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An efficient heuristic for large set covering problems. (English) Zbl 0534.90064
This paper presents an efficient heuristic algorithm for solving large set covering problems that uses a random selection rule on several criteria in order to build solutions. Unlike other set covering heuristics which use the same criterion throughout the covering process, this new heuristic dynamically changes the selection criteria while building a cover. This algorithm and five heuristics in E. Balas and A. C. Ho [Math. Program. Study 12, 37-60 (1980; Zbl 0435.90074)] were used to solve 30 large randomly generated set covering problems. The best solution generated by the five heuristics was never better than the authors’ algorithm and, in fact, this algorithm was strictly better for 50% of the problems. When the solutions for the first 15 problems were compared to the optimum, this algorithm obtained the optimum for 13 of the 15 problems, whereas, the best solution of five heuristics was optimal for only 7 of the 15 problems.

MSC:
90C10 Integer programming
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
65K05 Numerical mathematical programming methods
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