An Improved Heuristic Algorithm for the special case of the set covering problem

Abstract

The set covering problem is well known as an NP-complete problem. A common heuristic family of algorithms that solves the problem is the Greedy type algorithm. In this study, we have to cover N sites by allocating a minimum number of servers. Each server covers a predefined pattern and, by locating it to a site K, it covers its neighbours according to its pattern. The Improved Heuristic Algorithm (IHA) presented here looks, at each iteration, for the most "problematic" site to be covered and selects the best server that covers it. The study compares the IHA with the Greedy algorithm. The results show that in most cases, for symmetric severs, the IHA finds a better solution (more than 10,000 problems were tested). For big problems of above 600 sites, the probability of finding a better solution is over 80%. However, the computing time of the IHA is much higher than that of the Greedy algorithm. Analyzing some cases where the Greedy algorithm found better solutions than the IHA brought us to the conclusion that the weakness of the IHA resides in the selection part of the minimal server's location. However, we have not yet determined the best solution for these cases.