Node Selection Heuristics Using the Upper Bound in Interval Branch and Bound

International audienceWe present in this article a new strategy for selecting the current node in an interval Branch and Bound algorithm for constrained global optimization. The standard best-first strategy selects the node with the lowest lower bound of the objective estimate. We propose in this article new node selection policies where an upper bound of each node/box is also taken into account. The good accuracy of this upper bound achieved by several operators leads to a good performance of the criterion. These new strategies obtain better experimental results than classical best-first search on difficult instances

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

In Statistics, multi-modal and non-smooth likelihood (or, objective function) maximization problems often arise with known upper and lower bound of the parameters. A novel derivative-free global optimization technique is developed to optimize any black-box function on a hyper-rectangular euclidean space. In literature, pattern search technique has been shown to be a powerful tool for blackbox optimization. The proposed algorithm follows the principle of pattern search technique where new updated solution is obtained from the current solution making movements (within the constrained sample space) along the coordinates. Before making a jump from the current solution point to a new solution point, objective function is evaluated in several neighborhood points around the current solution and the best solution point is chosen based on the objective function values at those points. Parallel threading can be used to make the algorithm more scalable. Performance of the proposed method is evaluated based on optimization of upto 5000 dimensional multi-modal benchmark functions. The proposed algorithm is shown to perform upto 40 and 368 times faster compared to Genetic Algorithm (GA) and Simulated Annealing (SA) respectively. The proposed method is used to estimate the optimal biomarker combination from Alzheimer data by maximizing the empirical estimates of area under ROC curve

Certificates of infeasibility via nonsmooth optimization

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0802