets (based on common characteristics, like similar problem size), and afterwards running all available solvers on these subsets with problem class specic default parameters, e.g., timeout. Finally all tested solvers are compared with respect to some performance measure. In the literature, such comparisons typically exist for black box problems only, see, e.g., [17] for global optimization, or the large online collection [16], mainly for local optimization. Since in many real-life applications models are given as black box functions (e.g., the three examples we mentioned in the last paragraph) it is popular to focus comparisons on this problem class. However, the popularity of modeling languages like AMPL and GAMS, cf.[1], [9], that formulate objectives and constraints algebraically, is increasing. Thus rst steps are made towards comparisons of global solvers using modeling languages, e.g., on the Gamsworld website [11], which oers test sets and tools for comparing solvers with interface to GAMS.One main diculty of solver comparison is to determine a reasonable criterion to measure the performance of a solver. For our comparisons we will count for each solver the number of 2 Ferenc Domes, Martin Fuchs, and Hermann Schichl global solutions found, and the number of wrong and correct claims for the solutions. Here we consider the term global solution as the best solution found among all solvers.A severe showstopper of many current test environments is that it is uncomfortable to use them, i.e., the library and solver management are not very user-friendly, and features like automated L A T E X table creation are missing. Test environments like...

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Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Cited by 88 publications

References 45 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 decision making framework with MODFLOW-FMP2 via optimization: Determining trade-offs in crop selection

The optimization test environment

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