A comparison of local search algorithms for radio link frequency assignment problems

The frequency assignment problem, known to be NPcomplete, is to find an assignment of radio frequencies to a set of transmitters in a region. The interference level between the frequencies assigned to different communication links has to be acceptable, since otherwise communication will be distorted. Consequently, constraints are defined on pairs of links that limit the choice of frequencies for these pairs. Usually, a fixed number of frequency channels are available with which to make an assignment. The aim is to produce an assignment which minimizes the number of constraint violations. This paper compares the results obtained from using simulated annealing, genetic algorithms and tabu search for determining such an assignment. We report on our computational experiments in terms of the quality of the solutions obtained for realistic, computer-generated problem instances. 1 I N T R O D U C T I O N The radio spectrum is a vital but limited natural resource and the demand for frequencies is outpacing the increase in the usable spectrum. It is therefore vital "Permission to make digital/hard copy of all or part of this material without fee is grained provided that copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery, Inc.(ACM). To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee." © 1996 ACM0-89791-820-7 96 0002 3.50 that the spectrum be managed in the most effective way possible. The management of the spectrum would be eased if frequencies could always be assigned in an optimum or neax-optimum manner, so that some interference measure is at a minimum. However, the assignment of radio frequencies for problems of a practical size remains a considerable challenge. Computing methods based on exact algorithms and graph theory are successful for small problems but out of the question for large problems. Methods based on sequential heuristics [8], which mimic the way the problem might be solved manually, are fast enough for large problems but give results which are well short of the best possible. The main objective is to assign radio frequencies to a number of transmitters subject to a number of constraints, such that minimum interference is suffered. Ideally zero interference is desired, but given the limited region within which the transmitters operate, a more reasonable goal is to minimise the interference for a fixed set of frequencies i.e. a fixed spectrum. The problem is NP-complete [1]. Hence, no known algorithm can generate an optimal solution in a time that can be expressed as a polynomial function of the problem size. The aim of this paper is to implement several local searchalgorithms that have dominated the recent literature, namely, simulated annealing, genetic algorithms and tabu search and to compare the results. Data based on realistic sets of constraints axe used as test problems. 2 F R E Q U E N C Y A S S I G N M E N T We shall consider the problem where radio communi-