Naval Research Logistics (NRL) · 1996 · 54 citations · 0 references
BusinessDecision SciencesComputational GeometryDesign OptimizationOptimizationBranch And BoundCombinatorial OptimizationGreedy AlgorithmsHeuristic OptimizationInteger ProgrammingOptimization TheoryCovering ProblemsExact AlgorithmsGreedy HeuristicsHeuristic AlgorithmsHeuristic ComputationHeuristicsLagrangian Relaxation
The article develops a robust exact algorithm for the maximal covering problem using dual-based methods and greedy heuristics within a branch‑and‑bound framework. The algorithm employs dual‑based solution techniques and greedy heuristics, is validated on real‑world datasets, and is benchmarked against existing exact methods on large‑scale problems. Testing on randomly generated and real‑world instances demonstrates that the hybrid approach performs well across a wide range of MCP parameters, with Lagrangian relaxation bounding schemes yielding effective exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.
This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual-based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real-world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.