The impact of knowledge on algorithm performance in discrete optimization

Discrete optimization problems are usually NP hard. When choosing or designing an algorithm for solving a discrete optimization problem domain, if we have some knowledge about the characteristics of that problem domain, such knowledge will help us to make a decision. Thus, it is important to understand the relationship between knowledge about problem domains and algorithm performance. The goal of my research is to explore the impact of knowledge on algorithm performance and how to extract and incorporate knowledge into algorithm, especially during problem solving in a systematic way. ^ To achieve our goal, by restricting knowledge about a problem domain as a distribution of optimal solutions over the solution space, we developed a Directional Tree (DT) model which concurrently describes algorithm behavior and represents knowledge explicitly, and thus provides us with a tool to analyze the impact of knowledge on algorithm performance. We then generalize our DT model to take into account acquisition of problem knowledge during execution. Our generalized directional tree (GDT) model provides a framework for incorporating knowledge obtained online into algorithms, and thus enables us to develop online optimization algorithms that dynamically update their search decisions in response to knowledge obtained so far. Using GDT, we properly developed a structure-based approach which can adapt to problems by incorporating structural knowledge extracted online. More specifically, we used a reinforcement learning system to adaptively learn the structural characteristics of the problem, thereby grouping the decision variables of the problem into several groups. We then develop a structure-based Genetic Algorithm by introducing structural operations to work on these groups and recombine them to search for a better solution. We compared our approach against standard GA by testing on two NP-hard problems, belief revision over Bayesian Networks and the Tactical Fixed Interval Scheduling Problem. From experimental results, we see that for some problems our new online structural approach obtains better results than the standard GA.