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In statistics, it is common to encounter multi-modal and non-smoothlikelihood (or objective function) maximization problems, where the parametershave known upper and lower bounds. This paper proposes a novel derivative-freeglobal optimization technique that can be used to solve those problems evenwhen the objective function is not known explicitly or its derivatives aredifficult or expensive to obtain. The technique is based on the pattern searchalgorithm, which has been shown to be effective for black-box optimizationproblems. The proposed algorithm works by iteratively generating new solutionsfrom the current solution. The new solutions are generated by making movementsalong the coordinate axes of the constrained sample space. Before making a jumpfrom the current solution to a new solution, the objective function isevaluated at several neighborhood points around the current solution. The bestsolution point is then chosen based on the objective function values at thosepoints. Parallel threading can be used to make the algorithm more scalable. Theperformance of the proposed method is evaluated by optimizing up to5000-dimensional multi-modal benchmark functions. The proposed algorithm isshown to be up to 40 and 368 times faster than genetic algorithm (GA) andsimulated annealing (SA), respectively. The proposed method is also used toestimate the optimal biomarker combination from Alzheimer's disease data bymaximizing the empirical estimates of the area under the receiver operatingcharacteristic curve (AUC), outperforming the contextual popular alternative,known as step-down algorithm.

Black-box optimization on hyper-rectangle using Recursive Modified Pattern Search and application to ROC-based Classification Problem