Automated Problem Decomposition for the Boolean Domain with Genetic Programming

Researchers have been interested in exploring the regularities and modularity of the problem space in genetic programming (GP) with the aim of decomposing the original problem into several smaller subproblems. The main motivation is to allow GP to deal with more complex problems. Most previous works on modularity in GP emphasise the structure of modules used to encapsulate code and/or promote code reuse, instead of in the decomposition of the original problem. In this paper we propose a problem decomposition strategy that allows the use of a GP search to find solutions for subproblems and combine the individual solutions into the complete solution to the problem

Sequential Symbolic Regression with Genetic Programming

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference to GP. More importantly, they show the potential of the proposed strategy: an effective way of applying geometric semantic operators to combine different (partial) solutions, avoiding the exponential growth problem arising from the use of these operators

The Effect of Distinct Geometric Semantic Crossover Operators in Regression Problems

This paper investigates the impact of geometric semantic crossover operators in a wide range of symbolic regression problems. First, it analyses the impact of using Manhattan and Euclidean distance geometric semantic crossovers in the learning process. Then, it proposes two strategies to numerically optimize the crossover mask based on mathematical properties of these operators, instead of simply generating them randomly. An experimental analysis comparing geometric semantic crossovers using Euclidean and Manhattan distances and the proposed strategies is performed in a test bed of twenty datasets. The results show that the use of different distance functions in the semantic geometric crossover has little impact on the test error, and that our optimized crossover masks yield slightly better results. For SGP practitioners, we suggest the use of the semantic crossover based on the Euclidean distance, as it achieved similar results to those obtained by more complex operators

Geometric Semantic Grammatical Evolution

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Geometric Semantic Genetic Programming (GSGP) is a novel form of Genetic Programming (GP), based on a geometric theory of evolutionary algorithms, which directly searches the semantic space of programs. In this chapter, we extend this framework to Grammatical Evolution (GE) and refer to the new method as Geometric Semantic Grammatical Evolution (GSGE). We formally derive new mutation and crossover operators for GE which are guaranteed to see a simple unimodal fitness landscape. This surprising result shows that the GE genotypephenotype mapping does not necessarily imply low genotype-fitness locality. To complement the theory, we present extensive experimental results on three standard domains (Boolean, Arithmetic and Classifier)

Semantic variation operators for multidimensional genetic programming

Multidimensional genetic programming represents candidate solutions as sets of programs, and thereby provides an interesting framework for exploiting building block identification. Towards this goal, we investigate the use of machine learning as a way to bias which components of programs are promoted, and propose two semantic operators to choose where useful building blocks are placed during crossover. A forward stagewise crossover operator we propose leads to significant improvements on a set of regression problems, and produces state-of-the-art results in a large benchmark study. We discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. Finally, we look at the collinearity and complexity of the data representations that result from these architectures, with a view towards disentangling factors of variation in application.Comment: 9 pages, 8 figures, GECCO 201

Geometric semantic genetic programming for recursive boolean programs

This is the author accepted manuscript. The final version is available from ACM via the DOI in this record.Geometric Semantic Genetic Programming (GSGP) induces a unimodal fitness landscape for any problem that consists in finding a function fitting given input/output examples. Most of the work around GSGP to date has focused on real-world applications and on improving the originally proposed search operators, rather than on broadening its theoretical framework to new domains. We extend GSGP to recursive programs, a notoriously challenging domain with highly discontinuous fitness landscapes. We focus on programs that map variable-length Boolean lists to Boolean values, and design search operators that are provably efficient in the training phase and attain perfect generalization. Computational experiments complement the theory and demonstrate the superiority of the new operators to the conventional ones. This work provides new insights into the relations between program syntax and semantics, search operators and fitness landscapes, also for more general recursive domains.© 2017 Copyright held by the owner/author(s). Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]