作者：
Liuzzi, G.Lucidi, S.Piccialli, V.CNR
Ist Anal Sistemi & Informat A Ruberti Via Taurini 19 I-00185 Rome Italy Univ Roma La Sapienza
Dipartimento Ingn Informat Automat & Gestionale A Via Ariosto 25 I-00185 Rome Italy Univ Roma Tor Vergata
Dipartimento Ingn Civile & Ingn Informat Viale Politecn 1 I-00133 Rome Italy
In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems t...
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In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems the direct algorithm has been proposed which has a good ability to locate promising regions of the feasible domain and convergence properties based on the generation of a dense set of points over the feasible domain. However, the efficiency of direct deteriorates as the dimension and the ill-conditioning of the objective function increase. To overcome these limits, we propose direct-type algorithms enriched by the efficient use of derivative-free local searches combined with nonlinear transformations of the feasible domain and, possibly, of the objective function. We report extensive numerical results both on test problems from the literature and on an application in structural proteomics.
In this work, we introduce directGO, a new MATLAB toolbox for derivative-free global optimization. directGO collects various deterministic derivative-free direct-type algorithms for box-constrained, generally constrai...
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In this work, we introduce directGO, a new MATLAB toolbox for derivative-free global optimization. directGO collects various deterministic derivative-free direct-type algorithms for box-constrained, generally constrained, and problems with hidden constraints. Each sequential algorithm is implemented in two ways: using static and dynamic data structures for more efficient information storage and organization. Furthermore, parallel schemes are applied to some promising algorithms within directGO. The toolbox is equipped with a graphical user interface (GUI), ensuring the user-friendly use of all functionalities available in directGO. Available features are demonstrated in detailed computational studies using a comprehensive directGOLib v1.0 library of global optimization test problems. Additionally, 11 classical engineering design problems illustrate the potential of directGO to solve challenging real-world problems. Finally, the appendix gives examples of accompanying MATLAB programs and provides a synopsis of its use on the test problems with box and general constraints.
In this paper, black-box global optimization problem with expensive function evaluations is considered. This problem is challenging for numerical methods due to the practical limits on computational budget often requi...
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In this paper, black-box global optimization problem with expensive function evaluations is considered. This problem is challenging for numerical methods due to the practical limits on computational budget often required by intelligent systems. For its efficient solution, a new direct-type hybrid technique is proposed. The new algorithm incorporates a novel sampling on diagonals and bisection strategy (instead of a trisection which is commonly used in the existing direct-type algorithms), embedded into the globally-biased framework, and enriched with three different local minimization strategies. The numerical results on a test set of almost 900 problems from the literature and on a real-life application regarding nonlinear regression show that the new approach effectively addresses well-known direct weaknesses, has beneficial effects on the overall performance, and on average, gives significantly better results compared to several direct-type methods widely used in decision-making expert systems. (C) 2019 Elsevier Ltd. All rights reserved.
We consider a global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Our approach is based on the well-known direct (DIviding RECTangles) algorithm and motivated by the diag...
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We consider a global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Our approach is based on the well-known direct (DIviding RECTangles) algorithm and motivated by the diagonal partitioning strategy. One of the main advantages of the diagonal partitioning scheme is that the objective function is evaluated at two points at each hyper-rectangle and, therefore, more comprehensive information about the objective function is considered than using the central sampling strategy used in most direct-type algorithms. In this paper, we introduce a new direct-type algorithm, which we call BIRECT (BIsecting RECTangles). In this algorithm, a bisection is used instead of a trisection which is typical for diagonal-based and direct-type algorithms. The bisection is preferable to the trisection because of the shapes of hyper-rectangles, but usual evaluation of the objective function at the center or at the endpoints of the diagonal are not favorable for bisection. In the proposed algorithm the objective function is evaluated at two points on the diagonal equidistant between themselves and the endpoints of a diagonal. This sampling strategy enables reuse of the sampling points in descendant hyper-rectangles. The developed algorithm gives very competitive numerical results compared to the direct algorithm and its well know modifications.
We consider a box-constrained global optimization problem with a Lipschitz-continuous objective function and an unknown Lipschitz constant. The well known derivative-free global-search direct (DIvide a hyper-RECTangle...
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We consider a box-constrained global optimization problem with a Lipschitz-continuous objective function and an unknown Lipschitz constant. The well known derivative-free global-search direct (DIvide a hyper-RECTangle) algorithm performs well solving such problems. However, the efficiency of the direct algorithm deteriorates on problems with many local optima and when the solution with high accuracy is required. To overcome these difficulties different regimes of global and local search are introduced or the algorithm is combined with local optimization. In this paper we investigate a different direction of improvement of the direct algorithm and propose a new strategy for the selection of potentially optimal rectangles, what does not require any additional parameters or local search subroutines. An extensive experimental investigation reveals the effectiveness of the proposed enhancements.
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