Zero-one Integer Programming Problem Research Articles

Analogue computer solution of certain zero-one integer programming problems

This article investigates the possibilities of solving certain zero-one integer programming problems on an analogue computer. It is shown that. Excepting the cases where the variables with equal weights in the objective function are constrained with each other. The gradient search technique with suitable modifications yields unique and straightforward solutions for set covering set partitioning and weighted matching problems. Experimental results are presented and discussed to illustrate the concepts involved.

An implicit enumeration program for zero-one integer programming

This paper describes some techniques to improve the speed of the implicit enumeration method for solving zero-one integer programming problems. Among these techniques, the most powerful is the one of using a column vector which works as a tag for each inequality, indicating whether or not the inequality should be checked for the current partial solution. A new condition for underlining a variable and the concept of pseudo-underlining are also proposed. These techniques were implemented in the computer programil lip (ILLinois Integer Programming code). The computational results for different types of problems are discussed.

On the Establishment of Standards for Comparing Algorithm Performance

One of the most frustrating tasks encountered by the OR practitioner is that of attempting to select an existing algorithm for application to an immediate real world problem. For purposes of illustration only, consider the OR analyst who is faced with having to solve a large zero-one integer programming problem. Being a member of ORSA, TIMS, SIAM, and other organizations, he realizes that a considerable number of publications have been addressed to this topic and thus he might be able to use one of these to solve the problem at hand. This is sometimes his first mistake. Let us assume that he has surveyed the literature and found “n” publications presenting algorithms which deal directly with his particular problem. At this point in his search he will begin to discover that the mere existence of pertinent algorithms in the literature is not nearly sufficient.

Capital Budgeting and Mixed Zero-One Integer Programming

Abstract The capital budgeting problem for a firm deals with the allocation of limited amounts of capital among a specified set of investment opportunities. In this article, we assume the investment opportunities are indivisible in nature and that the firm desires to make this allocation in such a way as to maximize the discounted sum of dividends paid to its shareholders. From a mathematical programming standpoint, the problem may be classified as a mixed zero-one integer programming problem. Special solution techniques based on Benders's partitioning procedure and Balas's zero-one algorithm are developed for this problem. The solution algorithm may be extended to general mixed-integer programming problems.

On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints

Consider the zero-one integer programming problem P1i:minimize Z = c′x subject to Ax ≦ b, 0 ≦ xi ≦ 1, xj = 0 or 1, j = 1, 2, …, n, where A is an m × n matrix, c′ = (c1, …, cn), x′ = (x1, …, xn), and b is an m × 1 vector with b′ = (b1, …, bm). Assume the elements of A, b, c are all rational. This paper characterizes the feasible solutions of P1, shows that P1 is equivalent to a problem of minimizing a concave quadratic objective function over a convex set, and applies a method developed by Tul to solve such a problem to yield a procedure for the zero-one integer programming problem.