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 accompanied with live software demonstrations. Also, efficient implementation of semantic search operators may be challenging. We will illustrate very efficient, concise and elegant implementations of these operators, which are available for download from the web. As an important coordination and cooperation mechanism in multi-agent systems, coalition of agents exhibits some excellent characteristics and draws researchers' attention increasingly. Cooperation formation has been a very active area of research in multi-agent systems. An efficient algorithm is needed for this topic since the numbers of the possible coalitions are exponential in the number of agents. Genetic algorithm (GA) has been widely reckoned as a useful tool for obtaining high quality and optimal solutions for a broad range of combinatorial optimization problems due to its intelligent advantages of self-organization, self-adaptation and inherent parallelism. This paper proposes a GA-based algorithm for coalition structure formation which aims at achieving goals of high performance, scalability, and fast convergence rate simultaneously. A novel 2D binary chromosome encoding approach and corresponding crossover and mutation operators are presented in this paper. Two valid parental chromosomes are certain to produce a valid offspring under the operation of the crossover operator. This improves the efficiency and shortens the running time greatly. The proposed algorithm is evaluated through a robust comparison with heuristic search algorithms. We have confirmed that our new algorithm is robust, self-adaptive and very efficient by experiments. The results of the proposed algorithm are found to be satisfactory. Mutation and crossover are the main search operators of different variants of evolutionary algorithms. Despite the many discussions on the importance of crossover nobody has proved rigorously for some explicitly defined fitness functions f"n: 0,1 ^n->R that a genetic algorithm with crossover can optimize f"n in expected polynomial time while all evolution strategies based only on mutation (and selection) need expected exponential time. Here such functions and proofs are presented for a genetic algorithm without any idealization. For some functions one-point crossover is appropriate while for others uniform crossover is the right choice. In this paper we give a representation-independent topological defi- nition of crossover that links it tightly to the notion of fitness landscape. Building around this definition, a geometric topological framework for evolu- tionary algorithms is introduced that clarifies the connection between represen- tation, genetic operators, neighbourhood structure and distance in the land- scape. Traditional genetic operators for binary strings are shown to fit the framework. The advantages of this interpretation are discussed. The most salient feature of Grammatical Evolution (GE) is a procedure which maps genotypes to phenotypes using the grammar production rules; however, the search effectiveness of GE may be affected by low locality and high redundancy, which can prevent GE to comply with the basic principle that offspring should inherit some traits from their parents. Indeed, many studies previously investigated the locality and redundancy of GE as originally proposed in [31]. In this paper, we extend those results by considering redundancy and locality during the evolution, rather than statically, hence trying to understand if and how they are influenced by the selective pressure determined by the fitness. Moreover, we consider not only the original GE formulation, but three other variants proposed later (BGE, ( )GE, and SGE). We experimentally find that there is an interaction between locality redundancy and other evolution-related measures, namely diversity and growth of individual size. In particular, the combined action of the crossover operator and the genotype-phenotype mapper makes SGE less redundant at the beginning of the evolution, but with very high redundancy after some generations, due to the low phenotype diversity. We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Understanding the impact of crossover on performance is a major problem in the theory of genetic algorithms (GAs). We present new insight on working principles of crossover by analyzing the performance of crossover-based GAs on the simple functions OneMax and Jump. First, we assess the potential speedup by crossover when combined with a fitness-invariant bit shuffling operator that simulates a lineage of independent evolution on a function of unitation. Theoretical and empirical results show drastic speedups for both functions. Second, we consider a simple GA without shuffling and investigate the interplay of mutation and crossover on Jump. If the crossover probability is small, subsequent mutations create sufficient diversity, even for very small populations. Contrarily, with high crossover probabilities crossover tends to lose diversity more quickly than mutation can create it. This has a drastic impact on the performance on Jump. We complement our theoretical findings by Monte Carlo simulations on the population diversity. Due to experimental evidence it is incontestable that crossover is essential for some fitness functions. However, theoretical results without assumptions are difficult. So-called real royal road functions are known where crossover is proved to be essential, i.e., mutation-based algorithms have an exponential expected runtime while the expected runtime of a genetic algorithm is polynomially bounded. However, these functions are artificial and have been designed in such a way that crossover is essential only at the very end (or at other well-specified points) of the optimization process.Here, a more natural fitness function based on a generalized Ising model is presented where crossover is essential throughout the whole optimization process. Mutation-based algorithms such as (μ+λ) EAs with constant population size are proved to have an exponential expected runtime while the expected runtime of a simple genetic algorithm with population size 2 and fitness sharing is polynomially bounded. Crossover forms one of the core operations in genetic programming and has been the subject of many different investigations. We present a novel technique, based on semantic analysis of programs, which forces each crossover to make candidate programs take a new step in the behavioural search space. We demonstrate how this technique results in better performance and smaller solutions in two separate genetic programming experiments. In genetic programming, a search algorithm is expected to produce a program that achieves the desired final computation state (desired output). To reach that state, an executing program needs to traverse certain intermediate computation states. An evolutionary search process is expected to autonomously discover such states. This can be difficult for nontrivial tasks that require long programs to be solved. The semantic backpropagation algorithm proposed in this paper heuristically inverts the execution of evolving programs to determine the desired intermediate computation states. Two search operators, random desired operator and approximately geometric semantic crossover, use the intermediate states determined by semantic backpropagation to define subtasks of the original programming task, which are then solved using an exhaustive search. The operators outperform the standard genetic search operators and other semantic-aware operators when compared on a suite of symbolic regression and Boolean benchmarks. This result and additional analysis conducted in this paper indicate that semantic backpropagation helps evolution to identify the desired intermediate computation states and makes the search process more efficient.