A Survey of Parallel Search Algorithms for Discrete Optimization Problems

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 nding 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. Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling , computer aided design, robotics, game playing and constraint directed reasoning. Formally, a DOP can be stated as follows : Given a nite discrete set X and a function f(x) deened on the elements of X, nd an optimal element x opt , such that, f(x opt) = minff(x)=xxXg. In certain problems, the aim is to nd any member of a solution set S X. These problems can also be easily stated in the above format by making f(x) = 0 for all xxS, and f(x) = 1 for all other elements of X. In most problems of practical interest, the set X is quite large. Consequently, exhaustive enumeration of elements in X to determine x opt is not feasible. Often, elements of X can be viewed as paths in graphs/trees, the cost function can be deened in terms of the cost of the arcs, and the DOP can be formulated in terms of nding a (minimum cost) solution path in the graph from an initial node to a goal node. Branch and bound 85], dynamic programming 14] and heuristic 1