Tabu Search metaheuristic for
designing digital filters
A. Fanni, M. Marchesi, F. Pilo and A. Serri
Dipartimento di Ingegneria Elettrica ed Elettronica,
Universita’ di Cagliari, Cagliari, Italy
A variety of algorithms exist for the design of digital filters, each suitable for a
particular application. Integer programming methods are used for the design of
FIR digital filters with discrete valued coefficients, when the performance
criterion is the classical min-max (Kodek, 1980; Lawrence and Salazar, 1980;
Lim et al., 1982). These methods require a high computational time, and a large
amount of memory, and their applications are limited to the design of filters
with a low number of coefficients. Alternative optimisation techniques have
been introduced to cope with ill conditioned problems, introducing the concept
In Benvenuto et al. (1992) a simulated annealing (SA) algorithm is applied in
the context of designing Nyquist filters, and cascade form FIR filters. SA
algorithm is not a solution of all design problems, and is computationally very
expensive, but it may be very useful to design special digital filters, where
numerous or conflicting constraints are presented.
A parallel genetic algorithm (GA) is proposed in Xu and Daley (1995) to
design a direct form finite word length FIR low-pass digital filter. It has been
shown that the advantage of using GA with respect to other techniques
decreases as the coefficient word length increases.
Recently, a new metaheuristic, called tabu search (TS), has been introduced
for solving difficult optimisation problems in many domains (Glover, 1993). The
method basically makes use of adaptive memory, in contrast to the memoryless
approaches like SA and GA, or rigid memory approaches like branch and
In TS the process of finding optimal solution consists of applying, at each
step, a subordinate heuristic that must be designed for each particular problem.
It consists in systematically prohibiting some solutions to prevent cycling and,
at the same time, to avoid being trapped in local minima, and deeply explores
the search space in order to minimise the objective function. Some “aspiration
criteria” to allow overriding of tabu status can also be introduced.
In the design of digital filters, the cost function to be minimised is the
maximum weighted ripple in a finite number of normalised frequencies inside
the pass- and stop- band regions, and the optimisation problem can be modelled
as a search problem in a discrete domain. This kind of modelization is well
suited for the TS paradigm.
COMPEL – The International
Journal for Computation and
Mathematics in Electrical and
Vol. 17 No. 5/6, 1998, pp. 789-796.
© MCB University Press, 0332-1649