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.
Following different inspirations from the works presented above, the Multi-dimensional Archive of Phenotypic Elites () algorithm @cite_44 has been recently introduced. While this algorithm was first designed to illuminate'' the landscape of objective functions @cite_9 , it showed itself to be an effective algorithm to generate a collection of solutions that are both diverse and high-performing. The main difference with NSLC and BR-Evolution is that, in MAP-Elites, the population of the algorithms is the collection itself, and the selection, mutations and preservation mechanisms directly consider the solutions that are stored in the collection.
@cite_44 @cite_9
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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. The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, pre-defined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in a hexapod locomotion task. 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. 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. In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments. Previous research indicates that during the past 20 years, the highest-quality work has been published in an increasingly diverse and larger group of journals. In this article, we examine whether this diversification has also affected the handful of elite journals that are traditionally considered to be the best. We examine citation patterns during the past 40 years of seven long-standing traditionally elite journals and six journals that have been increasing in importance during the past 20 years. To be among the top 5 or 1 cited papers, papers now need about twice as many citations as they did 40 years ago. Since the late 1980s and early 1990s, elite journals have been publishing a decreasing proportion of these top-cited papers. This also applies to the two journals that are typically considered as the top venues and often used as bibliometric indicators of "excellence": Science and Nature. On the other hand, several new and established journals are publishing an increasing proportion of the most-cited papers. These changes bring new challenges and opportunities for all parties. Journals can enact policies to increase or maintain their relative position in the journal hierarchy. Researchers now have the option to publish in more diverse venues knowing that their work can still reach the same audiences. Finally, evaluators and administrators need to know that although there will always be a certain prestige associated with publishing in "elite" journals, journal hierarchies are in constant flux. 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. Learning in robotics typically involves choosing a simple goal (e.g. walking) and assessing the performance of each controller with regard to this task (e.g. walking speed). However, learning advanced, input-driven controllers (e.g. walking in each direction) requires testing each controller on a large sample of the possible input signals. This costly process makes difficult to learn useful low-level controllers in robotics. Here we introduce BR-Evolution, a new evolutionary learning technique that generates a behavioral repertoire by taking advantage of the candidate solutions that are usually discarded. Instead of evolving a single, general controller, BR-evolution thus evolves a collection of simple controllers, one for each variant of the target behavior; to distinguish similar controllers, it uses a performance objective that allows it to produce a collection of diverse but high-performing behaviors. We evaluated this new technique by evolving gait controllers for a simulated hexapod robot. Results show that a single run of the EA quickly finds a collection of controllers that allows the robot to reach each point of the reachable space. Overall, BR-Evolution opens a new kind of learning algorithm that simultaneously optimizes all the achievable behaviors of a robot. Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution(s) of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments. The differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. In contrast, micro-DE (MDE) algorithms employ a very small population size, which can converge faster to a reasonable solution. However, these algorithms are vulnerable to a premature convergence as well as to high risk of stagnation. In this paper, MDE algorithm with vectorized random mutation factor (MDEVM) is proposed, which utilizes the small size population benefit while empowers the exploration ability of mutation factor through randomizing it in the decision variable level. The idea is supported by analyzing mutation factor using Monte-Carlo based simulations. To facilitate the usage of MDE algorithms with very-small population sizes, new mutation schemes for population sizes less than four are also proposed. Furthermore, comprehensive comparative simulations and analysis on performance of the MDE algorithms over various mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, and mutation factor ranges are conducted by considering population diversity analysis for stagnation and trapping in local optimum situations. The studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance and convergence speed of the proposed MDEVM algorithm. Abstract The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability scheme is utilized to balance the global exploration and local exploitation. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and or premature convergence. Numerical experiments and comparisons on a set of well-known high dimensional benchmark functions indicate that the improved algorithm outperforms and is superior to other existing algorithms in terms of final solution quality, success rate, convergence rate, and robustness. Automatic generation of poetry has always been considered a hard nut in natural language generation.This paper reports some pioneering research on a possible generic algorithm and its automatic generation of SONGCI.In light of the characteristics of Chinese ancient poetry,this paper designed the level and oblique tones-based coding method,the syntactic and semantic weighted function of fitness,the elitism and roulette-combined selection operator,and the partially mapped crossover operator and the heuristic mutation operator.As shown by tests,the system constructed on the basis of the computing model designed in this paper is basically capable of generating Chinese SONGCI with some aesthetic merit.This work represents progress in the field of Chinese poetry automatic generation. Understanding the impact of crossover on performance is a major problem in the theory of genetic algorithms (GAs). We present new insight on working principles of crossover by analyzing the performance of crossover-based GAs on the simple functions OneMax and Jump. First, we assess the potential speedup by crossover when combined with a fitness-invariant bit shuffling operator that simulates a lineage of independent evolution on a function of unitation. Theoretical and empirical results show drastic speedups for both functions. Second, we consider a simple GA without shuffling and investigate the interplay of mutation and crossover on Jump. If the crossover probability is small, subsequent mutations create sufficient diversity, even for very small populations. Contrarily, with high crossover probabilities crossover tends to lose diversity more quickly than mutation can create it. This has a drastic impact on the performance on Jump. We complement our theoretical findings by Monte Carlo simulations on the population diversity. 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. Introduce a new time-dependent UAV heterogeneous fleet routing problem.Consider several objective functions and respect drones operational requirements.Design a MILP model in order to find sets of non-dominated solutions.Consider a model able to tackle multi-layer scenarios with package exchanging points.Integrate UAV into the new concepts of mini microgrid systems inside smart cities. This paper introduces an Unmanned Aerial Vehicle (UAV) heterogeneous fleet routing problem, dealing with vehicles limited autonomy by considering multiple charging stations and respecting operational requirements. A green routing problem is designed for overcoming difficulties that exist as a result of limited vehicle driving range. Due to the large amount of drones emerging in the society, UAVs use and efficiency should be optimized. In particular, these kinds of vehicles have been recently used for delivering and collecting products. Here, we design a new real-time routing problem, in which different types of drones can collect and deliver packages. These aerial vehicles are able to collect more than one deliverable at the same time if it fits their maximum capacity. Inspired by a multi-criteria view of real systems, seven different objective functions are considered and sought to be minimized using a Mixed-Integer Linear Programming (MILP) model solved by a matheuristic algorithm. The latter filters the non-dominated solutions from the pool of solutions found in the branch-and-bound optimization tree, using a black-box dynamic search algorithm. A case of study, considering a bi-layer scenario, is presented in order to validate the proposal, which showed to be able to provide good quality solutions for supporting decision making. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] 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. This article deals with optimization problems to be solved in the absence of a full power computer device. The goal is to solve a complex optimization problem by using a control card related to portable devices, e.g. for the control of commercial robots. In order to handle this class of optimization problems, a novel Memetic Computing approach is presented. The proposed algorithm employs a Differential Evolution framework which instead of processing an actual population of candidate solutions, makes use of a statistical representation of the population which evolves over time. In addition, the framework uses a stochastic local search algorithm which attempts to enhance the performance of the elite. In this way, the memetic logic of performing the optimization by observing the decision space from complementary perspectives can be integrated within computational devices characterized by a limited memory. The proposed algorithm, namely Memetic compact Differential Evolution (McDE), has been tested and compared with other algorithms belonging to the same category for a real-world industrial application, i.e. the control system design of a cartesian robot for variable mass movements. For this real-world application, the proposed McDE displays high performance and has proven to considerably outperform other compact algorithms representing the current state-of-the-art in this sub-field of computational intelligence. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. This abstract summarizes a previous publication in which we used Avida, a well-studied artificial life platform, to investigate the ability of natural selection to adjust and optimize mutation rates. Our initial experiments occurred in a previously studied environment with a complex fitness landscape ( Nature, 423, 2003) where Avidians were rewarded for performing any of nine logic tasks. We assessed the optimal mutation rate by empirically determining which unchanging mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve and we evaluated their proximity to the optimum. Although we chose conditions favorable for mutation rate optimization (asexual organisms not yet adapted to a new environment), the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings (Fig. 1). We hypothesized that the reason mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified 'counting ones' landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates (Fig. 2, top row). In contrast, once moderate fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost (Fig. 2, bottom two rows). Additional experiments revealed that lowering the rate at which mutation rates evolved did not preclude the evolution of suboptimal mutation rates (see original manuscript). We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation because of the short-term costs of traversing fitness valleys. This finding has important implications for evolutionary research in both biological and computational realms. A new efficient optimization method, called 'Teaching-Learning-Based Optimization (TLBO)', is proposed in this paper for the optimization of mechanical design problems. This method works on the effect of influence of a teacher on learners. Like other nature-inspired algorithms, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. The population is considered as a group of learners or a class of learners. The process of TLBO is divided into two parts: the first part consists of the 'Teacher Phase' and the second part consists of the 'Learner Phase'. 'Teacher Phase' means learning from the teacher and 'Learner Phase' means learning by the interaction between learners. The basic philosophy of the TLBO method is explained in detail. To check the effectiveness of the method it is tested on five different constrained benchmark test functions with different characteristics, four different benchmark mechanical design problems and six mechanical design optimization problems which have real world applications. The effectiveness of the TLBO method is compared with the other population-based optimization algorithms based on the best solution, average solution, convergence rate and computational effort. Results show that TLBO is more effective and efficient than the other optimization methods for the mechanical design optimization problems considered. This novel optimization method can be easily extended to other engineering design optimization problems.