Genotype–phenotype mapping implications for genetic programming representation: Commentary on “On the mapping of genotype to phenotype in evolutionary algorithms” by Peter A. Whigham, Grant Dick, and James Maclaurin
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Here we comment on the article “On the mapping of genotype to phenotype in evolutionary algorithms,” by Peter A. Whigham, Grant Dick, and James Maclaurin. The article reasons about analogies from molecular biology to evolutionary algorithms and discusses conditions for biological adaptations in the context of grammatical evolution, which provide a useful perspective to GP practitioners. However, the connection of the listed implications for GP is not sufficiently convincing for the reader . Therefore this commentary will (1) examine the proposed principles one by one, challenging the authors to provide more supporting evidence where felt that this was needed, and (2) propose a methodical way to GP practitioners to apply these principles when designing GP representations.
KeywordsGenotype–phenotype mapping Representation Practical guidelines for GP representation design
1 General comments
It is well-known that evolutionary computation can produce near-optimal solutions to a broad range of complex problems. This discussion paper is based around the assumption that the evolutionary search process, since it has been “sucessful” in nature, must itself be an optimal or near-optimal process. This, the authors argue, has been used to justify much work aiming at making evolutionary algorithms more biologically plausible, with the expectation to result in improved performance.
In general, we find the idea of optimality of solutions implying an optimality of process intriguing. Indeed, major scientific discoveries have often resulted from completely unusual processes that may have seemed at first sight unproductive and unlikely to lead to any breakthrough. In the article it is argued that since we know that evolutionary processes (usually) work, or work given sufficient time, this then implies (near-)optimality of the evolutionary process itself. We would like to read further justification for this apparent implication. To substantiate, how this is indeed an assumption made by many researchers in evolutionary computation and drives much of evolutionary computation work, we would like to see evidence and relevant references.
With this said, we agree with the authors that it is very important for evolutionary computation researchers and advocates to be clear about the role of the biological inspiration and evolutionary metaphor in metaheuristic search techniques, and where and how it can help or hinder. Every opportunity should be taken to clarify any potential misconceptions.
separation between genotype and phenotype for optimality;
stable and predictable mapping, where redundancy in behaviour via multiple expressions is possible;
smooth mapping (essentially locality); and
Interestingly, the authors chose grammatical evolution (GE) for illustration. In its aim to provide a generic representation, GE has inherent properties that violate Sterelny’s characteristics of effective genotype–phenotype mappings. Therefore the effectiveness of using both generic representations and generic operators at the same time is being questioned, despite their apparent success in nature. When a generic representation is used, the human effort shifts to the design of the genotype–phenotype mapping rather than the design of the representation or operators. In this case, the implication is that the operators have to be designed with the mapping in mind. Since one of the typical benefits of employing a generic representation is to be able to employ generic operators, is this benefit lost? What then is the implication for the design of artificial evolutionary systems in practice? Is the quest to design generic approaches to automated problem solving doomed to failure?
2 From principles to practical guidelines
Maintaining building blocks: in GP, these could be emerging as automatically defined functions or built into the representation (such as more complex mathematical functions in symbolic regression).
Although somewhat confusing in its statement (when using representation and behaviour, the terms search space and problem space become unclear), this principle advocates the design of genetic operators consciously of their effects in the phenotype space. It is not quite clear how the practitioner, once aware of the said relationship, should take it into account in the design of the genetic operators. We would like to see a concrete example.
Stability under small change follows on from the previous principle and is a somewhat controversial principle here. For GP, locality can be used as a measure of difficulty. Also, in addition to the authors' example, in a generic binary genetic algorithm a small change in the genotype can have rather different effect on the phenotype when the genotpye is mapped onto the phenotype, yet this genetic algorithm itself can be very effective on some problems, with no restrictions on operators necessary. We would like to see an example of how this would be achieved in practice, without limiting evolution such that an acceptable solution become beyond reach.
Modularity has been advocated in programming since the early days.
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