Generalized Networks: Parallel Algorithms and an Empirical Analysis

Abstract

The objective of this research was to develop and empirically test new simplex-based parallel algorithms for the generalized network optimization problem. One of these algorithms is essentially a “data parallel” method in which each processor executes identical code on a portion of the data. (However, since the data sets are not necessarily disjoint, “locks” are used to ensure exclusive access.) A second algorithm exhibits “control parallelism,” using different processors to simultaneously execute the different subtasks of the simplex method. “Locks” are not needed in this second approach, but, instead, at the beginning of each pivot, an “audit” of the proposed entering arc is performed in order to ensure correctness of the method. These parallel algorithms were implemented on the Sequent Symmetry multiprocessor, empirically tested on a variety of problems produced by two random problem generators, and compared with two leading state-of-the-art serial codes. Good speedups were obtained relative to the serial codes, and the relative performance of the two parallel methods was found to be dependent on connectedness properties of the optimal solutions of the test problems. The largest test problem, a generalized transportation problem having 30,000 nodes and 1.2 million arcs was optimized in approximately 11 minutes by our parallel code, displaying a speedup of 13 on 15 processors. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.