Optimal Anytime Search for Constrained Nonlinear Programming Table of Contents

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 differentiability 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 for solving general constrained NLPs are based on the theory of discrete constrained optimization using Lagrange multipliers that shows the equivalence between the set of constrained local minima (CLMdn) and the set of discrete-neighborhood saddle points (SPdn). To implement this theory, we propose a general procedural framework for locating an SPdn. By incorporating genetic algorithms in the framework, we evaluate new constrained search algorithms: constrained genetic algorithm (CGA) and combined constrained simulated annealing and genetic algorithm (CSAGA). All these algorithms are SSAs. One of the most important and difficult issues in using SSAs is the scheduling of SSAs in order to optimize the average search efficiency. Our research shows that SSAs can be scheduled in such a way that minimizes their expected search time. The theory proposes to use iterative deepening to identify the optimal (up to a constant factor) schedules in such a way that minimizes the expected search time when