Recent Computational Experience with Three Classes of Integer Linear Programs.
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.