Crossover In Genetic Programming Research Articles

Destructiveness of lexicographic parsimony pressure and alleviation by a concatenation crossover in genetic programming

For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation: the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts); and also the role and the realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had surprisingly little share in this work.We analyze a simple crossover operator in combination with randomized local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); we denote the resulting algorithm Concatenation Crossover GP. We consider three variants of the well-studied Majority test function, adding large plateaus in different ways to the fitness landscape and thus giving a test bed for analyzing the interplay of variation operators and bloat control mechanisms in a setting with local optima. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control.

Improved Evolvability in Genetic Programming with Polyandry

This paper proposes Polyandry, a new nature-inspired modification to canonical Genetic Programming (GP). Polyandry aims to improve evolvability in GP. Evolvability is a critically important GP trait, the maintenance of which determines the arrival of the GP at the global optimum solution. Specifically evolvability is defined as the ability of the genetic operators employed in GP to produce offspring that are fitter than their parents. When GP fails to exhibit evolvability, further adaptation of the GP individuals towards the global optimum solution becomes impossible.
 Polyandry improves evolvability by improving the typically disruptive standard GP crossover operator. The algorithm employs a dual strategy towards this goal. The chief part of this strategy is an incorporation of genetic material from multiple mating partners into broods of offspring. Given such a brood, the offspring in the brood then compete according to a culling function, which we make equivalent to the main GP fitness function. Polyandry’s incorporation of genetic material from multiple GP individuals into broods of offspring represents a more aggressive search for building block information. This characteristic of the algorithm leads to an advanced explorative capability in both GP structural space and fitness space. The second component of the Polyandry strategy is an attempt at multiple crossover points, in order to find crossover points that minimize building block disruption from parents to offspring. This strategy is employed by a similar algorithm, Brood Recombination. 
 We conduct experiments to compare Polyandry with the canonical GP. Our experiments demonstrate that Polyandry consistently exhibits better evolvability than the canonical GP. As a consequence, Polyandry achieves higher success rates and finds solutions faster than the latter. The result of these observations is that given certain brood size settings, Polyandry requires less computational effort to arrive at global optimum solution than the canonical GP.
 We also conduct experiments to compare Polyandry with the analogous nature-inspired modification to canonical GP, Brood Recombination. The adoption of Brood Recombination in order to improve evolvability is ubiquitous in GP literature. Our results demonstrate that Polyandry consistently exhibits better evolvability than Brood Recombination, due to a more explorative nature of the algorithm in both structural and fitness space. As a result, although the two algorithms exhibit similar success rates, the former consistently discovers global optimum GP solutions significantly faster than the latter. The key advantage of Polyandry over Brood Recombination is therefore faster solution discovery. As a consequence Polyandry consistently requires less computational effort to arrive at the global optimum solution compared to Brood Recombination. 
 Further, we establish that the computational effort exerted by Polyandry is competitively low, relative to other Evolutionary Algorithm (EA) methodologies in literature. We conclude that Polyandry is a better alternative to both the canonical GP as well as Brood Recombination with regards to the achievement and maintenance of evolvability.

On the roles of semantic locality of crossover in genetic programming

Locality has long been seen as a crucial property for the efficiency of Evolutionary Algorithms in general, and Genetic Programming (GP) in particular. A number of studies investigating the effects of locality in GP can be found in the literature. The majority of the previous research on locality focuses on syntactic aspects, and operator semantic locality has not been thoroughly tested. In this paper, we investigate the role of semantic locality of crossover in GP. We follow McPhee in measuring the semantics of a subtree using the fitness cases. We use this to define a semantic distance metric. This semantic distance supports the design of some new crossover operators, concentrating on improving semantic locality. We study the impact of these semantically based crossovers on the behaviour of GP. The results show substantial advantages accruing from the use of semantic locality.

DepthLimited crossover in GP for classifier evolution

Genetic Programming (GP) provides a novel way of classification with key features like transparency, flexibility and versatility. Presence of these properties makes GP a powerful tool for classifier evolution. However, GP suffers from code bloat, which is highly undesirable in case of classifier evolution. In this paper, we have proposed an operator named “DepthLimited crossover”. The proposed crossover does not let trees increase in complexity while maintaining diversity and efficient search during evolution. We have compared performance of traditional GP with DepthLimited crossover GP, on data classification problems and found that DepthLimited crossover technique provides compatible results without expanding the search space beyond initial limits. The proposed technique is found efficient in terms of classification accuracy, reduced complexity of population and simplicity of evolved classifiers.

Semantically-based crossover in genetic programming: application to real-valued symbolic regression

We investigate the effects of semantically-based crossover operators in genetic programming, applied to real-valued symbolic regression problems. We propose two new relations derived from the semantic distance between subtrees, known as semantic equivalence and semantic similarity. These relations are used to guide variants of the crossover operator, resulting in two new crossover operators--semantics aware crossover (SAC) and semantic similarity-based crossover (SSC). SAC, was introduced and previously studied, is added here for the purpose of comparison and analysis. SSC extends SAC by more closely controlling the semantic distance between subtrees to which crossover may be applied. The new operators were tested on some real-valued symbolic regression problems and compared with standard crossover (SC), context aware crossover (CAC), Soft Brood Selection (SBS), and No Same Mate (NSM) selection. The experimental results show on the problems examined that, with computational effort measured by the number of function node evaluations, only SSC and SBS were significantly better than SC, and SSC was often better than SBS. Further experiments were also conducted to analyse the perfomance sensitivity to the parameter settings for SSC. This analysis leads to a conclusion that SSC is more constructive and has higher locality than SAC, NSM and SC; we believe these are the main reasons for the improved performance of SSC.

Efficient graph-based genetic programming representation with multiple outputs

In this work, we explore and study the implication of having more than one output on a genetic programming (GP) graph-representation. This approach, called multiple interactive outputs in a single tree (MIOST), is based on two ideas. First, we defined an approach, called interactivity within an individual (IWI), which is based on a graph-GP representation. Second, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As a first step, we analyze the effects of IWI by using only mutations and analyze its implications (i.e., presence of neutrality). Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conducted extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this paper indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions.

A New Crossover Operator in Genetic Programming for Object Classification

The crossover operator has been considered "the centre of the storm" in genetic programming (GP). However, many existing GP approaches to object recognition suggest that the standard GP crossover is not sufficiently powerful in producing good child programs due to the totally random choice of the crossover points. To deal with this problem, this paper introduces an approach with a new crossover operator in GP for object recognition, particularly object classification. In this approach, a local hill-climbing search is used in constructing good building blocks, a weight called looseness is introduced to identify the good building blocks in individual programs, and the looseness values are used as heuristics in choosing appropriate crossover points to preserve good building blocks. This approach is examined and compared with the standard crossover operator and the headless chicken crossover (HCC) method on a sequence of object classification problems. The results suggest that this approach outperforms the HCC, the standard crossover, and the standard crossover operator with hill climbing on all of these problems in terms of the classification accuracy. Although this approach spends a bit longer time than the standard crossover operator, it significantly improves the system efficiency over the HCC method.

Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover

Genetic Programming (GP) homologous crossovers are a group of operators, including GP one-point crossover and GP uniform crossover, where the offspring are created preserving the position of the genetic material taken from the parents. In this paper we present an exact schema theory for GP and variable-length Genetic Algorithms (GAs) which is applicable to this class of operators. The theory is based on the concepts of GP crossover masks and GP recombination distributions that are generalisations of the corresponding notions used in GA theory and in population genetics, as well as the notions of hyperschema and node reference systems, which are specifically required when dealing with variable size representations. In this paper we also present a Markov chain model for GP and variable-length GAs with homologous crossover. We obtain this result by using the core of Vose's model for GAs in conjunction with the GP schema theory just described. The model is then specialised for the case of GP operating on 0/1 trees: a tree-like generalisation of the concept of binary string. For these, symmetries exist that can be exploited to obtain further simplifications. In the absence of mutation, the Markov chain model presented here generalises Vose's GA model to GP and variable-length GAs. Likewise, our schema theory generalises and refines a variety of previous results in GP and GA theory.

General schema theory for genetic programming with subtree-swapping crossover: Part II.

This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)). Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. The theory is based on a Cartesian node reference system, introduced in Part I, and on the notion of a variable-arity hyperschema, introduced here, which generalises previous definitions of a schema. The theory includes two main theorems describing the propagation of GP schemata: a microscopic and a macroscopic schema theorem. The microscopic version is applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. Therefore, this theorem is applicable to Koza's GP crossover with and without uniform selection of the crossover points, as well as one-point crossover, size-fair crossover, strongly-typed GP crossover, context-preserving crossover and many others. The macroscopic version is applicable to crossover operators in which the probability of selecting any two crossover points in the parents depends only on the parents' size and shape. In the paper we provide examples, we show how the theory can be specialised to specific crossover operators and we illustrate how it can be used to derive other general results. These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.