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.
The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm for the multidimensional knapsack problem with Java and C++ code that is able to solve publicly available instances in a very short computational duration. Our algorithm uses iteratively computed Lagrangian multipliers as constraint weights to augment the greedy algorithm for the multidimensional knapsack problem and uses that information in a greedy crossover …
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…
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…
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.
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…
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.
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.
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…
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 …
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.
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 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…
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…
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…
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…
We evolve binary mux-6 trees for up to 100000 generations evolving some programs with more than a hundred million nodes. Our unbounded Long-Term Evolution Experiment LTEE GP appears not to evolve building blocks but does suggests a limit to bloat. We do see periods of tens even hundreds of generations where the population is 100 percent functionally converged. The distribution of tree sizes is not as predicted by theory.
We summarise how a 3.0 GHz 16 core AVX512 computer can interpret the equivalent of up to on average 1103370000000 GPop/s. Citations to existing publications are given. Implementation stress is placed on both parallel computing, bandwidth limits and avoiding repeated calculation. Information theory suggests in digital computing, failed disruption propagation gives huge speed ups as FDP and incremental evaluation can be used to reduce fitness evaluation time in phenotypically converged populations. Conversely FDP may be responsible for evolution stagnation. So the wider Evolutionary Computing, A…
Most existing swarm pattern formation methods depend on a predefined gene regulatory network (GRN) structure that requires designers' priori knowledge, which is difficult to adapt to complex and changeable environments. To dynamically adapt to the complex and changeable environments, we propose an automatic design framework of swarm pattern formation based on multi-objective genetic programming. The proposed framework does not need to define the structure of the GRN-based model in advance, and it applies some basic network motifs to automatically structure the GRN-based model. In addition, a m…
Genetic Programming (GP) is a computationally intensive technique which is naturally parallel in nature. Consequently, many attempts have been made to improve its run-time from exploiting highly parallel hardware such as GPUs. However, a second methodology of improving the speed of GP is through efficiency techniques such as subtree caching. However achieving parallel performance and efficiency is a difficult task. This paper will demonstrate an efficiency saving for GP compatible with the harnessing of parallel CPU hardware by exploiting tournament selection. Significant efficiency savings ar…
Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regression require the use of protected operators, which can lead to perverse model characteristics and poor generalisation. In this paper, we revisit interval arithmetic as one possible solution to allow genetic programming to perform regression using unprotected operators. Using standard benchmarks, we show that using interval arithmetic within model evaluation does not prevent invalid solutions fro…
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 …
Most real-world optimization problems are difficult to solve with traditional statistical techniques or with metaheuristics. The main difficulty is related to the existence of a considerable number of local optima, which may result in the premature convergence of the optimization process. To address this problem, we propose a novel heuristic method for constructing a smooth surrogate model of the original function. The surrogate function is easier to optimize but maintains a fundamental property of the original rugged fitness landscape: the location of the global optimum. To create such a surr…
Semantics is a growing area of research in Genetic programming (GP) and refers to the behavioural output of a Genetic Programming individual when executed. This research expands upon the current understanding of semantics by proposing a new approach: Semantic-based Distance as an additional criteriOn (SDO), in the thus far, somewhat limited researched area of semantics in Multi-objective GP (MOGP). Our work included an expansive analysis of the GP in terms of performance and diversity metrics, using two additional semantic-based approaches, namely Semantic Similarity-based Crossover (SCC) and …
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…
We introduce and experimentally demonstrate the utility of tag-based genetic regulation, a new genetic programming (GP) technique that allows programs to dynamically adjust which code modules to express. Tags are evolvable labels that provide a flexible mechanism for referencing code modules. Tag-based genetic regulation extends existing tag-based naming schemes to allow programs to "promote" and "repress" code modules in order to alter expression patterns. This extension allows evolution to structure a program as a gene regulatory network where modules are regulated based on instruction execu…
Traditionally, signal classification is a process in which previous knowledge of the signals is needed. Human experts decide which features are extracted from the signals, and used as inputs to the classification system. This requirement can make significant unknown information of the signal be missed by the experts and not be included in the features. This paper proposes a new method that automatically analyses the signals and extracts the features without any human participation. Therefore, there is no need for previous knowledge about the signals to be classified. The proposed method is bas…
Multi Expression Programming (MEP) is a Genetic Programming variant which encodes multiple solutions in a single chromosome. This paper introduces and deeply describes several strategies for solving binary and multi-class classification problems within the \textit{multi solutions per chromosome} paradigm of MEP. Extensive experiments on various classification problems are performed. MEP shows similar or better performances than other methods used for comparison (namely Artificial Neural Networks and Linear Genetic Programming).
Despite many successful applications, Cartesian Genetic Programming (CGP) suffers from limited scalability, especially when used for evolutionary circuit design. Considering the multiplier design problem, for example, the 5x5-bit multiplier represents the most complex circuit evolved from a randomly generated initial population. The efficiency of CGP highly depends on the performance of the point mutation operator, however, this operator is purely stochastic. This contrasts with the recent developments in Genetic Programming (GP), where advanced informed approaches such as semantic-aware opera…
Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic Programming (GP) is not immune to this problem, which the field has frequently addressed. Recently, Geometric Semantic Genetic Programming (GSGP), a semantic-aware branch of GP, has shown robustness and high generalization capability. Researchers believe these characteristics may be associated with a lower sensibility to noisy data. However, there is no sys…
Credit card fraud detection based on machine learning has recently attracted considerable interest from the research community. One of the most important tasks in this area is the ability of classifiers to handle the imbalance in credit card data. In this scenario, classifiers tend to yield poor accuracy on the fraud class (minority class) despite realizing high overall accuracy. This is due to the influence of the majority class on traditional training criteria. In this paper, we aim to apply genetic programming to address this issue by adapting existing fitness functions. We examine two fitn…
The convolutional neural network (CNN), which is one of the deep learning models, has seen much success in a variety of computer vision tasks. However, designing CNN architectures still requires expert knowledge and a lot of trial and error. In this paper, we attempt to automatically construct CNN architectures for an image classification task based on Cartesian genetic programming (CGP). In our method, we adopt highly functional modules, such as convolutional blocks and tensor concatenation, as the node functions in CGP. The CNN structure and connectivity represented by the CGP encoding metho…
Recently, there emerged revived interests of designing automatic programs (e.g., using genetic/evolutionary algorithms) to optimize the structure of Convolutional Neural Networks (CNNs) for a specific task. The challenge in designing such programs lies in how to balance between large search space of the network structures and high computational costs. Existing works either impose strong restrictions on the search space or use enormous computing resources. In this paper, we study how to design a genetic programming approach for optimizing the structure of a CNN for a given task under limited co…
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.
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. Bloat is uncontrolled growth of code without any gain in fitness and important issue in GP. We surveyed and classified existing literature related to different techniques used by GP research community to deal with the issue of bloat. Moreover, the classifications of different bloat control approaches and measures for bloat are discussed. Next, we tested four bl…
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 rejectin…
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.
