James W. Chrissis

Mesh adaptive direct search algorithms for mixed variable optimization

This paper introduces a new derivative-free class of mesh adaptive direct search (MADS) algorithms for solving constrained mixed variable optimization problems, in which the variables may be continuous or categorical. This new class of algorithms, called mixed variable MADS (MV-MADS), generalizes both mixed variable pattern search (MVPS) algorithms for linearly constrained mixed variable problems and MADS algorithms for general constrained problems with only continuous variables. The convergence analysis, which makes use of the Clarke nonsmooth calculus, similarly generalizes the existing theory for both MVPS and MADS algorithms, and reasonable conditions are established for ensuring convergence of a subsequence of iterates to a suitably defined stationary point in the nonsmooth and mixed variable sense.

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.

A Hybrid Algorithm for Solving Polynomial Zero-One Mathematical Programming Problems

Abstract This paper presents an algorithm for solving large-scale polynomial (nonlinear) zero-one programming problems. The procedure incorporates a mixture of pseudo-Boolean concepts and time-proven implicit enumeration procedures. Significant savings in the time required to obtain optimal solutions results from the use of a minimum cover to analyze the future effect of a particular implicit enumeration iteration. Additional improvement is obtained through the use of a term ranking strategy to control the arborization of the implicit enumeration process. Computational experience demonstrates that this algorithm can reduce the magnitude of the computer solution time for large problems from several minutes to a matter of a few seconds.

Optimization of a Scramjet Fuel Injection Array: An Application of Mixed Variable Generalized Pattern Search with Kriging Surrogates

δ Injection angle N Number of injectors Nmax Maximum number of injectors PT Jet total pressure (psia) TT Jet total temperature (R) y1 Axial distance to combustor half-line penetration y2 Axial distance to adjacent plume merge y3 Axial distance to stoichiometric fuel concentration decay d∗ Injector diameter (inches) w Combustor width (inches) fST Stoichiometric fuel-air ratio Subscript i Performance measure number j Mach number

Direct Search Optimization of a Flapping Micro Air Vehicle Wing

This research addresses the optimization of an engineered flapping micro air vehicle wing. The engineered wing was developed using a finite element model of a Manduca Sexta forewing. A full factorial design was used to determine a representative model of the natural system. From this baseline wing, a constrained response surface was coupled with a Latin hypercube of the design space. Results from this provide an initial vector for a mesh adaptive direct search algorithm. Further investigation of the design space was carried out using a blind search approach. Initial results demonstrate significant reduction in mass, while maintaining features which are representative of the biological wing. A test article based on the optimized design will be fabricated and tested.

Considering the isolation set problem

Given a network, G=[N,E] the Isolation Set Problem (ISP) finds the set of arcs, D⊆E, that when removed will separate a predefined set of r distinguished nodes [2]. This involves eliminating connections from a specific set of nodes to the rest of a network. In our increasingly interconnected network-centric world, this might be isolating various units from Headquarters; isolating a portion of a computer network to disrupt communications or to quarantine a virus or some other form of cyber attack; or isolating a cell or sub-group in a terrorist or “dark” network, for example.

Modeling and Analysis of Multicommodity Network Flows via Goal Programming

Abstract In this work goal programming is used to solve a minimum cost multicommodity network flow problem with multiple objectives. The network consists of; linear objective function.linear cost arcs, fixed arc and node capacities, and specific origin-destination pairs for each commodity. This suggests a classic linear program. When properly modeled. Lagrangian relaxation. Daiitzig-Wolfe decomposition, and network flow techniques may be employed lo exploit the pure network structure. Lagrangian relaxation captures the essence of Ihe pure network flow problem as a master problem and sub-problems. The relaxation may be optimized directly, or be decomposed into subproblems, one tor each commodity with eaeh subproblem a minimum cost single commodity network flow problem. Postoptimalily analyses, viasensitivity analysis and parametric analysis, provide a variety of options under which the robustness of the optimal solution may be investigated. This mix of modeling options and analyses provides a powerful approach for producing insight into the modeling of a multicommodity network flow problem with multiple objeetives.