A Study on the Convergence Properties of Evolution Strategies (ES) with a Case Study on Finding the Global Optimum Solution of the Multi-Pulse Excitation Problem

Authors: Mübeccel DEMİREKLER, Afşar SARANLI

Abstract: In this study, an analysis of the global convergence properties of the Evolution Strategies (ES) class of algorithms is presented. An algorithm (CES) based on Evolution Strategies is considered as a way of findiing the global optimum solution to the Multi-Pulse Excitation problem in speech coding. The algorithm using the elitist strategy is considered as a finite-state Markov chain and ideas from Markov chain analysis are applied to prove its global convergence. Then, based on a detailed analysis of the structure of the extended probability transition matrix, a method of estimating the convergence speed of the CES algorithm is developed under certain smoothness conditions on the cost surface. These results are applied to give numerical values for the Multi-Pulse excitation problem considered. Simulation results on solving the problem on actual speech frames are presented and discussed with respect to the theoretically derived estimates.

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