Derivative-free methods for mixed-integer nonsmooth constrained optimization

In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative information) and we propose a new derivative-free linesearch-based algorithmic framework to suitably handle those problems. We first describe a scheme for bound constrained problems that combines a dense sequence of directions (to handle the nonsmoothness of the objective function) with primitive directions (to handle discrete variables). Then, we embed an exact penalty approach in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. We analyze the global convergence properties of the proposed algorithms toward stationary points and we report the results of an extensive numerical experience on a set of mixed-integer test problems

Optimal Design of a Hexakis Icosahedron Vacuum Based Lighter than Air Vehicle

Due to the rising cost and scarcity of helium, new methods to ensure buoyancy for lighter-than-air vehicles (LTAVs) are being sought. One alternative under study uses an internal vacuum to reduce the weight to buoyancy ratio. It\u27s a novel approach; however, the vacuum presents challenges for the vehicle\u27s structure. The structure must have minimum mass while preventing buckling and excess stress throughout the frame and membrane. The structure under analysis is a hexakis icosahedron with a membrane covering. Achieving minimum mass involves optimizing the structure under the loading conditions. Finite-element analysis (FEA) and direct-search methods are employed, providing an optimal design under various regimes. Specifically, ABAQUS R is used as a FEA modeler, and mesh-adaptive direct search (MADS) is the optimization procedure. The goal of this research is to reduce the diameter of the vehicle using optimization techniques to a goal size of 31 inches (0.7874 meters). The smallest design to date has a diameter of 20 feet (6.096 meters). This research demonstrates the feasibility of two designs, one at 15 feet (4.572 meters) and another at 4 feet (1.2192 meters). The problem formulation includes multiple black-box objectives and constraints. Results for a number of designs are presented and compared

Pattern search ranking and selection algorithms for mixed variable simulation-based optimization

The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems.Pattern search algorithms Mixed variable programming Nonlinear programming Simulation Ranking and selection

Air Force Institute of Technology Research Report 2009

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics