In this paper we consider a global optimization problem, where the objective function is supposed to be Lipschitz-continuous with an unknown Lipschitz constant. Based on the recently introduced BIRECT (BIsection of RECTangles) algorithm, a new diagonal partitioning and sampling scheme is introduced. 0ur framework, called BIRECT-V (where V stands for vertices), combines bisection with sampling two points, where in the initial hyper-rectangle, the points are located 1/3 and 1 of the way along the main diagonal. Contrary to most DIRECT-type algorithms, where the evaluation of the objective function at vertices is not suitable for bisection, this strategy combined with bisection provides much more comprehensive information about the objective function. However, newly created sampling points may coincide with old ones at some shared vertices, leading to additional re-evaluations of the objective function, which increases the number of function evaluations per iteration.
To overcome this situation, we suggest a modification of the original optimization domain to obtain a good approximation to the global solution. The experimental investigation shows that this modification has a positive impact on the performance of the BIRECT-V algorithm, and the proposal is a promising global optimization algorithm compared to the original BIRECT and two popular DIRECT-type algorithms on a set of test problems, and performs particularly well for high dimensional problems.
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View Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme