Using the bees algorithm with Kalman filtering to train an artificial neural network for pattern classification D T Pham* { and A Haj Darwish Manufacturing Engineering Centre, Cardiff University, Cardiff, UK The manuscript was received on 29 January 2010 and was accepted after revision for publication on 8 July 2010. DOI: 10.1243/09596518JSCE1004 Abstract: The current paper presents the use of the bees algorithm with Kalman filtering to train a radial basis function (RBF) neural network. An enhanced fuzzy selection system has been developed to choose local search sites depending on the error and training accuracy of the RBF network. The paper provides comparative results obtained when applying RBF neural clas- sifiers trained using the new bees algorithm, the original bees algorithm, and the conventional RBF procedure to an industrial pattern classification problem. Keywords: bees algorithm, fuzzy logic, Kalman filter, neural network, pattern classification 1 INTRODUCTION An artificial neural network (ANN) is a mathematical model of a biological nervous system. The model usu- ally comprises a large number of units or nodes called neurons. In the most common types of ANN, these neurons are arranged into layers and connected to- gether by adjustable weights to give the ANN the ability to learn. Deciding appropriate values for the weights of a neural network is a key task in the implementation of neural systems. This task can be solved using optimization methods such as the genetic algorithm [1], simulated annealing [2], and the bees algorithm [3]. The latter is an efficient optimization procedure inspired by the food-foraging behaviour of honeybees, which are known to adopt a judicious combination of global exploration and local exploitation to arrive at the best food source [4]. The current paper presents an enhancement to the original bees algorithm which involves combining it with Kalman filtering [5] and using the enhanced algorithm to adapt connection weights in a radial basis function (RBF) neural network. The purpose of adding Kalman filtering to the bees algorithm is to speed up its convergence. An application of the enhanced bees algorithm to train an RBF network for an industrial pattern classification problem, the automated visual identification of wood defects, is used to demonstrate the effectiveness of the enhanced algorithm compared with the original bees algorithm and the conventional RBF training procedure. The paper is organized as follows. Section 2 reviews the bees algorithm and Kalman filtering. Section 3 describes the enhanced bees algorithm. Section 4 presents the results obtained by the enhanced algo- rithm and compares them with those obtained using the original algorithm as well as the conventional RBF procedure. Section 5 concludes the paper. 2 THE BEES ALGORITHM AND KALMAN FILTERING 2.1 The bees algorithm The bees algorithm is a swarm-based optimization procedure which mimics the natural foraging beha- viour of honeybees to locate optima in complex search spaces. The algorithm employs a combina- tion of global exploratory and local exploitative search techniques. In the original algorithm, the global exploration and local exploitation both im- plement random search. For the global search, ‘scout bees’ are sent randomly to different parts of the search space to look for potential solutions. For *Corresponding author: Manufacturing Engineering Centre, Cardiff University, Queen’s Building, Newport Road, PO Box 925, Cardiff CF24 3AA, UK. email: phamdt@Cardiff.ac.uk { DT Plam is also a Visiting Professor of King Saud University (KSU) in Riyadh, Saudi Arabia. SPECIAL ISSUE PAPER 885 JSCE1004 Proc. IMechE Vol. 224 Part I: J. Systems and Control Engineering