Turbulent Particle Swarm Optimization Using Fuzzy Parameter Tuning

Particle Swarm Optimization (PSO) algorithm is a stochastic search technique, which has exhibited good performance across a wide range of applications. However, very often for multi-modal problems involving high dimensions the algorithm tends to suffer from premature convergence. Premature convergence could make the PSO algorithm very difficult to arrive at the global optimum or even a local optimum. Analysis of the behavior of the particle swarm model reveals that such premature convergence is mainly due to the decrease of velocity of particles in the search space that leads to a total implosion and ultimately fitness stagnation of the swarm. This paper introduces Turbulence in the Particle Swarm Optimization (TPSO) algorithm to overcome the problem of stagnation. The algorithm uses a minimum velocity threshold to control the velocity of particles. TPSO mechanism is similar to a turbulence pump, which supplies some power to the swarm system to explore new neighborhoods for better solutions. The algorithm also avoids clustering of particles and at the same time attempts to maintain diversity of population. We attempt to theoretically analyze that the algorithm converges with a probability of 1 towards the global optimal. The parameter, the minimum velocity threshold of the particles is tuned adaptively by a fuzzy logic controller embedded in the TPSO algorithm, which is further called as Fuzzy Adaptive TPSO (FATPSO). We evaluated the performance of FATPSO and compared it with the Standard PSO (SPSO), Genetic Algorithm (GA) and Simulated Annealing (SA). The comparison was performed on a suite of 20 widely used benchmark problems. Empirical results illustrate that the FATPSO could prevent premature convergence very effectively. It clearly outperforms the considered methods, especially for high dimension multi-modal optimization problems.