An Efficient Mean Field Approach to the Set Covering Problem

Details An Efficient Mean Field Approach to the Set Covering Problem An Efficient Mean Field Approach to the Set Covering Problem

1999-02-12

arxiv.org/abs/cs/9902025v1

Computer Science

Neural and Evolutionary Computing

17 pages, 2 figures

Scientific paper

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.

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