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The multiobjective set covering problem (MOSCP), a challenging combinatorial optimization problem, has received limited attention in the literature. This paper presents a heuristic algorithm to approximate the Pareto set of the MOSCP. The proposed algorithm applies a local branching approach on a tree structure and is enhanced with a node exploration strategy specially developed for the MOSCP. The main idea is to partition the search region into smaller subregions based on the neighbors of a reference solution and then to explore each subregion for the Pareto points of the MOSCP. Numerical experiments for instances with two, three and four objectives set covering problems are reported. Results on a performance comparison with benchmark algorithms from the literature are also included and show that the new algorithm is competitive and performs best on some instances. [ABSTRACT FROM AUTHOR]

We consider the class of biobjective mixed integer linear programs (BOMILPs). We review fathoming rules for general BOMILPs and present them in a unified manner. We then propose new fathoming rules that rely on solving specially designed LPs, hence making no assumption on the type of problem and only using polynomial-time algorithms. We describe an enhancement for carrying out these rules by performing a limited number of pivot operations on an LP, and then we provide insight that helps to make these rules even more efficient by either focusing on a smaller number of feasible solutions or by resorting to heuristics that limit the number of LPs solved. [ABSTRACT FROM AUTHOR]