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This paper considers fluid analogues for the standard linear programming problem and for a separable nonlinear programming problem. In the former case the usual duality results are demonstrated using the principle of minimum potential energy. In addition by examining the dynamics of the system a new method, referred to as the R-method, is derived for solving linear programmes, although it is not demonstrated that this has any computational advantages over the standard simplex method, except that degeneracy causes no problems. In the nonlinear case the weak Lagrangian principle is derived. The purpose of the paper is to demonstrate that analogue methods, while being impracticable as a physical method of solving optimisation problems, may give some insight into computational algorithms via dual energy concepts and/or dynamic behaviour. [ABSTRACT FROM AUTHOR]

In a previous article [7] the authors gave the theoretical validation of the sequential unconstrained minimization technique for solving the convex programming problem. The technique is based on an idea proposed by C. W. Carroll [2], [3]. The method has been implemented via an algorithm based on a second-order gradient technique that has proved extremely efficient on a considerable number of test problems of varying complexity. This paper explores the computational aspects of the method. Included are discussions of parameter selection, convergence criteria, and methods of minimizing an unconstrained function. It is shown that the problem variables, on the trajectory of minima of the sequence of unconstrained functions, can be developed as functions of a single parameter. This provides the theoretical basis for an extrapolation technique that significantly accelerates convergence in actual computations. The detailed computer solution of a small example is given to illustrate the typical convergence characteristics of the method. The speed and accuracy of the computational procedure are believed to be competitive with other known techniques for solving the convex programming problem. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for determining suboptimum relative location patterns for physical facilities. It presents a computer program governed by an algorithm which determines how relative location patterns should be altered to obtain sequentially the most improved pattern with each change, commands their alteration, evaluates the results of alterations, and identifies the sub-optimum relative location patterns. The computer output yields a block diagramatic layout of the facility areas, and the areas need not be equal. A manufacturing plant layout example is used because the methodology is well illustrated by reference to some kind of example, and this one is commonly known. The methodology itself, however, is general in nature and not restricted to such applications. [ABSTRACT FROM AUTHOR]

Group theory is used to integrate a wide variety of integer programming methods into a common computational process. Included are group optimization algorithms, Lagrangian methods, the cutting plane method, and the method of surrogate constraints. These methods are controlled by a supervisor which performs four main functions: set-up, directed search, subproblem analysis, and prognosis. Some computational experience is given. One appendix contains an algorithm for dynamically solving unconstrained group problems. A second appendix gives an algorithm for solving zero-one group problems. [ABSTRACT FROM AUTHOR]

Should military cargo be unloaded from ships by lighter or by helicopter? To evaluate various unloading vehicles, a simulation was constructed around a linear programming algorithm. It represented helicopters, lighters, trucks, and the maintenance, stevedoring, and supply units required on shore to support them. The type of helicopter performing best in the simulation was sensitive to the estimate of its productivity. A field test to determine this figure was planned, and data from the simulation was used to determine what mathematical characteristics the test design should have. As finally developed, the test selected was a three-quarter replication of an unblocked, fractional-factorial design employing an analysis of f. The design had to make provision for sudden changes arising during the course of test execution, as it was to be carried out in Vietnam. [ABSTRACT FROM AUTHOR]

A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems. The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class. Procedures to construct certain canonical problems in each equivalence class are described. The relationship of this theory to computational algorithms is discussed. [ABSTRACT FROM AUTHOR]

In this report, twenty-nine integer linear programming problems, ranging from very simple to apparently rather difficult, are introduced. The results of running these problems on four different computer codes, involving five distinct algorithms, are presented as both time and iteration data. A brief description of the codes used is also included. [ABSTRACT FROM AUTHOR]

This article comments on an article about an integer programming code. In the original article, Lawrence E. Briskin discussed the fact that LIP1, an integer programming code, gave a wrong answer. The author of this article gives two rules to describe how to avoid assuming an incorrect answer is right. First, he says not to assume the "optimum solution" is actually the best answer. Second, when an algorithm finds an "optimum solution" and is found by at least three other codes, the probability that this is the optimum solution is at least one half.