**3. Methodology**

2 Will-be-set-by-IN-TECH

behavioral phenotypic traits to be used by the quantitative genetics tools. We give some background of other tools used like the diversity measurements and bloat metrics to analyze and correlate the behavior of a GP problem. Three GP benchmark problems are explained in detail exemplifying how to design the phenotypic traits, the quantitative genetics analyses when using these traits in various configurations and evolutionary behaviors deduced from

Prior to the introduction of quantitative genetics to the EC community, research along similar lines was already being conducted. Most notable among these was the discovery that parent-offspring fitness correlation is a good predictor of an algorithm's ability to converge

Mühlenbein and Altenberg began to introduce elements of biology theory to EC at roughly the same time. Mühlenbein's work has focused mainly on adapting the equation for the response to selection (also known as the breeder's equation) for use with evolutionary algorithms [19] Initial work involved the development several improved EAs and reproductive operators [21, 23, 24], and progressed to the development of Estimation of Distribution Algorithms (EDAs)

Altenberg's work used Price's Theorem [27] as a foundation for his EC theory. One of his goals was to measure the ability of certain EA reproductive operators to produce high quality individuals, and identify what qualities were important in achieving this [1]. He referred to this as evolvability, and the equations he developed looked similar in some regards to the response to selection equation. In particular he provided a theoretics foundation for why the relationship between parent and offspring fitness (i.e. heritability of fitness) was important. Another aspect of Altenberg's work involved going beyond a simple aggregation of the relationships between parent and offspring fitness. He focused on the idea that the upper-tail of the distribution was a key element. After all, creating a few offspring that are more fit than their parents can be much more important than creating all offspring with the same fitness as their parents. This is why his equation really became a measure of variance instead of mean, which is what Price's Theorem typically measures. As an indication that his theories were in some sense fundamental to how EAs work, he was able to use them to re-derive the schema

Langdon [14] developed tools based on quantitative genetics for analyzing EA performance. He used both Price's Theorem and Fisher's Fundamental Theorem [26] to model GP gene

Work by Potter et al. [25] also used Price's Theorem as a basis for EA analysis. They also recognized the importance of variance, and developed some approaches to visualizing the

The work of Prügel-Bennett & Shapiro [29] [28] is based on statistical mechanics, but it has some important similarities to the methods used in quantitative genetics. Here, populations are also modeled as probability distributions, but the approach taken is more predictive than diagnostic. This means that detailed information about the fitness landscape and reproductive operators is needed in order to analyze an EA. Still, this approach has some

frequencies, and how they change in the population over time.

distributions during the evolutionary process [5, 6].

these analyses.

[20, 22].

theorem [2].

**2. Related work**

on highly fit solutions [18].
