Application of Continuous ACOR to Neural Network Training: Direction of Arrival Problem

In this chapter, a hybrid ACOR-based artificial neural network is investigated and applied to solve a Direction of Arrival (DoA) estimation problem. This approach is compared with Radial Basis Function Neural Network (RBFNN) that has been used broadly in the literature for DoA estimation. The Ant Colony Optimization is a stochastic optimization technique that has attracted much attention towards numerous optimization problems during the past decade. ACO is a subset of swarm intelligence methods in which the collective intelligence emerges in decentralized and self-organized systems with simple individuals. Social insects are distributed systems that carry out complex tasks, having individuals with very simple and rudimentary cognitive abilities. In many cases, these tasks exceed the capabilities of a single individual. In fact, social insects are self-organized systems and some simple principles and processes such as stigmergy can explain their social behaviour. Stigmergy is an indirect communication among individuals, in which different entities communicate by modifying the environment. Ants possess very limited visual and vocal perceptive abilities and some types are totally blind. Hence, the only efficient communication channel in these species is various types of chemicals, which are called pheromones. One specific type of pheromone is the trail pheromone that is deposited for instance while searching for food and the other ants smell the pheromone and tend to follow the paths with high pheromone concentration. Therefore, by indirect communication via pheromone and the simple rule of following the higher density of pheromone, one complex colony-level behaviour is emerged which is finding the short paths to the food. This behaviour is quite above the capabilities of each ant. In fact this collective capability emerges out of microscopic simple processes of pheromone laying and pheromone following. Ant colony optimization is an algorithm, which models foraging behaviour of ants to solve optimization problems and it has inspired many researchers to provide solutions to various combinatorial optimization problems such as travelling salesman problem (Dorigo et al., 1996), routing problem (Schoonderwoerd et al., 1997) and many other NP-hard problems in which the values for discrete variables are found to optimize an objective function. In fact ACO, models ant agents walking on a graph that implies typical discrete problems or structures. Since ACO was originally proposed for discrete optimization problems, its application to continuous domain was not straightforward. Among various adaptations of