Photomosaic images are a type of images consisting of various tiny images. A complete form can be seen clearly by viewing it from a long distance. Small tiny images which replace blocks of the original image can be seen clearly by viewing it from a short distance. In the past, many algorithms have been proposed trying to automatically compose photomosaic images. Most of these algorithms are designed with greedy algorithms to match the blocks with the tiny images. To obtain a better visual sense and satisfy some commercial requirements, a constraint that a tiny image should not be repeatedly used many times is usually added. With the constraint, the photomosaic problem becomes a combinatorial optimization problem. Evolutionary algorithms imitating the process of natural selection are popular and powerful in combinatorial optimization problems. However, little work has been done on applying evolutionary algorithms to photomosaic problem. In this paper, we present an algorithm called clustering based evolutionary programming to deal with the problem. We give prior knowledge to the optimization algorithm which makes the optimization process converges faster. In our experiment, the proposed algorithm is compared with the state of the art algorithms and software. The results indicate that our algorithm performs the best.
In parallel and distributed environments, generational evolutionary algorithms often do not exploit the full potential of the computation system since they have to wait until the entire population is evaluated before starting selection procedures. Steady-state algorithms are often seen as a solution to this problem, since fitness evaluation can be done by multiple threads in an asynchronous way. However, if the algorithm updates its state in a complicated way, the threads will eventually have to wait until this update finishes. State update procedures that are computationally expensive are common in multiobjective evolutionary algorithms. We have implemented an asynchronous steady-state version of the NSGA-II algorithm. Its most expensive part, non-dominated sorting, determines the time needed to update the state. We turned the existing incremental non-dominated sorting algorithm into an asynchronous one using several concurrency techniques: a single entry-level lock, finer-grained locks working with non-domination levels, and a non-blocking approach using compare-and-set operations. Our experimental results reveal the trade-off between the work-efficiency of the algorithm and the achieved amount of parallelism.
Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these algorithms are not well understood and the field is lacking a solid theoretical foundation that explains when and why memetic algorithms are effective. We provide a rigorous runtime analysis of a simple memetic algorithm, the $(1+1)$ MA, on the Hurdle problem class, a landscape class of tuneable difficulty that shows a "big valley structure", a characteristic feature of many hard problems from combinatorial optimisation. The only parameter of this class is the hurdle width w, which describes the length of fitness valleys that have to be overcome. We show that the $(1+1)$ EA requires $\Theta(n^w)$ expected function evaluations to find the optimum, whereas the $(1+1)$ MA with best-improvement and first-improvement local search can find the optimum in $\Theta(n^2+n^3/w^2)$ and $\Theta(n^3/w^2)$ function evaluations, respectively. Surprisingly, while increasing the hurdle width makes the problem harder for evolutionary algorithms, the problem becomes easier for memetic algorithms. We discuss how these findings can explain and illustrate the success of memetic algorithms for problems with big valley structures.
The area of computation called artificial intelligence (AI) is falsified by describing a previous 1972 falsification of AI by British mathematical physicist James Lighthill. How Lighthill's arguments continue to apply to current AI is explained. It is argued that AI should use the Popperian scientific method in which it is the duty of scientists to attempt to falsify theories and if theories are falsified to replace or modify them. The paper describes the Popperian method and discusses Paul Nurse's application of the method to cell biology that also involves questions of mechanism and behavior. It is shown how Lighthill's falsifying arguments especially combinatorial explosion continue to apply to modern AI. Various skeptical arguments against the assumptions of AI mostly by physicists especially against Hilbert's philosophical programme that defined knowledge and truth as provable formal sentences. John von Neumann's arguments from natural complexity against neural networks and evolutionary algorithms are discussed. Next the game of chess is discussed to show how modern chess experts have reacted to computer chess programs. It is shown that currently chess masters can defeat any chess program using Kasperov's arguments from his 1997 Deep Blue match and aftermath. The game of 'go' and climate models are discussed to show computer applications where combinatorial explosion may not apply. The paper concludes by advocating studying computation as Peter Naur's Dataology.
Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in ${\raise.17ex\hbox{$\scriptstyle\sim$}}$4 hours on one desktop or ${\raise.17ex\hbox{$\scriptstyle\sim$}}$1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.
We introduce a novel approach for discriminative classification using evolutionary algorithms. We first propose an algorithm to optimize the total loss value using a modified 0-1 loss function in a one-dimensional space for classification. We then extend this algorithm for multi-dimensional classification using an evolutionary algorithm. The proposed evolutionary algorithm aims to find a hyperplane which best classifies instances while minimizes the classification risk. We test particle swarm optimization, evolutionary strategy, and covariance matrix adaptation evolutionary strategy for optimization purpose. Finally, we compare our results with well-established and state-of-the-art classification algorithms, for both binary and multi-class classification, on 19 benchmark classification problems, with and without noise and outliers. Results show that the performance of the proposed algorithm is significantly (t-test) better than all other methods in almost all problems tested. We also show that the proposed algorithm is significantly more robust against noise and outliers comparing to other methods. The running time of the algorithm is within a reasonable range for the solution of real-world classification problems.
We establish global convergence of the (1+1) evolution strategy, i.e., convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the notion of a critical point to measurable functions. At its core, the analysis is based on a novel progress guarantee for elitist, rank-based evolutionary algorithms. By applying it to the (1+1) evolution strategy we are able to provide an accurate characterization of whether global convergence is guaranteed with full probability, or whether premature convergence is possible. We illustrate our results on a number of example applications ranging from smooth (non-convex) cases over different types of saddle points and ridge functions to discontinuous and extremely rugged problems.
Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimisation. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimisation. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimisation, but MOEAs based on non-dominance, such as PMODE, may not.
Recent advances in deep neuroevolution have demonstrated that evolutionary algorithms, such as evolution strategies (ES) and genetic algorithms (GA), can scale to train deep neural networks to solve difficult reinforcement learning (RL) problems. However, it remains a challenge to analyze and interpret the underlying process of neuroevolution in such high dimensions. To begin to address this challenge, this paper presents an interactive data visualization tool called VINE (Visual Inspector for NeuroEvolution) aimed at helping neuroevolution researchers and end-users better understand and explore this family of algorithms. VINE works seamlessly with a breadth of neuroevolution algorithms, including ES and GA, and addresses the difficulty of observing the underlying dynamics of the learning process through an interactive visualization of the evolving agent's behavior characterizations over generations. As neuroevolution scales to neural networks with millions or more connections, visualization tools like VINE that offer fresh insight into the underlying dynamics of evolution become increasingly valuable and important for inspiring new innovations and applications.
Many real-world control and classification tasks involve a large number of features. When artificial neural networks (ANNs) are used for modeling these tasks, the network architectures tend to be large. Neuroevolution is an effective approach for optimizing ANNs; however, there are two bottlenecks that make their application challenging in case of high-dimensional networks using direct encoding. First, classic evolutionary algorithms tend not to scale well for searching large parameter spaces; second, the network evaluation over a large number of training instances is in general time-consuming. In this work, we propose an approach called the Limited Evaluation Cooperative Co-evolutionary Differential Evolution algorithm (LECCDE) to optimize high-dimensional ANNs. The proposed method aims to optimize the pre-synaptic weights of each post-synaptic neuron in different subpopulations using a Cooperative Co-evolutionary Differential Evolution algorithm, and employs a limited evaluation scheme where fitness evaluation is performed on a relatively small number of training instances based on fitness inheritance. We test LECCDE on three datasets with various sizes, and our results show that cooperative co-evolution significantly improves the test error comparing to standard Differential Evolution, while the limited evaluation scheme facilitates a significant reduction in computing time.
Deep Reinforcement Learning (DRL) algorithms have been successfully applied to a range of challenging control tasks. However, these methods typically suffer from three core difficulties: temporal credit assignment with sparse rewards, lack of effective exploration, and brittle convergence properties that are extremely sensitive to hyperparameters. Collectively, these challenges severely limit the applicability of these approaches to real-world problems. Evolutionary Algorithms (EAs), a class of black box optimization techniques inspired by natural evolution, are well suited to address each of these three challenges. However, EAs typically suffer from high sample complexity and struggle to solve problems that require optimization of a large number of parameters. In this paper, we introduce Evolutionary Reinforcement Learning (ERL), a hybrid algorithm that leverages the population of an EA to provide diversified data to train an RL agent, and reinserts the RL agent into the EA population periodically to inject gradient information into the EA. ERL inherits EA's ability of temporal credit assignment with a fitness metric, effective exploration with a diverse set of policies, and stability of a population-based approach and complements it with off-policy DRL's ability to leverage gradients for higher sample efficiency and faster learning. Experiments in a range of challenging continuous control benchmarks demonstrate that ERL significantly outperforms prior DRL and EA methods.
Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions ${\rm O{\small NE}M{\small IN}M{\small AX}}$ and ${\rm LOTZ}$ can significantly improve their performance. Our theoretical results are accompanied by experimental studies that show a correspondence between theory and empirical results and motivate further theoretical investigations in terms of stagnation. We show that stagnation might occur when favouring individuals with a high diversity contribution in the parent selection step and provide a discussion on which scheme to use for more complex problems based on our theoretical and experimental results.
Fast Neural Architecture Construction (NAC) is a method to construct deep network architectures by pruning and expansion of a base network. In recent years, several automated search methods for neural network architectures have been proposed using methods such as evolutionary algorithms and reinforcement learning. These methods use a single scalar objective function (usually accuracy) that is evaluated after a full training and evaluation cycle. In contrast NAC directly compares the utility of different filters using statistics derived from filter featuremaps reach a state where the utility of different filters within a network can be compared and hence can be used to construct networks. The training epochs needed for filters within a network to reach this state is much less than the training epochs needed for the accuracy of a network to stabilize. NAC exploits this finding to construct convolutional neural nets (CNNs) with close to state of the art accuracy, in < 1 GPU day, faster than most of the current neural architecture search methods. The constructed networks show close to state of the art performance on the image classification problem on well known datasets (CIFAR-10, ImageNet) and consistently show better performance than hand constructed and randomly generated networks of the same depth, operators and approximately the same number of parameters.
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current mutation rate and the other half with half the current rate. The mutation rate is then updated to the rate used in that subpopulation which contains the best offspring. We analyze how the $(1+\lambda)$ evolutionary algorithm with this self-adjusting mutation rate optimizes the OneMax test function. We prove that this dynamic version of the $(1+\lambda)$ EA finds the optimum in an expected optimization time (number of fitness evaluations) of $O(n\lambda/\log\lambda+n\log n)$. This time is asymptotically smaller than the optimization time of the classic $(1+\lambda)$ EA. Previous work shows that this performance is best-possible among all $\lambda$-parallel mutation-based unbiased black-box algorithms. This result shows that the new way of adjusting the mutation rate can find optimal dynamic parameter values on the fly. Since our adjustment mechanism is simpler than the ones previously used for adjusting the mutation rate and does not have parameters itself, we are optimistic that it will find other applications.
Deep neural networks are vulnerable to adversarial examples, even in the black-box setting, where the attacker is restricted solely to query access. Existing black-box approaches to generating adversarial examples typically require a significant number of queries, either for training a substitute network or performing gradient estimation. We introduce GenAttack, a gradient-free optimization technique that uses genetic algorithms for synthesizing adversarial examples in the black-box setting. Our experiments on different datasets (MNIST, CIFAR-10, and ImageNet) show that GenAttack can successfully generate visually imperceptible adversarial examples against state-of-the-art image recognition models with orders of magnitude fewer queries than previous approaches. Against MNIST and CIFAR-10 models, GenAttack required roughly 2,126 and 2,568 times fewer queries respectively, than ZOO, the prior state-of-the-art black-box attack. In order to scale up the attack to large-scale high-dimensional ImageNet models, we perform a series of optimizations that further improve the query efficiency of our attack leading to 237 times fewer queries against the Inception-v3 model than ZOO. Furthermore, we show that GenAttack can successfully attack some state-of-the-art ImageNet defenses, including ensemble adversarial training and non-differentiable or randomized input transformations. Our results suggest that evolutionary algorithms open up a promising area of research into effective black-box attacks.
Evolutionary algorithms (EAs) are population-based metaheuristics, originally inspired by aspects of natural evolution. Modern varieties incorporate a broad mixture of search mechanisms, and tend to blend inspiration from nature with pragmatic engineering concerns; however, all EAs essentially operate by maintaining a population of potential solutions and in some way artificially 'evolving' that population over time. Particularly well-known categories of EAs include genetic algorithms (GAs), Genetic Programming (GP), and Evolution Strategies (ES). EAs have proven very successful in practical applications, particularly those requiring solutions to combinatorial problems. EAs are highly flexible and can be configured to address any optimization task, without the requirements for reformulation and/or simplification that would be needed for other techniques. However, this flexibility goes hand in hand with a cost: the tailoring of an EA's configuration and parameters, so as to provide robust performance for a given class of tasks, is often a complex and time-consuming process. This tailoring process is one of the many ongoing research areas associated with EAs.
We have previously shown how to socially integrate a fish robot into a group of zebrafish thanks to biomimetic behavioural models. The models have to be calibrated on experimental data to present correct behavioural features. This calibration is essential to enhance the social integration of the robot into the group. When calibrated, the behavioural model of fish behaviour is implemented to drive a robot with closed-loop control of social interactions into a group of zebrafish. This approach can be useful to form mixed-groups, and study animal individual and collective behaviour by using biomimetic autonomous robots capable of responding to the animals in long-standing experiments. Here, we show a methodology for continuous real-time calibration and refinement of multi-level behavioural model. The real-time calibration, by an evolutionary algorithm, is based on simulation of the model to correspond to the observed fish behaviour in real-time. The calibrated model is updated on the robot and tested during the experiments. This method allows to cope with changes of dynamics in fish behaviour. Moreover, each fish presents individual behavioural differences. Thus, each trial is done with naive fish groups that display behavioural variability. This real-time calibration methodology can optimise the robot behaviours during the experiments. Our implementation of this methodology runs on three different computers that perform individual tracking, data-analysis, multi-objective evolutionary algorithms, simulation of the fish robot and adaptation of the robot behavioural models, all in real-time.
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, e.g., the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. Surprisingly, the probability of deviating by an $r$-factor in lower order terms of the expected time decreases exponentially with $r$ on all these problems. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Moreover, our theorem can be specialized into virtually all existing drift theorems with drift towards the target from the literature. Finally, user-friendly specializations of the general drift theorem are given.
In this paper we propose a technique to reduce the number of function evaluations, which is often the bottleneck of the black-box optimization, in the information geometric optimization (IGO) that is a generic framework of the probability model-based black-box optimization algorithms and generalizes several well-known evolutionary algorithms, such as the population-based incremental learning (PBIL) and the pure rank-$\mu$ update covariance matrix adaptation evolution strategy (CMA-ES). In each iteration, the IGO algorithms update the parameters of the probability distribution to the natural gradient direction estimated by Monte-Carlo with the samples drawn from the current distribution. Our strategy is to reuse previously generated and evaluated samples based on the importance sampling. It is a technique to reduce the estimation variance without introducing a bias in Monte-Carlo estimation. We apply the sample reuse technique to the PBIL and the pure rank-$\mu$ update CMA-ES and empirically investigate its effect. The experimental results show that the sample reuse helps to reduce the number of function evaluations on many benchmark functions for both the PBIL and the pure rank-$\mu$ update CMA-ES. Moreover, we demonstrate how to combine the importance sampling technique with a variant of the CMA-ES involving an algorithmic component that is not derived in the IGO framework.
Continuous action policy search is currently the focus of intensive research, driven both by the recent success of deep reinforcement learning algorithms and the emergence of competitors based on evolutionary algorithms. In this paper, we present a broad survey of policy search methods, providing a unified perspective on very different approaches, including also Bayesian Optimization and directed exploration methods. The main message of this overview is in the relationship between the families of methods, but we also outline some factors underlying sample efficiency properties of the various approaches.