Robust Evolutionary Algorithm Design for Socio-Economic Simulation: Some Comments

Abstract

In the original papers by Alkemade et al. (2006Alkemade et al. ( , 2007, their evolutionary algorithms (EAs) exhibited an extreme degree of premature convergence when they were run according to approach I. This seemed a quite curious result. We are happy that the correction (Alkemade et al. 2008) makes clear that the degree of premature convergence is much lower than originally reported. There are three further comments that we would like to make on the work of Alkemade et al.First, Alkemade et al. state that "convergence behavior differs for different values of the EA parameters such as initial density and chromosome length". We would like to emphasize that the behavior of an EA depends on the initial density parameter only in the short run. In the long run, the initial density parameter has no effect on the behavior of an EA. This is because from a mathematical point of view an EA (or, more precisely, a genetic algorithm) is an ergodic Markov chain (e.g., Nix and Vose 1992; Dawid 1996). In the long run, the state of such a Markov chain no longer depends on the initial state. We agree with Alkemade et al. that the behavior of an EA depends on the chromosome length. This is the case not only in the short run but also in the long run. Since the chromosome length is a technical parameter that usually does not have a clear economic interpretation, we regard the dependence of EA behavior on the chromosome length as a disadvantage of the use of EAs for economic modeling.Second, Alkemade et al. point out that two popular approaches to the use of EAs for economic modeling can yield quite different results. This is a very interesting observation, especially since earlier studies usually simply took one of the two approaches

A mathematical analysis of the long-run behavior of genetic algorithms for social modeling

“…From a modeling point of view, a binary encoding in many cases has the disadvantage that it lacks a clear interpretation (e.g., Dawid 1996). The use of a binary encoding can therefore be difficult to justify and may even lead to artifacts (as shown in Waltman and Van Eck 2009;Waltman et al 2011). Probably for these reasons, some researchers use evolutionary algorithms without a binary encoding (e.g., Haruvy et al 2006;Lux and Schornstein 2005).…”

“…Especially genetic algorithms (GAs) are frequently used. Early work in this stream of research includes (Andreoni and Miller 1995;Arifovic 1994Arifovic , 1996Dawid 1996;Holland and Miller 1991;Marks 1992;Miller 1986), and examples of more recent work are Alkemade et al (2006), Georges (2006, Haruvy et al (2006), Lux and Schornstein (2005), Vriend (2000), Van Eck (2009), andWaltman et al (2011). The other stream of research is more closely related to traditional game theory and is referred to as evolutionary game theory (e.g., Gintis 2000;Maynard Smith 1982;Vega-Redondo 1996;Weibull 1995).…”

Confronting Deep Uncertainties in Risk Analysis

“…Similar to SARSA, this approach can learn optimal or nearly optimal polices for the underlying POMDP, if one exists, even without a model of the process. (14,73) Ongoing extensions and refinements of these ideas-especially, multi-agent (social) learning and evolutionary optimization algorithms, in which the (perhaps fatal) experiences of some agents help to inform the subsequent choices of others (84) -will bring further improvements in ability to solve practical problems. However, the techniques summarized in Table I already suffice to support many valuable applications.…”