Online Performance Measures for Metaheuristic Optimization

Abstract

(Global) optimization is one of the fundamental challenges in scientific computing. Frequently, one encounters objective functions or search space topologies that do not fulfill necessary requirements for well understood and efficient procedures like, e.g., linear programming. This methodological gap is filled by metaheuristic optimization approaches. Their search dynamics in high dimensional search spaces and for complicated objective functions is not well understood at present. In particular, the choice of parameters driving the procedures is a demanding task. In this contribution we show how insight from time series analysis help to investigate – on a pure empirical basis – metaheuristic schemes. Rather than deriving analytical results on convergence behavior, ex ante, we propose online observation of the search and optimization progress. To this end, we use the Detrended Fluctuation Analysis – a method from time series analysis – to investigate the search dynamics of metaheuristics as stochastic processes. We apply the proposed method to two different metaheuristic, namely differential evolution and basin hopping.