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Journal ArticleDOI

Differential Evolution: A Survey of the State-of-the-Art

01 Feb 2011-IEEE Transactions on Evolutionary Computation (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 15, Iss: 1, pp 4-31
TL;DR: A detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far are presented.
Abstract: Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Citations
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Book ChapterDOI
01 Jan 2014
TL;DR: This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation.
Abstract: Algorithms are important tools for solving problems computationally. All computation involves algorithms, and the efficiency of an algorithm largely determines its usefulness. This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation. A brief history of recent nature-inspired algorithms for optimization is outlined in this chapter.

8,285 citations

Journal ArticleDOI
TL;DR: This paper proposes a novel method for generating one-pixel adversarial perturbations based on differential evolution (DE), which requires less adversarial information (a black-box attack) and can fool more types of networks due to the inherent features of DE.
Abstract: Recent research has revealed that the output of deep neural networks (DNNs) can be easily altered by adding relatively small perturbations to the input vector. In this paper, we analyze an attack in an extremely limited scenario where only one pixel can be modified. For that we propose a novel method for generating one-pixel adversarial perturbations based on differential evolution (DE). It requires less adversarial information (a black-box attack) and can fool more types of networks due to the inherent features of DE. The results show that 67.97% of the natural images in Kaggle CIFAR-10 test dataset and 16.04% of the ImageNet (ILSVRC 2012) test images can be perturbed to at least one target class by modifying just one pixel with 74.03% and 22.91% confidence on average. We also show the same vulnerability on the original CIFAR-10 dataset. Thus, the proposed attack explores a different take on adversarial machine learning in an extreme limited scenario, showing that current DNNs are also vulnerable to such low dimension attacks. Besides, we also illustrate an important application of DE (or broadly speaking, evolutionary computation) in the domain of adversarial machine learning: creating tools that can effectively generate low-cost adversarial attacks against neural networks for evaluating robustness.

1,702 citations


Additional excerpts

  • ...DE is a population-based optimization algorithm for solving complex multi-modal optimization problems [6], [23]....

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Journal ArticleDOI
TL;DR: A comprehensive survey on adversarial attacks on deep learning in computer vision can be found in this paper, where the authors review the works that design adversarial attack, analyze the existence of such attacks and propose defenses against them.
Abstract: Deep learning is at the heart of the current rise of artificial intelligence. In the field of computer vision, it has become the workhorse for applications ranging from self-driving cars to surveillance and security. Whereas, deep neural networks have demonstrated phenomenal success (often beyond human capabilities) in solving complex problems, recent studies show that they are vulnerable to adversarial attacks in the form of subtle perturbations to inputs that lead a model to predict incorrect outputs. For images, such perturbations are often too small to be perceptible, yet they completely fool the deep learning models. Adversarial attacks pose a serious threat to the success of deep learning in practice. This fact has recently led to a large influx of contributions in this direction. This paper presents the first comprehensive survey on adversarial attacks on deep learning in computer vision. We review the works that design adversarial attacks, analyze the existence of such attacks and propose defenses against them. To emphasize that adversarial attacks are possible in practical conditions, we separately review the contributions that evaluate adversarial attacks in the real-world scenarios. Finally, drawing on the reviewed literature, we provide a broader outlook of this research direction.

1,542 citations

Journal ArticleDOI
TL;DR: The components and concepts that are used in various metaheuristics are outlined in order to analyze their similarities and differences and the classification adopted in this paper differentiates between single solution based metaheURistics and population based meta heuristics.

1,343 citations


Cites background from "Differential Evolution: A Survey of..."

  • ...For a more detailed description of many of the existing variants and major application areas of DE, readers should refer to [43,194,63]....

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Journal ArticleDOI
TL;DR: It is found that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research on DE.
Abstract: Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

1,265 citations


Cites background or methods from "Differential Evolution: A Survey of..."

  • ...In this respect, the first comprehensive survey on almost all aspects of the DE family of algorithms was published in 2011 by [40]....

    [...]

  • ...Since then, DE and its variants have emerged as one of the most competitive and versatile family of the evolutionary computing algorithms and have been successfully applied to solve numerous real world problems from diverse domains of science and technology [134,40]....

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  • ...Many DE-variants published subsequently (see [40]) have used this update strategy....

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  • ...The DE family of algorithms commonly uses two crossover methods-exponential (or two-point modulo) and binomial (or uniform) [40]....

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  • ...As was also pointed out in [40], almost eight years back from now, Langdon and Poli [96] made a very interesting study where certain fitness landscapes were evolved with Genetic Programming (GP) to indicate the benefits and weaknesses of a few population-based algorithms like PSO, DE, and CMA-ES....

    [...]

References
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Journal ArticleDOI
13 May 1983-Science
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

41,772 citations

Journal ArticleDOI
TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.

37,111 citations

Book
01 Jan 1975
TL;DR: Names of founding work in the area of Adaptation and modiication, which aims to mimic biological optimization, and some (Non-GA) branches of AI.
Abstract: Name of founding work in the area. Adaptation is key to survival and evolution. Evolution implicitly optimizes organisims. AI wants to mimic biological optimization { Survival of the ttest { Exploration and exploitation { Niche nding { Robust across changing environments (Mammals v. Dinos) { Self-regulation,-repair and-reproduction 2 Artiicial Inteligence Some deenitions { "Making computers do what they do in the movies" { "Making computers do what humans (currently) do best" { "Giving computers common sense; letting them make simple deci-sions" (do as I want, not what I say) { "Anything too new to be pidgeonholed" Adaptation and modiication is root of intelligence Some (Non-GA) branches of AI: { Expert Systems (Rule based deduction)

32,573 citations

Journal ArticleDOI
TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

27,271 citations

Journal ArticleDOI
Rainer Storn1, Kenneth Price
TL;DR: In this article, a new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented, which requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
Abstract: A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.

24,053 citations