. In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algorithm on a suite of test problems and observe that the algorithm performs particularly well when termination is based on a budget of function evaluations. Key words. DIRECT, local clustering, local bias 1. Introduction. The DIRECT (DIviding RECTangles) algorithm [13, 14] is a pattern search method (in the sense of [17]) that balances local and global search in a attempt to efficiently find a global optimizer. Other deterministic sampling methods, such as implicit filtering [9, 15], MDS [6], Hooke-Jeeves [10], or Nelder-Mead [16], drive an approximate gradient to zero and are not designed for g...

Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.

In this paper, the issue of adapting probabilities for Evolutionary Algorithm (EA) search operators is revisited. A framework is devised for distinguishing between measurements of performance and the interpretation of those measurements for purposes of adaptation. Several examples of measurements and statistical interpretations are provided. Probability value adaptation is tested using an EA with 10 search operators against 10 test problems with results indicating that both the type of measurement and its statistical interpretation play significant roles in EA performance. We also find that selecting operators based on the prevalence of outliers rather than on average performance is able to provide considerable improvements to adaptive methods and soundly outperforms the non-adaptive case.

this report we compare two stochastic algorithms for global optimization, PGSL by Raphael & Smith [7] and global by Csendes [2] with the deterministic algorithm MCS by Huyer & Neumaier [4] on the test set used by Jones et al. [6], which consists of the seven standard test functions from Dixon & Szeg o [3] and two test functions from Yao [8] with the standard box bounds as given in [4]. For simplicity, we refer to this test set as the Jones test set