David Karney

A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees

Abstract : This paper examines different algorithms for calculating the shortest path from one node to all other nodes in a network. More specifically, we seek to advance the state-of-the-art of computer implementation technology for such algorithms and the problems they solve by examining the effect of innovative computer science list structures and labeling techniques on algorithmic performance. The study shows that the procedures examined indeed exert a powerful influence on solution efficiency, with the identity of the best dependent upon the topology of the network and the range of the arc distance coefficients. The study further discloses that the shortest path algorithm previously documented as the most efficient is dominated for all problem structures by the new methods, which are sometimes an order of magnitude faster. (Author)

Implementation and Computational Study on an In-Core, Out-of-Core Primal Network Code

This paper presents extensive computational experience with a special-purpose primal simplex code using the augmented threaded index method for solving capacitated and uncapacitated transshipment and transportation problems. This code is distinguished from other codes for solving such problems in that not all of the data resides in central memory simultaneously; thus, it is referred to as an in-core, out-of-core code. The major advantages of such a code over an in-core code are 1 it can solve problems that the latter can not solve because of central memory requirements; 2 even for problems that the latter can solve, it requires less central memory, which is critical for fast job processing on multiprogrammed computer systems; and 3 the code can also be used as an in-core code. The design of such codes presents numerous computational difficulties in selecting the best starting and pivot procedures in order to minimize central as well as peripheral processing time. We present computational experience with various pivot, start and capacity buffer procedures, as well as different buffer sizes. Computational results are also provided for different types of network problems, including assignment, transportation, and minimum cost flow problems. These computational results are compared with in-core, out-of-kilter, negative cycle, and primal simplex network codes for problem sizes that these codes could solve.

Past, present and future of large scale transshipment computer codes and applications

Abstract Three generations of computers have elapsed since the first satisfactory method for solving transportation and transshipment problems was devised. During this time many computational advances have taken place in developing computer codes to solve these problems. For example, recent breakthroughs in the solution and human engineering aspects of transshipment problems have made it possible to solve problems in only a few minutes that require many hours of computing time with commercial LP packages. Additionally the computer memory requirements of new methods have enabled the solution of vastly larger problems than previously imagined possible (50,000 equations and 62 million variables). Enhancing the significance of these developments, new ways have been discovered for modelling broad classes of real world problems as transshipment or transshipment-related problems. The primary purpose of this paper is to summarize these events and to do some crystal ball gazing to provide what we believe to be “best estimates” of future trends.

A Study of Alternative Relaxation Approaches for a Manpower Planning Problem

This paper examines a variety of relaxation strategies for zero-one integer programming problems, containing from 54 to 2,683 variables, that arise in manpower planning applications. These strategies are compared by a primal criterion, which emphasizes the ability to obtain high quality feasible solutions. This contrasts with the usual dual criterion for comparing relaxations, which emphasizes objective function bounds obtained from solutions that are generally not feasible. The changed emphasis requires a change in the use of relaxations, which may be viewed from the standpoint of generating trial solutions for heuristic programming or as a fundamental component of branch and bound. Computer tests show that a combined surrogate-Lagrangean strategy is the most effective for the problems examined followed by a pure surrogate relaxation strategy. All other approaches, including generalized Lagrangean relaxation, fared substantially worse, particularly in terms of solution quality.

Shortest path forest with topological ordering: An algorithm description in SDL

This short note presents a formal description of a fast and robust shortest path algorithm. Modeled on an algorithm of Pape (1974), it requires less memory store than most algorithms and at the same time permits arc lengths to range between -[chi] and +[chi]. It is described in a machine processable language called SDL. The note opens with a brief introduction to SDL syntax.

A note on computational studies for solving transportation problems

This note provides a mathematical explanation for the superiority of certain pivot criterion heuristics when using the Row-Column Sum Method to solve transportation problems. In addition, new pivot criteria are developed using this mathematical explanation which are shown to be computationally superior to the previously best pivot criteria.