This chapter presents the application of a comprehensive statistical analysis for both algorithmic performance comparison and optimal parameter estimation on a multi-objective digital signal processing problem. The problem of designing optimum digital finite impulse response (FIR) filters with the simultaneous approximation of the filter magnitude and phase is posed as a multi- objective optimization problem. Several computational-intelligence-based algorithms for solving this particular optimization problem are presented: genetic algorithms (GA), particle swarm optimization (PSO) and simulated annealing (SA) with multi-objective scalarization methods. Algorithms with Pareto sampling methods, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective simulated annealing (MOSA) are also applied as a way of dealing with multi-objective optimization. Instead of using a process of trial and error, a statistical exploratory analysis is used to estimate optimal parameters. A comprehensive statistical comparison of the applied algorithms is addressed, which indicates a particularly strong performance of NSGA-II and pure GA with weighting scalarization.
Sequential Approximation Method in Multi-objective Optimization by Using Computational Intelligence
