Solving the maximal covering location problem with heuristic concentration

The metaheuristic heuristic concentration (HC) is applied here to the solution of large instances of the maximal covering location problem with high percentage coverage. In these instances, exact methods may be too cumbersome for practical use, and heuristics can allow faster solution times with near-optimal results. We examined the performance of HC based on its ability to approach the optimal solutions to these problems and the run times of the algorithm compared to LP-IP runtimes. Exact solutions, generated by linear programming and branch and bound, provided a benchmark for comparison when the LP-IP problems could be run to completion. In all cases, HC found solutions with objective values no worse than 0.543% below the best known LP-IP objective value. In several instances, LP-IP runtime ballooned to as much as 38.5 h, while HC took no longer than 1.6 h in any instance. In one particular instance, LP-IP took 38.5 h to terminate, while HC found a near-optimal solution (within 0.306% of optimality) in only 25 min. Furthermore, in 62.5% of the runs, the second stage of HC improved on the first stage 1-opt algorithm.