Modern heuristic techniques for combinatorial problems
Haplotypes and informative SNP selection algorithms: don't block out information
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
A Heuristic Method for the Set Covering Problem
Operations Research
Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization
INFORMS Journal on Computing
Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment
INFORMS Journal on Computing
A greedier approach for finding tag SNPs
Bioinformatics
The Lagrangian Relaxation Method for Solving Integer Programming Problems
Management Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
A probabilistic heuristic for a computationally difficult set covering problem
Operations Research Letters
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The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with path-relinking heuristic for the set k-covering problem, as well as the template of a family of Lagrangean heuristics. The hybrid GRASP Lagrangean heuristic employs the GRASP with path-relinking heuristic using modified costs to obtain approximate solutions for the original problem. Computational experiments carried out on 135 test instances show experimentally that the Lagrangean heuristics performed consistently better than GRASP as well as GRASP with path-relinking. By properly tuning the parameters of the GRASP Lagrangean heuristic, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, the GRASP Lagrangean heuristic makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, when other Lagrangean strategies fail to find new improving solutions.