Application of Continuous ACOR to Neural Network Training: Direction of Arrival Problem
Hamed Movahedipour · InTech eBooks · 2011
In this chapter, a hybrid ACO R -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 www.intechopen.comAnt Colony Optimization -Methods and Applications 160 ACO algorithm for continuous optimization problems, the approach of Socha tries to avoid conceptual changes to principles of ACO by introducing ACO R algorithm (Socha, 2004;Socha & Blum, 2007;Socha & Dorigo, 2008).Socha's approach to adapt ACO to continuous domain is utilized in this work to optimize the numerical weights of a Multi-Layer Perceptron (MLP) network for interpolation of the nonlinear relation of antenna array outputs and Angle of Arrival (AoA).In other words, ACO R is used to minimize Mean Square Error (MSE) of the output layer of the neural network by adjusting continuous variables of weights during training phase.Direction of arrival estimation has turned out to be a substantial part of many applications like channel characterization, car tracking (Danneville et al., 2005), source localization in radar and sonar (Godara, 2002), receiver algorithm design and co-channel interference reduction (Christodoulou, 2001).Spectral-based algorithmic solutions like Multiple Signal Classification (MUSIC) and parametric methods such as Maximum Likelihood (ML) have been the major methods to tackle DoA problem for a long period.The foremost drawback of these techniques is that they are computationally expensive and do not perform quite efficiently in real time operation.Artificial neural networks have been also utilized to estimate DoA, often using RBF networks due to its acceptable estimation error, capability of inexpensive implementation and fast performance (Zooghby et al., 2000; Titus et al., 1994).In this chapter, after a general introduction to ant colony optimization, ACO R adaptation to continuous domain is explained.ACO R has been applied to train a classifier neural network (Socha & Blum, 2007) and in this work, its application to an interpolator neural network is investigated.The possibilities to enhance the performance of ACO R are studied as well. Ant Colony Optimization Combinatorial OptimizationCombinatorial optimization (CO) problem P = (S,f ) is an optimization problem in which f:S→R + is an objective function that assigns a positive value, called cost to each solution s ∈ S in the finite search space S which encompasses feasible solutions.The goal of this kind of problem is to find a solution in the search space with the lowest cost (Papadimitriou & Steiglitz, 1982).The search space in combinatorial problems includes variables X i , i=1, …, n in discrete domains, therefore combinatorial problems are in fact discrete optimization problems.CO problems are arisen in industry and in applied sciences such as statistics, physics and chemistry.Some instances in industry are manufacturing and distribution, telecommunication network design and routing, airline crew scheduling, etc. Meanwhile this field is connected to various areas of mathematics such as algebra, analysis and continuous optimization, geometry, numerical analysis, topology, graph theory and enumerative combinations (Lee, 2004).Therefore, due to the wide range of important applications of CO problems, various algorithms and methods have been developed to attack them. ACO algorithmACO is an algorithm which finds an approximate optimal solution in a reduced amount of time for NP-hard problems and it was introduced by Dorigo and colleagues (Dorrigo et al., 1991 and1996) in the early 1990's.ACO simulates the foraging behavior of ants, which communicate using pheromone trails and manage to find the shortest path from their nest to feeding source.The significant features of this model are positive feedback, distributed computation and incremental construction of solutions.