A Metaheuristic Approach to Two Dimensional Recursive Digital Filter Design - Advances in Heuristic Signal Processing and Applications - page 166

The most popular design procedures of 2D IIR filters fall under two main cate-
gories [ 4 , 8 , 16 , 18 ]:
- Those based on appropriate transformation of one dimensional (1D) filters [ 14 ,
26 ];
- Those based on appropriate optimization techniques such as linear programming,
Remez exchange algorithm, etc. [ 3 , 10 , 13 , 15 , 23 , 29 ].
However, the majority of these algorithms result in an unstable filter. Although
various methods have been proposed to tackle the instability problem, yet their prac-
tical implementation suffers from a very small stability margin [ 18 ]. The applica-
tions of evolutionary computation techniques to the design of digital IIR filters have
been investigated in [ 4 , 8 , 16 , 18 ]. The results reported in [ 4 , 8 , 16 , 18 ] suggest
that modern search heuristics are more efficient in the filter design problem. In [ 18 ]
and [ 16 ], the authors propose a Neural Network (NN) and Genetic Algorithm (GA)
approach to the recursive filter design. However, the computer language GENET-
ICA [ 8 ] was able to outperform the above mentioned algorithms. Recently Das et
al. [ 4 ] formulated a new variant of Particle Swarm Optimization (MEPSO) for the
purpose. In this chapter, we focus on the application of an improved version of a
recently proposed metaheuristic, namely, Invasive Weed Optimization (IWO).
IWO [ 17 ] is a derivative-free optimization technique that mimics the ecological
behavior of weeds. This metaheuristic algorithm has attracted researchers because
of its reduced computational cost and efficiency in tackling real world optimiza-
tion problems. However, it is not free from the problems of stagnation and pre-
convergence. Here, we attempt to improve the performance of the traditional IWO
algorithm by incorporating a learning strategy in the weed population to efficiently
disperse seeds throughout the problem space during the reproduction phase. Such a
memetic learning technique helps in balancing the exploration and exploitation ca-
pabilities of the weeds which is necessary for providing precise solutions to global
optimization problems.
The concept of Memetic Algorithm (MA) [ 5 ] falls in a broad category of popula-
tion based metaheuristics that incorporate strategies for individual learning. Evolu-
tionary Algorithms (EAs) determine the global optima in a given search landscape
in ways inspired by natural evolution and the Darwinian principles of the struggle
for existence and survival of the fittest. Traditional EAs fail to exploit local infor-
mation and generally become impractical due to excessively large time required to
locate a more or less accurate solution. However, cultural evolution is capable of
local refinement. Thus, MA captures the power of global search by its evolutionary
component and local search by its cultural component, and has successfully outper-
formed conventional EAs in several fields of science and engineering [ 12 , 19 , 20 ].
The earliest research regarding Memetic Algorithms can be traced back to the
work of Moscato [ 19 ]. Our research falls in the domain of Adaptive Memetic Al-
gorithms (AMAs) which involve adaptive selection of memes from the meme pool.
This adaptive selection is controlled by the ability of the meme to perform improve-
ment in fitness value. Several variants of AMAs are found in the literature [ 2 ].
The AMA to be proposed, named Intelligent Invasive Weed Optimization
(IIWO), includes an Invasive Weed Optimization (IWO) algorithm for global search