In a steady-state evolution, tournament selection traditionally uses the fitness function to select the parents, and negative selection chooses an individual to be replaced with an offspring. This contribution focuses on analyzing the behavior, in terms of performance, of different heuristics when used instead of the fitness function in tournament selection. The heuristics analyzed are related to measuring the similarity of the individuals in the semantic space. In addition, the analysis includes random selection and traditional tournament selection. These selection functions were implemented on our Semantic Genetic Programming system, namely EvoDAG, which is inspired by the geometric genetic operators and tested on 30 classification problems with a variable number of samples, variables, and classes. The result indicated that the combination of accuracy and the random selection, in the negative tournament, produces the best combination, and the difference in performances between this combination and the tournament selection is statistically significant. Furthermore, we compare EvoDAG's performance using the selection heuristics against 18 classifiers that included traditional approaches as well as auto-machine-learning techniques. The results indicate that our proposal is competitive with state-of-art classifiers. Finally, it is worth to mention that EvoDAG is available as open source software.
Moraglio @cite_21 @cite_27 proposed Geometric Semantic Genetic Programming (GSGP). Their work called the attention of the GP scientific community because the crossover operator produces an offspring that stands in the segment joining the parents' semantics. Therefore, offspring fitness cannot be worse than the worst fitness of the parents. Given two parents @math and @math , the crossover operator generates an offspring as @math , where @math is a real value between @math and @math . This property transforms the fitness landscape into a cone. Unfortunately, the offspring is always bigger than the sum of the size of its parents; this makes the operator unusable in practice. Later, some operators appear intending to improve Moraglio's GSGP. For example, Approximately Geometric Semantic Crossover (SX) @cite_10 , Deterministic Geometric Semantic Crossover @cite_16 , Locally Geometric Crossover (LGX) @cite_7 @cite_2 and Approximated Geometric Crossover (AGX) @cite_8 , Semantic Crossover and Mutation based on projections @cite_24 @cite_19 and Subtree Semantic Geometric Crossover (SSGX) @cite_47 .
@cite_7 @cite_8 @cite_21 @cite_24 @cite_19 @cite_27 @cite_2 @cite_47 @cite_16 @cite_10
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Genetic Programming (GP) is an evolutionary method for generating tree structural programs. Normal subtree crossover in GP randomly selects a crossover point in each parental tree, and offspring are created by exchanging the selected subtrees. In the normal crossover, it is difficult to control the global and local search because the similarity between the subtrees is not considered. In this paper, we propose a new crossover operation based on the semantic distance between the subtrees. We call this operation Semantic Control Crossover. By using the Semantic Control Crossover, the global search can be performed in the early stage of search, and the search property can be shifted to the local search as the search proceeds. As the results of experiments, the Semantic Control Crossover showed better performance than the conventional crossover. The semantic geometric crossover (SGX) proposed by has achieved very promising results and received great attention from researchers, but has a significant disadvantage in the exponential growth in size of the solutions. We propose a crossover operator named subtree semantic geometric crossover (SSGX), with the aim of addressing this issue. It is similar to SGX but uses subtree semantic similarity to approximate the geometric property. We compare SSGX to standard crossover (SC), to SGX, and to other recent semantic-based crossover operators, testing on several symbolic regression problems. Overall our new operator out-performs the other operators on test data performance, and reduces computational time relative to most of them. Further analysis shows that while SGX is rather exploitative, and SC rather explorative, SSGX achieves a balance between the two. A simple method of further enhancing SSGX performance is also demonstrated. We propose a crossover operator that works with genetic programming trees and is approximately geometric crossover in the semantic space. By defining semantic as program's evaluation profile with respect to a set of fitness cases and constraining to a specific class of metric-based fitness functions, we cause the fitness landscape in the semantic space to have perfect fitness-distance correlation. The proposed approximately geometric semantic crossover exploits this property of the semantic fitness landscape by an appropriate sampling. We demonstrate also how the proposed method may be conveniently combined with hill climbing. We discuss the properties of the methods, and describe an extensive computational experiment concerning logical function synthesis and symbolic regression. We propose Locally Geometric Crossover (LGX) for genetic programming. For a pair of homologous loci in the parent solutions, LGX finds a semantically intermediate procedure from a previously prepared library, and uses it as replacement code. The experiments involving six symbolic regression problems show significant increase in search performance when compared to standard subtree-swapping cross-over and other control methods. This suggests that semantically geometric manipulations on subprograms propagate to entire programs and improve their fitness. This study presents an extensive account of Locally Geometric Semantic Crossover (LGX), a semantically-aware recombination operator for genetic programming (GP). LGX is designed to exploit the semantic properties of programs and subprograms, in particular the geometry of semantic space that results from distance-based fitness functions used predominantly in GP. When applied to a pair of parents, LGX picks in them at random a structurally common (homologous) locus, calculates the semantics of subprograms located at that locus, finds a procedure that is semantically medial with respect to these subprograms, and replaces them with that procedure. The library of procedures is prepared prior to the evolutionary run and indexed by a multidimensional structure (kd-tree) allowing for efficient search. The paper presents the rationale for LGX design and an extensive computational experiment concerning performance, computational cost, impact on program size, and capability of generalization. LGX is compared with six other operators, including conventional tree-swapping crossover, semantic-aware operators proposed in previous studies, and control methods designed to verify the importance of homology and geometry of the semantic space. The overall conclusion is that LGX, thanks to combination of the semantically medial operation with homology, improves the efficiency of evolutionary search, lowers the variance of performance, and tends to be more resistant to overfitting. There is a great interest in the Genetic Programming (GP) community to develop semantic genetic operators. Most recent approaches includes the genetic programming framework for symbolic regression called Error Space Alignment GP, the geometric semantic operators, and our previous work the semantic crossover based on the partial derivative error. To the best of our knowledge, there has not been a semantic genetic operator similar to the point mutation. In this contribution, we start filling this gap by proposing a semantic point mutation based on the derivative of the error. This novel operator complements our previous semantic crossover and, as the results show, there is an improvement in performance when this novel operator is used, and, furthermore, the best performance in our setting is the system that uses the semantic crossover and the semantic point mutation. There is great interest for the development of semantic genetic operators to improve the performance of genetic programming. Semantic genetic operators have traditionally been developed employing experimentally or theoretically-based approaches. Our current work proposes a novel semantic crossover developed amid the two traditional approaches. Our proposed semantic crossover operator is based on the use of the derivative of the error propagated through the tree. This process decides the crossing point of the second parent. The results show that our procedure improves the performance of genetic programming on rational symbolic regression problems. 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. Geometric semantic genetic programming (GP) has recently attracted much attention. The key innovations are inducing a unimodal fitness landscape in the semantic space and providing a theoretical framework for designing geometric semantic operators. The geometric semantic operators aim to manipulate the semantics of programs by making a bounded semantic impact and generating child programs with similar or better behavior than their parents. These properties are shown to be highly related to a notable generalization improvement in GP. However, the potential ineffectiveness and difficulties in bounding the variations in these geometric operators still limits their positive effect on generalization. This paper attempts to further explore the geometry and search space of geometric operators to gain a greater generalization improvement in GP for symbolic regression. To this end, a new angle-driven selection operator and two new angle-driven geometric search operators are proposed. The angle-awareness brings new geometric properties to these geometric operators, which are expected to provide a greater leverage for approximating the target semantics in each operation, and more importantly, be resistant to overfitting. The experiments show that compared with two state-of-the-art geometric semantic operators, our angle-driven geometric operators not only drive the evolutionary process to fit the target semantics more efficiently but also improve the generalization performance. A further comparison between the evolved models shows that the new method generally produces simpler models with a much smaller size and is more likely to evolve toward the correct structure of the target models. Semantic genetic programming is a recent, rapidly growing trend in Genetic Programming (GP) that aims at opening the 'black box' of the evaluation function and make explicit use of more information on program behavior in the search. In the most common scenario of evaluating a GP program on a set of input-output examples (fitness cases), the semantic approach characterizes program with a vector of outputs rather than a single scalar value (fitness). The past research on semantic GP has demonstrated that the additional information obtained in this way facilitates designing more effective search operators. In particular, exploiting the geometric properties of the resulting semantic space leads to search operators with attractive properties, which have provably better theoretical characteristics than conventional GP operators. This in turn leads to dramatic improvements in experimental comparisons. The aim of the tutorial is to give a comprehensive overview of semantic methods in genetic programming, illustrate in an accessible way a formal geometric framework for program semantics to design provably good mutation and crossover operators for traditional GP problem domains, and to analyze rigorously their performance (runtime analysis). A number of real-world applications of this framework will be also presented. Other promising emerging approaches to semantics in GP will be reviewed. In particular, the recent developments in the behavioral programming, which aims at characterizing the entire program behavior (and not only program outputs) will be covered as well. Current challenges and future trends in semantic GP will be identified and discussed. Selected methods and concepts will be acco