3 research outputs found
GNBG: A Generalized and Configurable Benchmark Generator for Continuous Numerical Optimization
As optimization challenges continue to evolve, so too must our tools and
understanding. To effectively assess, validate, and compare optimization
algorithms, it is crucial to use a benchmark test suite that encompasses a
diverse range of problem instances with various characteristics. Traditional
benchmark suites often consist of numerous fixed test functions, making it
challenging to align these with specific research objectives, such as the
systematic evaluation of algorithms under controllable conditions. This paper
introduces the Generalized Numerical Benchmark Generator (GNBG) for
single-objective, box-constrained, continuous numerical optimization. Unlike
existing approaches that rely on multiple baseline functions and
transformations, GNBG utilizes a single, parametric, and configurable baseline
function. This design allows for control over various problem characteristics.
Researchers using GNBG can generate instances that cover a broad array of
morphological features, from unimodal to highly multimodal functions, various
local optima patterns, and symmetric to highly asymmetric structures. The
generated problems can also vary in separability, variable interaction
structures, dimensionality, conditioning, and basin shapes. These customizable
features enable the systematic evaluation and comparison of optimization
algorithms, allowing researchers to probe their strengths and weaknesses under
diverse and controllable conditions
A robust Gauss-Newton algorithm for the optimization of hydrological models: benchmarking against industry-standard algorithms
Optimization of model parameters is a ubiquitous task in hydrological and environmental modeling. Currently, the environmental modeling community tends to favor evolutionary techniques over classical Newtonâtype methods, in the light of the geometrically problematic features of objective functions, such as multiple optima and general nonsmoothness. The companion paper (Qin et al., 2018, https://doi.org/10.1029/2017WR022488) introduced the robust GaussâNewton (RGN) algorithm, an enhanced version of the standard GaussâNewton algorithm that employs several heuristics to enhance its explorative abilities and perform robustly even for problematic objective functions. This paper focuses on benchmarking the RGN algorithm against three optimization algorithms generally accepted as âbest practiceâ in the hydrological community, namely, the LevenbergâMarquardt algorithm, the shuffled complex evolution (SCE) search (with 2 and 10 complexes), and the dynamically dimensioned search (DDS). The empirical case studies include four conceptual hydrological models and three catchments. Empirical results indicate that, on average, RGN is 2â3 times more efficient than SCE (2 complexes) by achieving comparable robustness at a lower cost, 7â9 times more efficient than SCE (10 complexes) by trading off some speed to more than compensate for a somewhat lower robustness, 5â7 times more efficient than LevenbergâMarquardt by achieving higher robustness at a moderate additional cost, and 12â26 times more efficient than DDS in terms of robustnessâperâfixedâcost. A detailed analysis of performance in terms of reliability and cost is provided. Overall, the RGN algorithm is an attractive option for the calibration of hydrological models, and we recommend further investigation of its benefits for broader types of optimization problems.Youwei Qin, Dmitri Kavetski, George Kuczer
Global optimization using q-gradients
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Previous issue date: 2016Coordenação de Aperfeiçoamento de Pessoal de NĂvel Superior (CAPES)Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq)The q-gradient vector is a generalization of the gradient vector based on the q-derivative. We present two global optimization methods that do not require ordinary derivatives: a q-analog of the Steepest Descent method called the q-G method and a q-analog of the Conjugate Gradient method called the q-CG method. Both q-G and q-CG are reduced to their classical versions when q equals 1. These methods are implemented in such a way that the search process gradually shifts from global in the beginning to almost local search in the end. Moreover, Gaussian perturbations are used in some iterations to guarantee the convergence of the methods to the global minimum in a probabilistic sense. We compare q-G and q-CG with their classical versions and with other methods, including CMA-ES, a variant of Controlled Random Search, and an interior point method that uses finite-difference derivatives, on 27 well-known test problems. In general, the q-G and q-CG methods are very promising and competitive, especially when applied to multimodal problems. (C) 2016 Elsevier B.V. All rights reserved.[Gouvea, Erica J. C.; Soterroni, Aline C.; Scarabello, Marluce C.; Ramos, Fernando M.] Natl Inst Space Res INPE, Lab Comp & Appl Math, Sao Jose Dos Campos, SP, Brazil[Gouvea, Erica J. C.] Universidade de TaubatĂ© (Unitau), Exact Sci Inst[Regis, Rommel G.] St Josephs Univ, Dept Math, Philadelphia, PA 19131 US