A distributed processing algorithm for solving integer programs using a cluster of workstations

Abstract

The sequential branch and bound algorithm is the most established method for solving mixed integer and discrete programming problems. It is based on the tree search of the possible subproblems of the original problem. There are two goals in carrying out a tree search, namely, (i) finding a good and ultimately the best integer solution, and (ii) to prove that the best solution has been found or no integer feasible solution exists. We call these the stage 1 and stage 2 of tree search. In general it is extremely difficult to choose the ideal search strategy in stage 1 or stage 2 for a given integer programming (IP) problem. On the other hand by investigating a number of different strategies (and hence different search trees) a good solution can be reached quickly in respect of many practical IP problems. Starting from this observation a parallel branch and bound algorithm has been designed which exploits this two stage approach. In the first stage we investigate a number of alternative search trees (forest search) in the hope of finding a good solution quickly. This we call the multiple heuristic search (MHS). In this approach the best integer solution is broadcast to other processors involved in MHS tree development. In the second stage we reorganise the search to investigate branches of a chosen tree in parallel. This two stage algorithm has been implemented on a cluster of SUN workstations using the Parallel Virtual Machine (PVM) harness [12]. The results of our investigation for a range of well known test problems taken from the MIPLIB set and others from the literature are reported here.