Relaxation heuristics for the set multicover problem with generalized upper bound constraints
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We consider an extension of the set covering problem (SCP) introducing (i) multicover and (ii) generalized upper bound (GUB) constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and several efficient heuristic algorithms based on such reduction techniques have been developed to solve large-scale instances. However, GUB constraints often make the pricing method less effective, because they often prevent solutions from containing highly evaluated variables together. To overcome this, we develop heuristic algorithms to reduce the size of instances, in which new evaluation schemes of variables are introduced taking account of GUB constraints. We also develop an efficient implementation of a 2-flip neighborhood local search algorithm that reduces the number of candidates in the neighborhood without sacrificing the solution quality. According to computational comparison on benchmark instances with the recent solvers, the proposed algorithm performs quite effectively for instances having large gaps between lower and upper bounds.
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