In-core Code Research Articles

A primary/secondary memory implementation of a forward network simplex algorithm for multiperiod network flow problems

The minimum cost, multiperiod network flow problem is an optimization model that is frequently used to assist decision makers in the areas of resource planning, scheduling and distribution. This model describes network structured decision making problems over time. Important problems in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, economic systems, etc. can be described by this model. Usually, standard network codes are used to solve such problems because of their availability and perceived efficiency. To date, few researchers have considered the multiperiod structure in devising efficient solution methods. The forward network simplex algorithm of Aronson and Chen is one such method. It is a forward algorithm that exploits the natural decomposition of the problem by limiting its pivoting activity to later time periods. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for the multiperiod linear programming problem, some of its specializations and generalizations and a large number of specially structured models. The forward network simplex algorithm solves multiperiod network flow problems efficiently. Encouraging computational results indicate that the forward network simplex implementation is significantly more efficient than standard network optimization codes that do not exploit the multiperiod structure. Even though the forward network simplex method is efficient, there are still limitations to the size of problems that can be solved in-core. In this paper, we discuss a primary/secondary storage implementation of the forward network simplex method and report computational results. This implementation is capable of solving much larger problems than the in-core code and is more efficient than standard codes. Problems having 700 time periods for a total of 3500 nodes and 9095 arcs were solved in less than one third the time of the standard code on which the forward network implementation is based. Furthermore, problems up to about double this size, which the standard code could not solve, were solved by the primary/secondary implementation.

An in-core/out-of-core method for solving large scale assignment problems

We describe how the shortest augmenting path method can be used as basis for a so called “in-core/out-of-core” approach for solving large assignment problems in which the data cannot be kept in central memory of a computer. Here we start by solving the assignment problem on a sparse subgraph and then we introduce the remaining edges in an outpricing/reoptimization phase. We introduce several strategies which enable to keep the working subgraph sparse throughout the procedure and even lead to an all in-core code which is faster than the basic shortest augmenting path code.

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.