Heuristic 0-1 Linear Programming: An Experimental Comparison of Three Methods

This paper examines the performance of three heuristic methods (Senju-Toyoda, Kochen-berger et al. and Hillier) when applied to the 0-1 linear programming problem with nonnegative coefficients. Their effectiveness, measured in terms of computing time, error and relative error, is evaluated on a set of problems from the literature and randomly generated 0-1 test problems with nonnegative coefficients. Analysis of variance and stepwise regressions are employed to study the effect of the number of variables, number of constraints and degree of constraint slackness. The methods exhibited some similarities bui also marked differences in their behavior. Interestingly enough, the larger the number of variables the belter the accuracy of each method. Error differences among the three methods were significant (1:0.8:0.2) yet small (less than 2% on the average) for many practical situations. Hillier's algorithm was the most accurate but much slower and more core demanding than the other two, which makes it difficult or impossible to use for solving large 0-1 problems. Kochenberger's et al. heuristic was the fastest (most accurate) of the three in tightly (loosely) constrained problems. In general the Senju-Toyoda algorithm was the fastest, but least accurate on small and medium size problems. Suggestions are made for selecting the "best" heuristic based on the problem characteristics.