What is Multidimensional Optimization

This chapter presents a mutation-based particle swarm optimization (PSO) approach for designing a linear phase digital low pass FIR filter (LPF). Since conventional gradient-based methods are susceptible to being trapped in local optima, the stochastic search methods have proven to be effective in a multi-dimensional non-linear environment. In this chapter, LPF with 20 coefficients has been designed. Since filter design is a multidimensional optimization problem, the concept of mutation helps in maintaining diversity in the swarm population and thereby efficiently controlling the local search and convergence to the global optimum solution. Given the filter specifications to be realized, the Mutation PSO (MPSO) tries to meet the ideal frequency response characteristics by generating an optimal set of filter coefficients. The simulation results have been compared with basic PSO and state of artworks on filter design. The results justify that the proposed technique outperforms not only in convergence speed but also in the quality of the solution obtained.