In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions; the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated problem. The FSA method invokes a multi-start diversification scheme in order to achieve an e#cient exploration process.

In this thesis, we study optimal anytime stochastic search algorithms (SSAs) for solving general constrained nonlinear programming problems (NLPs) in discrete, continuous and mixed-integer space. The algorithms are general in the sense that they do not assume di#erentiability or convexity of functions. Based on the search algorithms, we develop the theory of SSAs and propose optimal SSAs with iterative deepening in order to minimize their expected search time. Based on the optimal SSAs, we then develop optimal anytime SSAs that generate improved solutions as more search time is allowed. Our SSAs

In this dissertation, we propose a general approach that can significantly reduce the com-plexity in solving discrete, continuous, and mixed constrained nonlinear optimization (NLP) problems. A key observation we have made is that most application-based NLPs have struc-tured arrangements of constraints. For example, constraints in AI planning are often lo-calized into coherent groups based on their corresponding subgoals. In engineering design problems, such as the design of a power plant, most constraints exhibit a spatial structure based on the layout of the physical components. In optimal control applications, constraints are localized by stages or time. We have developed techniques to exploit these constraint structures by partitioning the constraints into subproblems related by global constraints. Constraint partitioning leads to much relaxed subproblems that are significantly easier to solve. However, there exist global constraints relating multiple subproblems that must be resolved. Previous methods cannot exploit such structures using constraint partitioning because they cannot resolve inconsistent global constraints efficiently.

Center for there assistance and guidance in completing this thesis and dissertation. Each provided a unique point of reference that helped me to improve the presentation of material and general readability. Additionally, I would like to thank Dr. Bryce Roth, Dani Soban, and Elena Garcia for there assistance over the course of this project, and Mr. Brian German for his assistance in assuring that the some of the more esoteric concepts contained within this thesis are understandable.

In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theory and methods are targeted at discrete problems and can be extended to continuous and mixed-integer problems by coding continuous variables using a floating-point representation (discretization). We have characterized the errors incurred due to such discretization and have proved that there exists upper bounds on the errors. Hence, continuous and mixed-integer constrained problems, as well as discrete ones, can be handled by DLM in a unified way with bounded errors.

A general mixed-integer nonlinear programming problem (MINLP) is formulated as follows: where z = (x, y) T ∈ Z; x ∈ Rv and y ∈ D w are, respectively, bounded continuous and discrete variables; f(z) is a lower-bounded objective function; g(z) = (g1(z),…, gr(z)) T is a vector of r inequality constraint functions; 2 and h(z) = (h1(z),…,hm(z)) T is a vector of m equality constraint

The field of information visualization tries to find graphical representations of data to explore regions of interest in potentially large data sets. Additionally, the use of algorithms to obtain exact solutions, which cannot be provided by basic visualization techniques, is a common approach in data analysis. This work focuses on optimization, distance computation and data estimation algorithms in the context of information visualization. Furthermore, information visualization is closely connected to interaction. To involve human abilities in the computation process, the goal is to embed these algorithms into an interactive environment. In an analysis dialog, the user observes the current solution, interprets the results and then formulates a strategy of how to proceed. This forms a tight loop of interaction, which uses human evaluation to improve the quality of the results. Optimization is a crucial approach in decision making. This work presents an interactive optimization approach, exemplified by parallel coordinates, which are