Recent Computational Experience with Three Classes of Integer Linear Programs.

by A. M. Geoffrion

Purchase

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback9 pages $20.00 $16.00 20% Web Discount

An extension of a previous study (RM-5406) that presented an implicitly enumerative algorithm for integer linear programming that involves the repeated solution of smaller continuous linear programs. The study showed that imbedded linear programming greatly improves a "bare bones" implicit enumeration procedure. The present study presents further computational results of tests to determine how fast the solution time increases with the number of variables. A range of 30-90 variables was investigated for three classes of problems: (1) set covering; (2) optimal routing in networks; and (3) knapsack with several constraints. For classes (1) and (2), solution times increased approximately as the square of the number of variables, bringing similar problems with many hundreds of variables within reach of the present machine code. For class (3), solution times increased approximately as the fourth power of the number of variables, bringing problems on the order of 150 variables within reach. 9 pp. Ref.

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.