Particle Swarms in Engineering Design Problems

Abstract

Many modern computational techniques are inspired by biological systems. For example, artificial neural network is a simplified model of the human brain whereas genetic algorithm is inspired by the evolution of living forms. Here we discuss another type of biologically based intelligence system called particle swarm. It is an artificial intelligence technique based on the study of social behaviour in the systems of self-organized population. Such a system is made of a group of simple agents which interact with one another and with their environment. The sum of local interactions results in a global behaviour of the population. Ant colonies, bird flocking and fish schooling can serve as examples of swarm intelligence systems found in nature. Nowadays, the most popular swarm inspired method in computational intelligence area is Particle Swarm Optimization (PSO). PSO shares many similarities with evolutionary computation techniques such as genetic algorithms. The system is initialized with a population of random solutions. Taking into account the best positions of particles at subsequent iteration steps the algorithm searches for optima by updating generations. However, unlike genetic algorithms, PSO has no evolution operators such as crossover and mutation. In PSO, particles being potential solutions fly through the problem space searching for the optimum configuration. In past several years, PSO has been successfully applied in many application areas being the basis of the most commonly used non-gradient based stochastic search algorithms. It is demonstrated that in many cases PSO leads to better results obtained in a faster, less expensive way compared with other methods. Another reason that makes PSO attractive is that there are only few parameters to adjust. Usually one version, with slight modifications, works well in a wide range of applications. In this paper a new improved algorithm based on the Particle Swarm Optimization concept is developed and its application to engineering optimization is presented. Many extensions to the original version of the Particle Swarm method introduced by Kennedy and Eberhart in 1995 are proposed. The amendments regard constraint handling as well as modification of the rules of velocities updating. The two-state version of the algorithm is developed in which two weighting factors are used and their values are selected according to the swarm performance. If a particle moves to a better position a history information is disregarded and the free move in this direction is allowed for - state 1, otherwise the new position is calculated based on the swarm performance history - state 2. This new switching technique allows natural creation of swarm leaders. Their behaviour has then great impact on other swarm members what finally speeds up search process convergence. In classic PSO algorithm velocities are limited by arbitrarily selected values what should be treated as a weakness of the algorithm. For example, if many local optima exist and the distance between them is larger than move limits imposed, finding global optimum among them may be even impossible. Here more flexible approach to limiting velocities values is proposed. The algorithm starts with large kinetic energy of particles, which is then limited while exploring search space. As for engineering optimization the implementation of mixed integer/continuous design variables is discussed in detail, and the effective application technique is proposed. The paper is illustrated by numerical results of selected engineering design problems.