Edgar Galván-López

Defining locality as a problem difficulty measure in genetic programming

A mapping is local if it preserves neighbourhood. In Evolutionary Computation, locality is generally described as the property that neighbouring genotypes correspond to neighbouring phenotypes. A representation has high locality if most genotypic neighbours are mapped to phenotypic neighbours. Locality is seen as a key element in performing effective evolutionary search. It is believed that a representation that has high locality will perform better in evolutionary search and the contrary is true for a representation that has low locality. When locality was introduced, it was the genotype-phenotype mapping in bitstring-based Genetic Algorithms which was of interest; more recently, it has also been used to study the same mapping in Grammatical Evolution. To our knowledge, there are few explicit studies of locality in Genetic Programming (GP). The goal of this paper is to shed some light on locality in GP and use it as an indicator of problem difficulty. Strictly speaking, in GP the genotype and the phenotype are not distinct. We attempt to extend the standard quantitative definition of genotype-phenotype locality to the genotype-fitness mapping by considering three possible definitions. We consider the effects of these definitions in both continuous- and discrete-valued fitness functions. We compare three different GP representations (two of them induced by using different function sets and the other using a slightly different GP encoding) and six different mutation operators. Results indicate that one definition of locality is better in predicting performance.

An analysis of genotype-phenotype maps in grammatical evolution

We present an analysis of the genotype-phenotype map in Grammatical Evolution (GE). The standard map adopted in GE is a depth-first expansion of the non-terminal symbols during the derivation sequence. Earlier studies have indicated that allowing the path of the expansion to be under the guidance of evolution as opposed to a deterministic process produced significant performance gains on all of the benchmark problems analysed. In this study we extend this analysis to include a breadth-first and random map, investigate additional benchmark problems, and take into consideration the implications of recent results on alternative grammar representations with this new evidence. We conclude that it is possible to improve the performance of grammar-based Genetic Programming by the manner in which a genotype-phenotype map is performed.

Semantic similarity based crossover in GP: the case for real-valued function regression

In this paper we propose a new method for implementing the cross-over operator in Genetic Programming (GP) called Semantic Similarity based Crossover (SSC). This new operator is inspired by Semantic Aware Crossover (SAC) [20]. SSC extends SAC by adding semantics to control the change of the semantics of the individuals during the evolutionary process. The new crossover operator is then tested on a family of symbolic regression problems and compared with SAC as well as Standard Crossover (SC). The results from the experiments show that the change of the semantics (fitness) in the new SSC is smoother compared to SAC and SC. This leads to performance improvement in terms of percentage of successful runs and mean best fitness.

Towards an understanding of locality in genetic programming

Locality - how well neighbouring genotypes correspond to neighbouring phenotypes - has been defined as a key element affecting how Evolutionary Computation systems explore and exploit the search space. Locality has been studied empirically using the typical Genetic Algorithm (GA) representation (i.e., bitstrings), and it has been argued that locality plays an important role in EC performance. To our knowledge, there are few explicit studies of locality using the typical Genetic Programming (GP) representation (i.e., tree-like structures). The aim of this paper is to address this important research gap. We extend the genotype-phenotype definition of locality to GP by studying the relationship between genotypes and fitness. We consider a mutation-based GP system applied to two problems which are highly difficult to solve by GP (a multimodal deceptive landscape and a highly neutral landscape). To analyse in detail the locality in these instances, we adopt three popular mutation operators. We analyse the operators genotypic step sizes in terms of three distance measures taken from the specialised literature and in terms of corresponding fitness values. We also analyse the frequencies of different sizes of fitness change.

Tree-adjunct grammatical evolution

In this paper we investigate the application of tree-adjunct grammars to grammatical evolution. The standard type of grammar used by grammatical evolution, context-free grammars, produce a subset of the languages that tree-adjunct grammars can produce, making tree-adjunct grammars, expressively, more powerful. In this study we shed some light on the effects of tree-adjunct grammars on grammatical evolution, or tree-adjunct grammatical evolution. We perform an analytic comparison of the performance of both setups, i.e., grammatical evolution and tree-adjunct grammatical evolution, across a number of classic genetic programming benchmarking problems. The results firmly indicate that tree-adjunct grammatical evolution has a better overall performance (measured in terms of finding the global optima).

Evolving a ms. pacman controller using grammatical evolution

In this paper we propose an evolutionary approach capable of successfully combining rules to play the popular video game, Ms. Pac-Man. In particular we focus our attention on the benefits of using Grammatical Evolution to combine rules in the form of “if then perform ”. We defined a set of high-level functions that we think are necessary to successfully maneuver Ms. Pac-Man through a maze while trying to get the highest possible score. For comparison purposes, we used four Ms. Pac-Man agents, including a hand-coded agent, and tested them against three different ghosts teams. Our approach shows that the evolved controller achieved the highest score among all the other tested controllers, regardless of the ghost team used.

Defining locality in genetic programming to predict performance

A key indicator of problem difficulty in evolutionary computation problems is the landscapes locality, that is whether the genotype-phenotype mapping preserves neighbourhood. In genetic programming the genotype and phenotype are not distinct, but the locality of the genotype-fitness mapping is of interest. In this paper we extend the original standard quantitative definition of locality to cover the genotype-fitness case, considering three possible definitions. By relating the values given by these definitions with the results of evolutionary runs, we investigate which definition is the most useful as a predictor of performance.

On the effects of locality in a permutation problem: The Sudoku Puzzle

We present an analysis of an application of Evolutionary Computation to the Sudoku Puzzle. In particular, we are interested in understanding the locality of the search operators employed, and the difficulty of the problem landscape. Treating the Sudoku puzzle as a permutation problem we analyse the locality of four permutation-based crossover operators, named One Cycle Crossover, Multi-Cycle Crossover, Partially Matched Crossover (PMX) and Uniform Swap Crossover. These were analysed using different crossover rates. Experimental evidence is found to support the hypothesis that PMX and Uniform Swap Crossover operators have better properties of locality relative to the other operators examined regardless of the crossover rates used. Fitness distance correlation, a well-known measure of hardness, is used to analyse problem difficulty and the results are consistent with the difficulty levels associated with the benchmark Sudoku puzzles analysed.

Implementing an intuitive mutation operator for interactive evolutionary 3D design

Locality — how well neighbouring genotypes correspond to neighbouring phenotypes — has been described as a key element in Evolutionary Computation. Grammatical Evolution (GE) is a generative system as it uses grammar rules to derive a program from an integer encoded genome. The genome, upon which the evolutionary process is carried out, goes through several transformations before it produces an output. The aim of this paper is to investigate the impact of locality during the generative process using both qualitative and quantitative techniques. To explore this, we examine the effects of standard GE mutation using distance metrics and conduct a survey of the output designs. There are two different kinds of event that occur during standard GE Mutation. We investigate how each event type affects the locality on different phenotypic stages when applied to the problem of interactive design generation.

A fine-grained view of GP locality with binary decision diagrams as ant phenotypes

The property that neighbouring genotypes tend to map to neighbouring phenotypes, i.e. locality, is an important criterion in the study of problem difficulty. Locality is problematic in tree-based genetic programming (GP), since typically there is no explicit phenotype. Here, we define multiple phenotypes for the artificial ant problem, and use them to describe a novel fine-grained view of GP locality. This allows us to identify the mapping from an ants behavioural phenotype to its concrete path as being inherently non-local, and show that therefore alternative genetic encodings and operators cannot make the problem easy. We relate this to the results of evolutionary runs.