The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named Quality-Diversity optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, Quality-Diversity algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. Firstly, we present a unifying framework of Quality-Diversity optimization algorithms that covers the two main algorithms of this family (Multi-dimensional Archive of Phenotypic Elites and the Novelty Search with Local Competition), and that highlights the large variety of variants that can be investigated within this family. Secondly, we propose algorithms with a new selection mechanism for Quality-Diversity algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of Quality-Diversity algorithms on three different experimental scenarios.
The authors of Novelty Search also introduced the Novelty Search with Local Competition'' algorithm (NSLC) @cite_42 , in which the exploration focuses on solutions that are both novel (according to the novelty score) and locally high-performing. The main insight consists of comparing the performance of a solution only to those that are close in the descriptor space. This is achieved with a local quality score'' that is defined as the number of the k-nearest neighboring solutions in the novelty archive with a lower performance (e.g., slower walking speed @cite_42 ) than the considered solution. The exploration is then achieved with a multi-objective optimization algorithm (e.g., NSGA-II @cite_28 ) that optimizes both the novelty and local quality scores of the solutions. However, the local quality score does not influence the threshold used to select whether an individual is added to the novelty archive. The final result of NSLC is the population of the optimization algorithm, which contains solutions that are both novel and high-performing compared to other local solutions. In other words, the population gathers solutions that are both different from those saved in the novelty archive, and high-performing when compared to similar types of solutions.
@cite_28 @cite_42
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The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named quality-diversity (QD) optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, QD algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. First, we present a unifying framework of QD optimization algorithms that covers the two main algorithms of this family (multidimensional archive of phenotypic elites and the novelty search with local competition), and that highlights the large variety of variants that can be investigated within this family. Second, we propose algorithms with a new selection mechanism for QD algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of QD algorithms on three different experimental scenarios. In this paper, we propose using local learning for multiclass novelty detection, a framework that we call local novelty detection. Estimating the novelty of a new sample is an extremely challenging task due to the large variability of known object categories. The features used to judge on the novelty are often very specific for the object in the image and therefore we argue that individual novelty models for each test sample are important. Similar to human experts, it seems intuitive to first look for the most related images thus filtering out unrelated data. Afterwards, the system focuses on discovering similarities and differences to those images only. Therefore, we claim that it is beneficial to solely consider training images most similar to a test sample when deciding about its novelty. Following the principle of local learning, for each test sample a local novelty detection model is learned and evaluated. Our local novelty score turns out to be a valuable indicator for deciding whether the sample belongs to a known category from the training set or to a new, unseen one. With our local novelty detection approach, we achieve state-of-the-art performance in multi-class novelty detection on two popular visual object recognition datasets, Caltech-256 and Image Net. We further show that our framework: (i) can be successfully applied to unknown face detection using the Labeled-Faces-in-the-Wild dataset and (ii) outperforms recent work on attribute-based unfamiliar class detection in fine-grained recognition of bird species on the challenging CUB-200-2011 dataset. Novelty Search is applied for the first time to supervised classification with GP.Two new variants of NS are proposed, overcoming some of its main shortcomings.NS achieves competitive results compared to objective-based search.Results show bloat control properties in binary tasks for NS. Novelty Search (NS) is a unique approach towards search and optimization, where an explicit objective function is replaced by a measure of solution novelty. However, NS has been mostly used in evolutionary robotics while its usefulness in classic machine learning problems has not been explored. This work presents a NS-based genetic programming (GP) algorithm for supervised classification. Results show that NS can solve real-world classification tasks, the algorithm is validated on real-world benchmarks for binary and multiclass problems. These results are made possible by using a domain-specific behavior descriptor. Moreover, two new versions of the NS algorithm are proposed, Probabilistic NS (PNS) and a variant of Minimal Criteria NS (MCNS). The former models the behavior of each solution as a random vector and eliminates all of the original NS parameters while reducing the computational overhead of the NS algorithm. The latter uses a standard objective function to constrain and bias the search towards high performance solutions. The paper also discusses the effects of NS on GP search dynamics and code growth. Results show that NS can be used as a realistic alternative for supervised classification, and specifically for binary problems the NS algorithm exhibits an implicit bloat control ability. An ambitious challenge in artificial life is to craft an evolutionary process that discovers a wide diversity of well-adapted virtual creatures within a single run. Unlike in nature, evolving creatures in virtual worlds tend to converge to a single morphology because selection therein greedily rewards the morphology that is easiest to exploit. However, novelty search, a technique that explicitly rewards diverging, can potentially mitigate such convergence. Thus in this paper an existing creature evolution platform is extended with multi-objective search that balances drives for both novelty and performance. However, there are different ways to combine performance-driven search and novelty search. The suggested approach is to provide evolution with both a novelty objective that encourages diverse morphologies and a local competition objective that rewards individuals outperforming those most similar in morphology. The results in an experiment evolving locomoting virtual creatures show that novelty search with local competition discovers more functional morphological diversity within a single run than models with global competition, which are more predisposed to converge. The conclusions are that novelty search with local competition may complement recent advances in evolving virtual creatures and may in general be a principled approach to combining novelty search with pressure to achieve. Numerous algorithms have been proposed to allow legged robots to learn to walk. However, most of these algorithms are devised to learn walking in a straight line, which is not sufficient to accomplish any real-world mission. Here we introduce the Transferability-based Behavioral Repertoire Evolution algorithm TBR-Evolution, a novel evolutionary algorithm that simultaneously discovers several hundreds of simple walking controllers, one for each possible direction. By taking advantage of solutions that are usually discarded by evolutionary processes, TBR-Evolution is substantially faster than independently evolving each controller. Our technique relies on two methods: 1 novelty search with local competition, which searches for both high-performing and diverse solutions, and 2 the transferability approach, which combines simulations and real tests to evolve controllers for a physical robot. We evaluate this new technique on a hexapod robot. Results show that with only a few dozen short experiments performed on the robot, the algorithm learns a repertoire of controllers that allows the robot to reach every point in its reachable space. Overall, TBR-Evolution introduced a new kind of learning algorithm that simultaneously optimizes all the achievable behaviors of a robot. While evolutionary computation and evolutionary robotics take inspiration from nature, they have long focused mainly on problems of performance optimization. Yet evolution in nature can be interpreted as more nuanced than a process of simple optimization. In particular, natural evolution is a divergent search that optimizes locally within each niche as it simultaneously diversifies. This tendency to discover both quality and diversity at the same time differs from many of the conventional algorithms of machine learning, and also thereby suggests a different foundation for inferring the approach of greatest potential for evolutionary algorithms. In fact, several recent evolutionary algorithms called quality diversity (QD) algorithms(e.g. novelty search with local competition and MAP-Elites) have drawn inspiration from this more nuanced view, aiming to fill a space of possibilities with the best possible example of each type of achievable behavior. The result is a new class of algorithms that return an archive of diverse, high-quality behaviors in a single run. The aim in this paper is to study the application of QD algorithms in challenging environments (in particular complex mazes) to establish their best practices for ambitious domains in the future. In addition to providing insight into cases when QD succeeds and fails, a new approach is investigated that hybridizes multiple views of behaviors (called behavior characterizations) in the same run, which succeeds in overcoming some of the challenges associated with searching for QD with respect to a behavior characterization that is not necessarily sufficient for generating both quality and diversity at the same time. We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1 + λ) and (μ | λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks. Recently, the hybridization between evolutionary algorithms and other metaheuristics has shown very good performances in many kinds of multiobjective optimization problems (MOPs), and thus has attracted considerable attentions from both academic and industrial communities. In this paper, we propose a novel hybrid multiobjective evolutionary algorithm (HMOEA) for real-valued MOPs by incorporating the concepts of personal best and global best in particle swarm optimization and multiple crossover operators to update the population. One major feature of the HMOEA is that each solution in the population maintains a nondominated archive of personal best and the update of each solution is in fact the exploration of the region between a selected personal best and a selected global best from the external archive. Before the exploration, a selfadaptive selection mechanism is developed to determine an appropriate crossover operator from several candidates so as to improve the robustness of the HMOEA for different instances of MOPs. Besides the selection of global best from the external archive, the quality of the external archive is also considered in the HMOEA through a propagating mechanism. Computational study on the biobjective and three-objective benchmark problems shows that the HMOEA is competitive or superior to previous multiobjective algorithms in the literature. Exploration of the search space through the optimisation of phenotypic diversity is of increasing interest within the field of evolutionary robotics. Novelty search and the more recent MAP-Elites are two state of the art evolutionary algorithms which diversify low dimensional phenotypic traits for divergent exploration. In this paper we introduce a novel alternative for rapid divergent search of the feature space. Unlike previous phenotypic search procedures, our proposed Spatial, Hierarchical, Illuminated Neuro-Evolution (SHINE) algorithm utilises a tree structure for the maintenance and selection of potential candidates. SHINE penalises previous solutions in more crowded areas of the landscape. Our experimental results show that SHINE significantly outperforms novelty search and MAP-Elites in both performance and exploration. We conclude that the SHINE algorithm is a viable method for rapid divergent search of low dimensional, phenotypic landscapes. We study the index selection problem: Given a workload consisting of SQL statements on a database, and a user-specified storage constraint, recommend a set of indexes that have the maximum benefit for the given workload. We present a formal statement for this problem and show that it is computationally "hard" to solve or even approximate it. We develop a new algorithm for the problem which is based on treating the problem as a knapsack problem. The novelty of our approach lies in an LP (linear programming) based method that assigns benefits to individual indexes. For a slightly modified algorithm, that does more work, we prove that we can give instance specific guarantees about the quality of our solution. We conduct an extensive experimental evaluation of this new heuristic and compare it with previous solutions. Our results demonstrate that our solution is more scalable while achieving comparable quality. We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems. We introduce a new notion of classification accuracy based on the top τ-quantile values of a scoring function, a relevant criterion in a number of problems arising for search engines. We define an algorithm optimizing a convex surrogate of the corresponding loss, and discuss its solution in terms of a set of convex optimization problems. We also present margin-based guarantees for this algorithm based on the top τ-quantile value of the scores of the functions in the hypothesis set. Finally, we report the results of several experiments in the bipartite setting evaluating the performance of our solution and comparing the results to several other algorithms seeking high precision at the top. In most examples, our solution achieves a better performance in precision at the top. A common setting for novelty detection assumes that labeled examples from the nominal class are available, but that labeled examples of novelties are unavailable. The standard (inductive) approach is to declare novelties where the nominal density is low, which reduces the problem to density level set estimation. In this paper, we consider the setting where an unlabeled and possibly contaminated sample is also available at learning time. We argue that novelty detection in this semi-supervised setting is naturally solved by a general reduction to a binary classification problem. In particular, a detector with a desired false positive rate can be achieved through a reduction to Neyman-Pearson classification. Unlike the inductive approach, semi-supervised novelty detection (SSND) yields detectors that are optimal (e.g., statistically consistent) regardless of the distribution on novelties. Therefore, in novelty detection, unlabeled data have a substantial impact on the theoretical properties of the decision rule. We validate the practical utility of SSND with an extensive experimental study. We also show that SSND provides distribution-free, learning-theoretic solutions to two well known problems in hypothesis testing. First, our results provide a general solution to the general two-sample problem, that is, the problem of determining whether two random samples arise from the same distribution. Second, a specialization of SSND coincides with the standard p-value approach to multiple testing under the so-called random effects model. Unlike standard rejection regions based on thresholded p-values, the general SSND framework allows for adaptation to arbitrary alternative distributions in multiple dimensions. Recent studies have emphasized the merits of search processes that lack overarching objectives, instead promoting divergence by rewarding behavioral novelty. While this less objective search paradigm is more open-ended and divergent, it still differs significantly from nature's mechanism of divergence. Rather than measuring novelty explicitly nature is guided by a single, fundamental constraint: survive long enough to reproduce. Surprisingly, this simple constraint produces both complexity and diversity in a continual process unparalleled by any algorithm to date. Inspired by the relative simplicity of open-endedness in nature in comparison to recent non-objective algorithms, this paper investigates the extent to which interactions between two coevolving populations, both subject to their own constraint, or minimal criterion, can produce results that are both functional and diverse even without any behavior characterization or novelty archive. To test this new approach, a novel maze navigation domain is introduced wherein evolved agents must learn to navigate mazes whose structures are simultaneously coevolving and increasing in complexity. The result is a broad range of maze topologies and successful agent trajectories in a single run, thereby suggesting the viability of minimal criterion coevolution as a new approach to non-objective search and a step towards genuinely open-ended algorithms. Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to some generative distribution, effectively modelling the tails of that distribution. In novelty detection, or one-class classification, we wish to determine if data are “normal” with respect to some model of normality. If that model consists of generative distributions, then EVT is appropriate for describing the behaviour of extremes generated from the model, and can be used to determine the location of decision boundaries that separate “normal” areas of data space from “abnormal” areas in a principled manner. This paper introduces existing work in the use of EVT for novelty detection, shows that existing work does not accurately describe the extrema of multivariate, multimodal generative distributions, and proposes a novel method for overcoming such problems. The method is numerical, and provides optimal solutions for generative multivariate, multimodal distributions of arbitrary complexity. In a companion paper, we present analytical closed-form solutions which are currently limited to unimodal, multivariate generative distributions. We investigate the complexity of finding locally optimal solutions to NP-hard combinatorial optimization problems. Local optimality arises in the context of local search algorithms, which try to find improved solutions by considering perturbations of the current solution (“neighbors” of that solution). If no neighboring solution is better than the current solution, it is locally optimal. Finding locally optimal solutions is presumably easier than finding optimal solutions. Nevertheless, many popular local search algorithms are based on neighborhood structures for which locally optimal solutions are not known to be computable in polynomial time, either by using the local search algorithms themselves or by taking some indirect route. We define a natural class PLS consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and show that there are complete problems for this class. In particular, finding a partition of a graph that is locally optimal with respect to the well-known Kernighan-Lin algorithm for graph partitioning is PLS-complete, and hence can be accomplished in polynomial time only if local optima can be found in polynomial time for all local search problems in PLS. Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering. Abstract This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http: www.alimirjalili.com SCA.html . The speed of optical flow algorithm is crucial for many video editing tasks such as slow motion synthesis, selection propagation, tone adjustment propagation, and so on. Variational coarse-to-fine optical flow algorithms can generally produce high-quality results but cannot fulfil the speed requirement of many practical applications. Besides, large motions in real-world videos also pose a difficult problem to coarse-to-fine variational approaches. We, in this paper, present a fast optical flow algorithm that can handle large displacement motions. Our algorithm is inspired by recent successes of local methods in visual correspondence searching as well as approximate nearest neighbor field algorithms. The main novelty is a fast randomized edge-preserving approximate nearest neighbor field algorithm, which propagates self-similarity patterns in addition to offsets. Experimental results on public optical flow benchmarks show that our method is significantly faster than state-of-the-art methods without compromising on quality, especially when scenes contain large motions. Finally, we show some demo applications by applying our technique into real-world video editing tasks. We address the problem of temporal action localization in videos. We pose action localization as a structured prediction over arbitrary-length temporal windows, where each window is scored as the sum of frame-wise classification scores. Additionally, our model classifies the start, middle, and end of each action as separate components, allowing our system to explicitly model each action's temporal evolution and take advantage of informative temporal dependencies present in this structure. In this framework, we localize actions by searching for the structured maximal sum, a problem for which we develop a novel, provably-efficient algorithmic solution. The frame-wise classification scores are computed using features from a deep Convolutional Neural Network (CNN), which are trained end-to-end to directly optimize for a novel structured objective. We evaluate our system on the THUMOS 14 action detection benchmark and achieve competitive performance.