**1. Introduction**

When evolving executable objects, the primary focus is on the behavioral repertoire that objects exhibit. For an evolutionary algorithm (EA) approach to be effective, a fitness function must be devised that provides differential feedback across evolving objects and provides some sort of fitness gradient to guide an EA in useful directions. It is fairly well understood that needle-in-a-haystack fitness landscapes should be avoided (e.g., was the tasked accomplished or not), but much less well understood as to the alternatives.

One approach takes its cue from animal trainers who achieve complex behaviors via some sort of "shaping" methodology in which simpler behaviors are learned first, and then more complex behaviors are built up from these behavior "building blocks". Similar ideas and approaches show up in the educational literature in the form of "scaffolding" techniques. The main concern with such an approach in EC in general and GP in particular is the heavy dependence on a trainer within the evolutionary loop.

As a consequence most EA/GP approaches attempt to capture this kind of information in a single fitness function with the hope of providing the necessary bias to achieve the desired behavior without any explicit intervention along the way. One attempt to achieve this involves identifying important quantifiable behavior traits and including them in the EA/GP fitness function. If one then proceeds with a standard "blackbox" optimization approach in which behavioral fitness feedback is just a single scalar, there are in general a large number of genotypes (executable objects) that can produce identical fitness values and small changes in executable structures can lead to large changes in behavioral fitness. In general, what is needed is a notion of behavioral inheritance.

We believe that there are existing tools and techniques that have been developed in the field of quantitative genetics that can be used to get at this notion of behavioral inheritability. In this chapter we first give a basic tutorial on the quantitative genetics approach and metrics required to analyze evolutionary dynamics, as the first step in understanding how this can be used for GP analysis. We then discuss some higher level issues for obtaining useful

©2012 Kamath et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2012 Kamath et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Will-be-set-by-IN-TECH 4 Genetic Programming – New Approaches and Successful Applications Using Quantitative Genetics and Phenotypic Traits in Genetic Programming <sup>3</sup>

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 these analyses.

interesting capabilities. For example, up to six higher-order cumulants are used to describe the distributions, allowing it to move beyond assumptions of normality, and thus providing

Using Quantitative Genetics and Phenotypic Traits in Genetic Programming 5

Radcliffe [30] developed a theoretical framework that, while not directly related to quantitative genetics, has certain similarities. His formae theory is a more general extension

Quantitative Genetics theory [9, 31]is concerned with tracking quantitative phenotypic traits within an evolving population in order to analyze the evolutionary process. One group that commonly uses the approach are animal breeders for the purpose of estimating what would be involved in accentuating certain traits (such as size, milk production or pelt color) within

A quantitative trait is essentially any aspect of an individual that can be measured. Since much of the theory was developed before the structure of DNA was known, traits have tended to measure phenotypic qualities like the ones listed in the paragraph above. Traits can measure real values, integer or boolean (threshold) properties, although real valued properties are

This approach offers a potential advantage to EC practitioners. Most EC theory is defined in terms of the underlying representation. As a consequence, it becomes difficult to adapt these theories to new types of problems and representations when they are developed. This generally means that the practitioner must modify or re-derive the theoretical equations before they can apply these theories to a new EA that has been customized for a new problem. For the few theories where this is not the case, a detailed understanding of the problem landscape is typically needed instead. Again this presents problems for the practitioner. After all, if they knew this much about their problem, they would not need an EA to solve it in the first place. Quantitative genetics is one of the few theories that does not suffer from these problems.

Populations are modeled as probability distributions of traits by using simple statistical measures like mean, variance and covariance. A set of equations then describe how the distributions change from one generation to the next as a result of certain evolutionary forces

An extended version of the theory called multivariate quantitative genetics [13] aims to model the behaviors and interactions of multiple traits within the population simultaneously. This approach represents multiple traits as a vector. As a result, means are also represented as a vector, and variance calculations produce covariance matrices, as do cross-covariance calculations. In other words, a vector and a covariance matrix are needed to describe a joint probability distribution. Other than this change, the equations remain largely the same.

It is difficult to do any long term prediction with this theory [11]. Instead, its value lies in its ability to perform analysis after the fact [11]. In other words, for our purposes the theory is most useful for understanding the forces at work inside an existing algorithm during or after

it has been run, rather than predicting how an proposed algorithm might work.

much more accurate descriptions of the actual distributions.

**3. Methodology**

their populations.

generally preferred [9].

like selection and heritability.

**3.1. Quantitative genetics basics**

of the schema theorem, and can be applicable at a phenotypic level.
