A generalization of the popular and widely used Particle Swarm Optimization (PSO) algorithm is presented in this chapter. This novel optimizer, named Generalized PSO (GPSO), is inspired by linear control theory. It enables direct control over the key aspects of particle dynamics during the optimization process, overcoming some typical flaws of classical PSO. The basic idea of this algorithm with its detailed theoretical and empirical analysis is presented, and parameter-tuning schemes are proposed. GPSO is also compared to the classical PSO and Genetic Algorithm (GA) on a set of benchmark problems. The results clearly demonstrate the effectiveness of the proposed algorithm. Finally, two practical engineering applications of the GPSO algorithm are described, in the area of electrical machines fault detection and classification, and in optimal control of water distribution systems.
TopIntroduction
Successful optimizers are often inspired by natural processes and phenomena. The field of global optimization has prospered much from these nature-inspired techniques, such as Genetic Algorithms (GAs) (Michalewitz, 1999), Simulated Annealing (SA) (Kirkpatrick et al, 1983), Ant Colony Optimization (ACO) (Dorigo & Blum, 2005) and others. Among these search strategies, the Particle Swarm Optimization (PSO) algorithm is relatively novel, yet well studied and proven optimizer based on the social behavior of animals moving in large groups (particularly birds) (Kennedy & Eberhart, 1995). PSO uses a set of particles called swarm to investigate the search space, imitating the movement of birds in a flock. The position of each particle is a potential solution, characterized by the value of the optimality criterion. During the search process, particles move through the search space and eventually discover the location(s) which provide the best value of the optimality criterion.
Compared to other evolutionary techniques, PSO has only a few adjustable parameters and it is computationally inexpensive and very easy to implement (Ratnaweera et al, 2004; Schutte & Groenwold, 2005). Thus, it provides high calculation speed, compared to other evolutionary algorithms. However, this algorithm also has some flaws, such as premature convergence tendency and the inability to independently control various aspects of the search - oscillation frequency and the impact of personal and global knowledge.
In this chapter a modification of the original PSO algorithm will be presented, named Generalized Particle Swarm Optimization (GPSO) (Kanović et al, 2011). The idea of this modification is to address PSO in a new and conceptually different fashion, i.e., to consider each particle within the swarm as a second-order linear stochastic system. Such systems are extensively studied in engineering literature. The authors found and explained that the stability and response properties of such a system can be directly related to its performance as an optimizer, i.e., its explorative and exploitative properties.
Based on formal analysis of response properties and stability of the control system, which represents a particle and simulates its dynamics, a new algorithm formulation with a new set of parameters is proposed, which enables more direct and independent control over key aspects of the search process. This way, one can overcome the mentioned inherent flaws of the PSO, keeping at the same time all advantages of the original version of the algorithm, concerning its simplicity, small number of parameters and easy practical implementation.
Using the stability criterions well-known from the control theory, some recommendations for parameter tuning are also proposed, resulting in desired properties of the algorithm, concerning its convergence, exploration and exploitation properties.
Extensive experimental analysis of the proposed algorithm is also presented in this chapter. The algorithm is tested on a set of standard benchmark functions and the results are compared to some earlier versions of the PSO algorithm, including the modification with time-varying coefficients. The obtained results are discussed and some crucial conclusions are emphasized regarding performance of algorithms used in comparison.
This chapter will also present two engineering applications of GPSO algorithm. Firstly, the application of this algorithm in induction motor fault detection and classification procedure based on vibration analysis will be described. GPSO is used in a cross-validation procedure of a Support Vector Machines classifier in order to provide a more reliable and accurate fault detection and classification process. Some of the most common faults are considered, such as damaged bearings, broken rotor bar and static rotor eccentricity. This application is tested and already implemented in real industrial system, demonstrating the potential of GPSO algorithm for practical applications. Secondly, the application in water distribution systems will be presented, where GPSO is used to determine the optimal variable-speed pump control strategy. This solution is implemented as a part of SCADA system of water distribution facility and provides better, more reliable and more efficient water distribution with minimal energy costs.