DIRECTGO : A New DIRECT -Type MATLAB Toolbox for Derivative-Free Global Optimization

Abstract

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, eleven 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.

Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates

“…To illustrate the effectiveness of PWAS and PWASp in solving the target problems ( 1) and ( 13), we have considered various global optimization benchmarks: a set of standard nonlinear programming problems (NLP) [31] with diverse dimensions (up to 10-D with 11 linear inequality constraints), several integer linear problems (up to 30 integer variables), three unconstrained mixed-variable synthetic benchmarks and two unconstrained mixedvariable real-world benchmarks taken from [19], and two constrained mixed-variable synthetic problems.…”

Experimental Study of Excessive Local Refinement Reduction Techniques for Global Optimization DIRECT-Type Algorithms

“…Since the original algorithm introduction, many researchers have suggested various modifications or extensions of the DIRECT algorithm in various directions. Recent extensive numerical studies [1,16,17] show that DIRECT-type algorithms are often among the most efficient derivative-free global optimization solution techniques. Various hybridized approaches [10,18,19] that are enriched with local search procedures are among the most effective [16,17,20].…”

“…Recent extensive numerical studies [1,16,17] show that DIRECT-type algorithms are often among the most efficient derivative-free global optimization solution techniques. Various hybridized approaches [10,18,19] that are enriched with local search procedures are among the most effective [16,17,20]. However, on average, among traditional (non-hybridized) DIRECT-type algorithms, two-step (global and local) Pareto selection scheme-based approaches, DIRECT-GL [17], 1-DTC-GL [21], often showed the best performance [17].…”

“…Various hybridized approaches [10,18,19] that are enriched with local search procedures are among the most effective [16,17,20]. However, on average, among traditional (non-hybridized) DIRECT-type algorithms, two-step (global and local) Pareto selection scheme-based approaches, DIRECT-GL [17], 1-DTC-GL [21], often showed the best performance [17]. Moreover, for complex multi-modal and non-convex problems, they often outperformed hybrid ones.…”

“…We note that some proposals and studies have already been carried out in the context of the DIRECT algorithm. In [17], we have experimentally investigated a few strategies [7,[23][24][25][26] devoted to preventing the original DIRECT algorithm from selecting tiny hyper-rectangles around current local minima. Moreover, the same study also investigated different strategies for balancing global and local phases [10,18,27,28].…”