Statistical Analysis of Computational Intelligence Algorithms on a Multi-Objective Filter Design Problem

Statistical Analysis of Computational Intelligence Algorithms on a Multi-Objective Filter Design Problem

Flávio Teixeira (University of Victoria, Canada) and Alexandre Ricardo Soares Romariz (University of Brasilia, Brazil)
DOI: 10.4018/978-1-60566-798-0.ch009
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Abstract

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.
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Introduction

This chapter addresses the application of several computational-intelligence-based algorithms for solving a nonlinear multi-objective digital signal processing problem. Also, this work develops multi-objective extensions to existing single-objective statistical exploratory analysis. The developed methodology is primarily intended to obtain an estimate of best parameter values for the adaptive algorithms and also to effectively compare performance. In this regard, a binary quality indicator will be used for comparison of the Pareto front approximations obtained.

The rest of the chapter is organized as follows: in the next section, the digital signal processing problem is described – more specifically, it is a multi-objective optimization problem on digital filter design. Optimization theory to better analyze the problem at hand is subsequently discussed. Following which, the optimization algorithms that will be applied to the signal processing problem are addressed. After that, the statistical exploratory analysis and its extensions to the multi-objective case are developed. The results on the digital signal processing problem are then presented, and finally, the last section presents conclusions about the work.

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