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We present an algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem. The novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm. The heuristics are continuous adaptations of the well-known greedy and 3-opt methods that have been applied to a variety of combinatorial optimization problems. Our algorithm has outperformed the current best set covering algorithm of Balas and Ho (1980) by about a factor of 3, and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude.
Fisher et al. (Fri,) studied this question.