Mattias Ohlsson, Carsten Peterson and Bo Söderberg
An Efficient Mean Field Approach to the Set Covering Problem
European Journal of Operations Research 133, 583-595 (2001)
Abstract:A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate energy minimum is obtained by iterating a set of mean field equations, in combination with annealing. The approach is numerically tested against a set of publicly available test problems with sizes ranging up to 5x10 ^{3} rows
and 10^{6} columns. When comparing the performance with exact results
for sizes where these are available, the approach yields results
within a few percent from the optimal solutions. Comparisons with
other approximate methods also come out well, in particular given the
very low CPU consumption required -- typically a few seconds.
Arbitrary problems can be processed using the algorithm via a public
domain server.
LU TP 98-29 |