Filter-based DIRECT method for constrained global optimization

Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite Manuela da G. P.

doi:10.1007/s10898-017-0596-8

Cited by 17 publications

(20 citation statements)

References 39 publications

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“…To complement the information of the table, Figure 2 presents the performance profile, as proposed in [13], for the four algorithms for solving this set of 26 problems, related to the performance measure |favg − f * |/max(1, |f * |) as suggested in [11]. The plot reports (on the vertical axis) the percentage of problems solved by each algorithm that is within a certain threshold, t, (on the horizontal axis) of the best result.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The filter method uses the concept of dominance, borrowed from multi-objective optimization, to build a filter that accepts iterates if they improve the objective function or improve a constraint violation function based on the Pareto dominance rule. Ever since, an abundance of filter-based approaches have been proposed [4,10,11,14,15,21,31,46,48].…”

Section: Introductionmentioning

confidence: 99%

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Filter-based stochastic algorithm for global optimization

et al. 2020

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We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Filter-based stochastic algorithm for global optimization

et al. 2020

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“…Costa et al [7] introduce a constrained version of DIRECT that also handles constraints via a modification of rectangle selection. Motivated by the filter methodology of Fletcher and Leyffer [16], they identify infeasible rectangles that are non-dominated with respect to the sum of constraint violations and centerpoint function value.…”

Section: Other Extensions Of Directmentioning

confidence: 99%

The DIRECT algorithm: 25 years Later

Jones

Martins

2020

J Glob Optim

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Introduced in 1993, the DIRECT global optimization algorithm provided a fresh approach to minimizing a black-box function subject to lower and upper bounds on the variables. In contrast to the plethora of nature-inspired heuristics, DIRECT was deterministic and had only one hyperparameter (the desired accuracy). Moreover, the algorithm was simple, easy to implement, and usually performed well on low-dimensional problems (up to six variables). Most importantly, DIRECT balanced local and global search (exploitation vs. exploration) in a unique way: in each iteration, several points were sampled, some for global and some for local search. This approach eliminated the need for “tuning parameters” that set the balance between local and global search. However, the very same features that made DIRECT simple and conceptually attractive also created weaknesses. For example, it was commonly observed that, while DIRECT is often fast to find the basin of the global optimum, it can be slow to fine-tune the solution to high accuracy. In this paper, we identify several such weaknesses and survey the work of various researchers to extend DIRECT so that it performs better. All of the extensions show substantial improvement over DIRECT on various test functions. An outstanding challenge is to improve performance robustly across problems of different degrees of difficulty, ranging from simple (unimodal, few variables) to very hard (multimodal, sharply peaked, many variables). Opportunities for further improvement may lie in combining the best features of the different extensions.

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“…An auxiliary function that combines in a special manner information on the objective and constraints is presented in [5]. Other techniques that involve the handling of the objective function and constraints violation separately can be found in [6,7,8]. This paper addresses the exploration of the DIRECT method in order to solve CGO problems.…”

Section: Introductionmentioning

confidence: 99%

Objective and Violation Upper Bounds on a DIRECT-Filter Method for Global Optimization

Costa

Rocha

Fernandes

2020

Lecture Notes in Computer Science

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This paper addresses the problem of solving a constrained global optimization problem using a modification of the DIRECT method that incorporates the filter methodology to simultaneously minimize the objective function and the constraints violation. Thus, in the "Selection" step of the herein proposed DIRECT-filter algorithm, the hyperrectangles are classified in four categories and subsequently handled separately. The new algorithm also imposes upper bounds on the objective function and constraints violation aiming to discard some hyperrectangles from the process of identifying the potentially optimal ones. A heuristic to avoid the exploration of the hyperrectangles that have been mostly divided is also implemented. Preliminary numerical experiments are carried out to show the effectiveness of the imposed upper bounds on the objective and violation as well as the goodness of the heuristic.

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Filter-based DIRECT method for constrained global optimization

Cited by 17 publications

References 39 publications

Filter-based stochastic algorithm for global optimization

Filter-based stochastic algorithm for global optimization

The DIRECT algorithm: 25 years Later

Objective and Violation Upper Bounds on a DIRECT-Filter Method for Global Optimization

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