Heuristic Concentration: A Study of Stage One

Heuristic concentration (HC) is a metaheuristic for the solution of certain combinatorial problems. In stage one, a concentration set (CS), consisting of nodes likely to be in the optimal solution, is developed by multiple runs of an interchange heuristic. In stage two, a good, usually optimal, solution is constructed by selecting the best nodes from the CS. The CS is effective when it is small but comprehensive. Both of these characteristics depend upon: (1) the robustness of the heuristic; (2) the number of times it is run, q; and (3) the number of “best” solutions used to create the CS, m. Stage two is thus totally dependent upon the efficiency of stage one for the improved, and at least potentially optimal, solution. Proper values for the parameters m and q increase the probability of selecting correct elements to construct the optimal solution in stage two and to decrease the work in its identification. After a consideration of the robustness of two alternative interchange heuristics I will concentrate on the appropriate values for the parameters m and q. This is an empirical examination and the p-median problem is used throughout.