. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of finding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods such as branch-and-bound and dynamic programming. Availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete optimization problems. This article provides an overview of parallel search algorithms for solving discrete optimization problems.

In discrete optimization problems, we search for an optimal solution among all vectors in a discrete solution space that satisfy a set of constraints, and the search efficiency is of considerable importance since exhaustive search is often impracticable. The method called branch-andbound (noted B&B) is a heuristic tree search algorithm used in this context. Its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found, and the search avoids visiting some subproblems which are known not to contain an optimal solution. Given that disjoint subproblems can be decomposed simultaneously and independently, parallel processing has been widely considered as an additional source of improvement in search efficiency, using the set of processors to concurrently decompose several subproblems at each iteration. Parallel B&B is traditionally considered as an irregular parallel algorithm due to the fact that the structure o...

The goal of this research is to develop a systematic, integrated method of designing efficient search algorithms that solve optimization problems in real time. Search algorithms studied in this thesis comprise meta-control and primitive search. The class of optimization problems addressed are called combinatorial optimization problems, examples of which include many NP-hard scheduling and planning problems, and problems in operations research and artificial-intelligence applications. The problems we have addressed have a well-defined problem objective and a finite set of well-defined problem constraints. In this research, we use state-space trees as problem representations. The approach we have undertaken in designing efficient search algorithms is an engineering approach and consists of two phases: (a) designing generic search algorithms, and (b) improving by genetics-based machine learning methods parametric heuristics used in the search algorithms designed. Our approach is a systematic method that integrates domain knowledge, search techniques, and automated learning techniques for designing better search algorithms. Knowledge captured in designing one search algorithm can be carried over for designing new ones. iv ACKNOWLEDGEMENTS I express my sincere gratitude to all the people who have helped me in the course of my graduate study. My thesis advisor, Professor Benjamin W. Wah, was always available for discussions and encouraged me to explore new ideas. I am deeply grateful to the committee

In this paper we study search heuristics for box decomposition methods that solve problems such as global optimization, minimax optimization, or quantified constraint solving. For this we unify these methods as nested branch-and-bound algorithms, and develop a model that is more convenient for studying heuristics for these algorithms than the traditional models from Artificial Intelligence. We use the result to prove various theorems about heuristics and apply the outcome to the box decomposition methods under consideration. We support the findings with timings for the method of quantified constraint solving developed by the author.

Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of finding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods. Availability of parallel computers has created substantial interest in exploring parallel formulations of these graph and tree search methods. This article provides a survey of various parallel search algorithms such as Backtracking, IDA*, A*, Branch-and-Bound techniques and Dynamic Programming. It addresses issues related to load balancing, communication costs, scalability and the phenomenon of speedup anomalies in parallel search.

In this report, we propose new concurrent data structures and load balancing strategies for Branch-and-Bound (B&B)/A* algorithms in two models of parallel programming : shared and distributed memory. For the shared memory model (SMM), we present a general methodology which allows concurrent manipulations for most tree data structures, and show its usefulness for implementation on multiprocessors with global shared memory. Some priority queues which are suited for basic operations performed by B&B algorithms are described : the Skew-heaps, the funnels and the Splay-trees. We also detail a specific data structure, called treap and designed for A* algorithm. These data structures are implemented on a parallel machine with shared memory : KSR1. For the distributed memory model (DMM), we show that the use of partial cost in the B&B algorithms is not enough to balance nodes between the local queues. Thus, we introduce another notion of priority, called potentiality, between nodes that take...