Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming. We set up several simplified genetic programming algorithms and analyze them on two separable model problems, ORDER and MAJORITY, each of which captures an important facet of typical genetic programming problems. Both analyses give first rigorous insights on aspects of genetic programming design, highlighting in particular the impact of accepting or rejecting neutral moves and the importance of a local mutation operator.
Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented as trees and are evolved using genetic programming (GP) techniques. The proposed approach is tested with real benchmark functions and an analysis of operator evolution is provided.
We introduce a genetic programming method for solving multiple Boolean circuit synthesis tasks simultaneously. This allows us to solve a set of elementary logic functions twice as easily as with a direct, single-task approach.
Cartesian Genetic Programming (CGP) has many modifications across a variety of implementations, such as recursive connections and node weights. Alternative genetic operators have also been proposed for CGP, but have not been fully studied. In this work, we present a new form of genetic programming based on a floating point representation. In this new form of CGP, called Positional CGP, node positions are evolved. This allows for the evaluation of many different genetic operators while allowing for previous CGP improvements like recurrency. Using nine benchmark problems from three different cla…
C++ code snippets from a multi-core parallel memory-efficient crossover for genetic programming are given. They may be adapted for separate generation evolutionary algorithms where large chromosomes or small RAM require no more than M + (2 times nthreads) simultaneously active individuals.
Genetic programming has been widely used in the engineering field. Compared with the conventional genetic programming and artificial neural network, geometric semantic genetic programming (GSGP) is superior in astringency and computing efficiency. In this paper, GSGP is adopted for the classification and regression analysis of a sample dataset. Furthermore, a model for slope stability analysis is established on the basis of geometric semantics. According to the results of the study based on GSGP, the method can analyze slope stability objectively and is highly precise in predicting slope stabi…
TU Dortmund University（多特蒙德工业大学）；Department of Computer Science（计算机科学系）
Cartesian Genetic Programming is often used with a point mutation as the sole genetic operator. In this paper, we propose two phenotypic mutation techniques and take a step towards advanced phenotypic mutations in Cartesian Genetic Programming. The functionality of the proposed mutations is inspired by biological evolution which mutates DNA sequences by inserting and deleting nucleotides. Experiments with symbolic regression and boolean functions problems show a better search performance when the proposed mutations are in use. The results of our experiments indicate that the use of phenotypic …
In Search Based Software Engineering, Genetic Programming has been used for bug fixing, performance improvement and parallelisation of programs through the modification of source code. Where an evolutionary computation algorithm, such as Genetic Programming, is to be applied to similar code manipulation tasks, the complexity and size of source code for real-world software poses a scalability problem. To address this, we intend to inspect how the Software Engineering concepts of modularity, granularity and localisation of change can be reformulated as additional mechanisms within a Genetic Prog…
Premature convergence is one of the important issues while using Genetic Programming for data modeling. It can be avoided by improving population diversity. Intelligent genetic operators can help to improve the population diversity. Crossover is an important operator in Genetic Programming. So, we have analyzed number of intelligent crossover operators and proposed an algorithm with the modification of soft brood crossover operator. It will help to improve the population diversity and reduce the premature convergence. We have performed experiments on three different symbolic regression problem…
While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat (unnecessary growth of solutions) slowing down optimization. Theoretical analyses could so far not bound bloat and required explicit assumptions on the magnitude of bloat. In this paper we analyze bloat in mutation-based genetic programming for the two test functions ORDER and MAJORITY. We overcome previous assumptions on the magnitude of blo…
This paper concerns applications of genetic algorithms and genetic programming to tasks for which it is difficult to find a representation that does not map to a highly complex and discontinuous fitness landscape. In such cases the standard algorithm is prone to getting trapped in local extremes. The paper proposes several adaptive mechanisms that are useful in preventing the search from getting trapped.
GitHub Copilot, an extension for the Visual Studio Code development environment powered by the large-scale language model Codex, makes automatic program synthesis available for software developers. This model has been extensively studied in the field of deep learning, however, a comparison to genetic programming, which is also known for its performance in automatic program synthesis, has not yet been carried out. In this paper, we evaluate GitHub Copilot on standard program synthesis benchmark problems and compare the achieved results with those from the genetic programming literature. In addi…
Semantic diversity in Genetic Programming has proved to be highly beneficial in evolutionary search. We have witnessed a surge in the number of scientific works in the area, starting first in discrete spaces and moving then to continuous spaces. The vast majority of these works, however, have focused their attention on single-objective genetic programming paradigms, with a few exceptions focusing on Evolutionary Multi-objective Optimization (EMO). The latter works have used well-known robust algorithms, including the Non-dominated Sorting Genetic Algorithm II and the Strength Pareto Evolutiona…
We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic regression, dCGP offers a new approach to the long unsolved problem of constant representation in GP expressions. On several problems of increasin…
Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionallyaware genetic programming search spaces on a subset of equations from Richard Feynmans well-known lectures. We define…
A genetic programming (GP) variant called traceless genetic programming (TGP) is proposed in this paper. TGP is a hybrid method combining a technique for building individuals and a technique for representing individuals. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. Two genetic operators are used in conjunction with TGP: crossover and insertion. TGP is applied for evolving digital circuits for the even-parity problem. Numerical experiments show that TGP outperforms standard GP with several orders of magnitude.
We evolve floating point Sextic polynomial populations of genetic programming binary trees for up to a million generations. Programs with almost four hundred million instructions are created by crossover. To support unbounded Long-Term Evolution Experiment LTEE GP we use both SIMD parallel AVX 512 bit instructions and 48 threads to yield performance of up to 139 billion GP operations per second, 139 giga GPops, on a single Intel Xeon Gold 6126 2.60GHz server.
We study a generic program to investigate the scope for automatically customising it for a vital current task, which was not considered when it was first written. In detail, we show genetic programming (GP) can evolve models of aspects of BLAST's output when it is used to map Solexa Next-Gen DNA sequences to the human genome.
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems with isolated program semantics. With this paper, we push forward the computational complexity analysis of GP on a problem with dependent program semantics. We study the well-known sorting problem in this context and analyze rigorously how GP can deal with different measures of sortedness.
The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences the runtime behavior. We consider generalizations of ORDER and MAJORITY and present a computational complexity analysis of (1+1) GP using multi-criteria fitness functions that take into account the original objective and the complexity of a syntax tree as a secondary measure. Furthermore, we study the expected time until population-based mult…
The paper describes an approach to implementing genetic programming, which uses the LLVM library to just-in-time compile/interpret the evolved abstract syntax trees. The solution is described in some detail, including a parser (based on FlexC++ and BisonC++) that can construct the trees from a simple toy language with C-like syntax. The approach is compared with a previous implementation (based on direct execution of trees using polymorphic functors) in terms of execution speed.
Three approaches to implement genetic programming on GPU hardware are compilation, interpretation and direct generation of machine code. The compiled approach is known to have a prohibitive overhead compared to other two. This paper investigates methods to accelerate compilation of individuals for genetic programming on GPU hardware. We apply in-process compilation to minimize the compilation overhead at each generation; and we investigate ways to parallelize in-process compilation. In-process compilation doesn't lend itself to trivial parallelization with threads; we propose a multiprocess pa…
This Paper will deal with a combination of Ant Colony and Genetic Programming Algorithm to optimize Travelling Salesmen problem (NP-Hard). However, the complexity of the algorithm requires considerable computational time and resources. Parallel implementation can reduce the computational time. In this paper, emphasis in the parallelizing section is given to Multi-core architecture and Multi-Processor Systems which is developed and used almost everywhere today and hence, multi-core parallelization to the combination of algorithm is achieved by OpenMP library by Intel Corporation.
We apply genetic programming techniques to the `shepherding' problem, in which a group of one type of animal (sheep dogs) attempts to control the movements of a second group of animals (sheep) obeying flocking behavior. Our genetic programming algorithm evolves an expression tree that governs the movements of each dog. The operands of the tree are hand-selected features of the simulation environment that may allow the dogs to herd the sheep effectively. The algorithm uses tournament-style selection, crossover reproduction, and a point mutation. We find that the evolved solutions generalize wel…
Among the evolutionary methods, one that is quite prominent is Genetic Programming, and, in recent years, a variant called Geometric Semantic Genetic Programming (GSGP) has shown to be successfully applicable to many real-world problems. Due to a peculiarity in its implementation, GSGP needs to store all the evolutionary history, i.e., all populations from the first one. We exploit this stored information to define a multi-generational selection scheme that is able to use individuals from older populations. We show that a limited ability to use "old" generations is actually useful for the sear…
In recent years the field of genetic programming has made significant advances towards automatic programming. Research and development of contemporary program synthesis methods, such as PushGP and Grammar Guided Genetic Programming, can produce programs that solve problems typically assigned in introductory academic settings. These problems focus on a narrow, predetermined set of simple data structures, basic control flow patterns, and primitive, non-overlapping data types (without, for example, inheritance or composite types). Few, if any, genetic programming methods for program synthesis hav…
We present new techniques for synthesizing programs through sequences of mutations. Among these are (1) a method of local scoring assigning a score to each expression in a program, allowing us to more precisely identify buggy code, (2) suppose-expressions which act as an intermediate step to evolving if-conditionals, and (3) cyclic evolution in which we evolve programs through phases of expansion and reduction. To demonstrate their merits, we provide a basic proof-of-concept implementation which we show evolves correct code for several functions manipulating integers and lists, including some …
Traceless Genetic Programming (TGP) is a new Genetic Programming (GP) that may be used for solving difficult real-world problems. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. In this paper, TGP is used for solving real-world classification problems taken from PROBEN1. Numerical experiments show that TGP performs similar and sometimes even better than other GP techniques for the considered test problems.
Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the problem is increased. In these systems, the density D of working programs in the universe of all possible programs is measured. The relationship G ~ 1/sqrt(D) is observed to approximately hold for two program-like systems. For parallel systems (systems that look like several independent programs evolving in parallel), the relationship G ~ 1/(n ln n) is observ…
Genetic Programming (GP) is an evolutionary algorithm commonly used for machine learning tasks. In this paper we present a method that allows GP to transform the representation of a large-scale machine learning dataset into a more compact representation, by means of processing features from the original representation at individual level. We develop as a proof of concept of this method an autoencoder. We tested a preliminary version of our approach in a variety of well-known machine learning image datasets. We speculate that this method, used in an iterative manner, can produce results competi…
For simple digital circuits, conventional method of designing circuits can easily be applied. But for complex digital circuits, the conventional method of designing circuits is not fruitfully applicable because it is time-consuming. On the contrary, Genetic Programming is used mostly for automatic program generation. The modern approach for designing Arithmetic circuits, commonly digital circuits, is based on Graphs. This graph-based evolutionary design of arithmetic circuits is a method of optimized designing of arithmetic circuits. In this paper, a new technique for evolutionary design of di…
Event-driven genetic programming representations have been shown to outperform traditional imperative representations on interaction-intensive problems. The event-driven approach organizes genome content into modules that are triggered in response to environmental signals, simplifying simulation design and implementation. Existing work developing event-driven genetic programming methodology has largely used the SignalGP library, which caters to traditional program synthesis applications. The SignalGP-Lite library enables larger-scale artificial life experiments with streamlined agents by reduc…
In this paper, we continue the efforts of the Computational Theory of Intelligence (CTI) by extending concepts to include computational processes in terms of Genetic Algorithms (GA's) and Turing Machines (TM's). Active, Passive, and Hybrid Computational Intelligence processes are also introduced and discussed. We consider the ramifications of the assumptions of CTI with regard to the qualities of reproduction and virility. Applications to Biology, Computer Science and Cyber Security are also discussed.
Traceless Genetic Programming (TGP) is a Genetic Programming (GP) variant that is used in cases where the focus is rather the output of the program than the program itself. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. Two genetic operators are used in conjunction with TGP: crossover and insertion. In this paper, we shall focus on how to apply TGP for solving multi-objective optimization problems which are quite unusual for GP. Each TGP individual stores the output of a computer program (tree) representing a point i…
In this paper, we develop a set of genetic programming operators and an initialization population process based on concepts of functional programming rewriting for boosting inductive genetic programming. Such genetic operators are used within a hybrid adaptive evolutionary algorithm that evolves operator rates at the same time it evolves the solution. Solutions are represented using recursive functions where genome is encoded as an ordered list of trees and phenotype is written in a simple functional programming language that uses rewriting as operational semantic (computational model). The fi…
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem, and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.
Very recently new genetic operators, called geometric semantic operators, have been defined for genetic programming. Contrarily to standard genetic operators, which are uniquely based on the syntax of the individuals, these new operators are based on their semantics, meaning with it the set of input-output pairs on training data. Furthermore, these operators present the interesting property of inducing a unimodal fitness landscape for every problem that consists in finding a match between given input and output data (for instance regression and classification). Nevertheless, the current defini…
Genetic programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP is to evolve computer programs with a given functionality. While many GP applications have produced human competitive results, the theoretical understanding of what problem characteristics and algorithm properties allow GP to be effective is comparatively limited. Compared with traditional evolutionary algorithms for function optimization, GP applications are…
Genetic programming is a powerful heuristic search technique that is used for a number of real world applications to solve among others regression, classification, and time-series forecasting problems. A lot of progress towards a theoretic description of genetic programming in form of schema theorems has been made, but the internal dynamics and success factors of genetic programming are still not fully understood. In particular, the effects of different crossover operators in combination with offspring selection are largely unknown. This contribution sheds light on the ability of well-known GP…
Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院）
Ensemble learning is a powerful paradigm that has been usedin the top state-of-the-art machine learning methods like Random Forestsand XGBoost. Inspired by the success of such methods, we have devel-oped a new Genetic Programming method called Ensemble GP. The evo-lutionary cycle of Ensemble GP follows the same steps as other GeneticProgramming systems, but with differences in the population structure,fitness evaluation and genetic operators. We have tested this method oneight binary classification problems, achieving results significantly betterthan standard GP, with much smaller models. Alth…
Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear transformations that preserve the most important structure of the original data. State-of-the-art manifold learning methods directly optimise an embedding without mapping between the original space and the discovered embedded space. This makes interpretability - a key requirement in exploratory data analysis - nearly impossible. Recently, genetic programming…
Interpretability can be critical for the safe and responsible use of machine learning models in high-stakes applications. So far, evolutionary computation (EC), in particular in the form of genetic programming (GP), represents a key enabler for the discovery of interpretable machine learning (IML) models. In this short paper, we argue that research in GP for IML needs to focus on searching in the space of low-complexity models, by investigating new kinds of search strategies and recombination methods. Moreover, based on our experience of bringing research into clinical practice, we believe tha…
Cartesian Genetic Programming Approach for Designing Convolutional Neural Networks
AGH University of Krakow（克拉科夫AGH大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；University of Technology Sydney（悉尼科技大学）；Óbuda University（奥布达大学）
Evolutionary Computation has been successfully used to synthesise controllers for embodied agents and multi-agent systems in general. Notwithstanding this, continuous on-line adaptation by the means of evolutionary algorithms is still under-explored, especially outside the evolutionary robotics domain. In this paper, we present an on-line evolutionary programming algorithm that searches in the agent design space for the appropriate behavioural policies to cope with the underlying environment. We discuss the current problems of continuous agent adaptation, present our on-line evolution testbed …
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component…
General program synthesis has become an important application area for genetic programming (GP), and for artificial intelligence more generally. Code Building Genetic Programming (CBGP) is a recently introduced GP method for general program synthesis that leverages reflection and first class specifications to support the evolution of programs that may use arbitrary data types, polymorphism, and functions drawn from existing codebases. However, neither a formal description nor a thorough benchmarking of CBGP have yet been reported. In this work, we formalize the method of CBGP using algorithms …
Research on the performance of recycled concrete as building material in the current world is an important subject. Given the complex composition of recycled concrete, conventional methods for forecasting slump scarcely obtain satisfactory results. Based on theory of nonlinear prediction method, we propose a recycled concrete slump prediction model based on geometric semantic genetic programming (GSGP) and combined it with recycled concrete features. Tests show that the model can accurately predict the recycled concrete slump by using the established prediction model to calculate the recycled …
In the field of empirical modeling using Genetic Programming (GP), it is important to evolve solution with good generalization ability. Generalization ability of GP solutions get affected by two important issues: bloat and over-fitting. We surveyed and classified existing literature related to different techniques used by GP research community to deal with these issues. We also point out limitation of these techniques, if any. Moreover, the classification of different bloat control approaches and measures for bloat and over-fitting are also discussed. We believe that this work will be useful t…
Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP) methods were proposed to overcome this issue through a probability model that captures the structure of the fit individuals and use it to sample new individuals. This work proposes the use of LGP with a Stochastic Context-Free Grammar (SCFG), that has a probability distribution that is …
Josef Ressel Centre for Symbolic Regression（约瑟夫·雷塞尔符号回归中心）；University of Applied Sciences Upper Austria（上奥地利应用科学大学）；Johannes Kepler University（约翰内斯·开普勒大学）
We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population diversity and algebraic simplification of symbolic expression trees. Based on this hashing approach, we propose a simple diversity-preservation mechanism with promising results on a collection of symbolic regression benchmark problems.
Advances in Geometric Semantic Genetic Programming (GSGP) have shown that this variant of Genetic Programming (GP) reaches better results than its predecessor for supervised machine learning problems, particularly in the task of symbolic regression. However, by construction, the geometric semantic crossover operator generates individuals that grow exponentially with the number of generations, resulting in solutions with limited use. This paper presents a new method for individual simplification named GSGP with Reduced trees (GSGP-Red). GSGP-Red works by expanding the functions generated by the…
This paper presents a Genetic Programming (GP) approach to solving multi-robot path planning (MRPP) problems in single-lane workspaces, specifically those easily mapped to graph representations. GP's versatility enables this approach to produce programs optimizing for multiple attributes rather than a single attribute such as path length or completeness. When optimizing for the number of time steps needed to solve individual MRPP problems, the GP constructed programs outperformed complete MRPP algorithms, i.e. Push-Swap-Wait (PSW), by $54.1\%$. The GP constructed programs also consistently out…
Society has come to rely on algorithms like classifiers for important decision making, giving rise to the need for ethical guarantees such as fairness. Fairness is typically defined by asking that some statistic of a classifier be approximately equal over protected groups within a population. In this paper, current approaches to fairness are discussed and used to motivate algorithmic proposals that incorporate fairness into genetic programming for classification. We propose two ideas. The first is to incorporate a fairness objective into multi-objective optimization. The second is to adapt lex…
