DESIGN AND APPLICATIONS OF PARTICLE SWARM OPTIMIZATION

Abstract

in many real world optimization problems it is often desired to determine a global optimal solution rather than a local optimal solution. Determining the global optimal solution of a nonlinear optimization problem is generally more difficult as compared to the problem of determining a local optimal solution. In fact, whereas it is easy to check mathematically whether a local optimal solution has been achieved or not, it is not so in the case of a global optimal solution. However because of the practical necessity the search for the point of global optimum often becomes necessary. Conventional computing paradigms usually face difficulty in dealing with such real world problems. Natural systems have emerged over millennia to solve such problems. They have inspired several natural computing paradigms that can be used where conventional computing techniques perform unsatisfactorily. Particle Swarm Optimization (PSO) is one of the most effective natural computing paradigms with reduced memory requirement, computationally effective and easier to implement, emerged in the last decade. PSO is based on the simulation of the behavior of a group of birds or a school of fish looking for food. The power of the technique is its fairly simple computations and sharing of information within the algorithm as it derives its internal communications from the social behavior of individuals. The individuals, called particles, are flown through the multi-dimensional search space with each particle representing a possible solution to the multidimensional optimization problem. Each solution's fitness is based on a performance function related to the optimization problem being solved. PSO has undergone many changes since its introduction. As researchers have learned about the technique, they have derived new versions, developed new applications, and published theoretical studies of the effects of the various parameters and aspects of the algorithm. This Thesis aims to improve the efficiency and reliability of real and binary versions of Particle Swarm Optimization. The main contribution of this Thesis is the proposal of, three new Particle Swarm Optimization algorithms for determining the global optimal solution of unconstrained and constrained nonlinear continuous optimization problems and one for binary optimization problems. Continuous PSO algorithms are tested on benchmark problems while Binary PSO is tested on Knapsack and Multidimensional Knapsack problems. Continuous PSO algorithms are used to solve two real world nonlinear optimization problems. The first problem is a continuous unconstrained problem which concerns the error minimization for model order reduction of single input single output systems. The second problem is a continuous constrained nonlinear optimization problem related to optimization of directional overcurrent relay times arising in electrical power systems. ii