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What is it?

A collection of papers on divergence and quality diversity.

Table of Contents

Divergent algorithms

Novelty Search


In evolutionary computation, the fitness function normally measures progress towards an objective in the search space, effectively acting as an objective function. Through deception, such objective functions may actually prevent the objective from being reached. While methods exist to mitigate deception, they leave the underlying pathology untreated: Objective functions themselves may actively misdirect search towards dead ends. This paper proposes an approach to circumventing deception that also yields a new perspective on open-ended evolution: Instead of either explicitly seeking an objective or modeling natural evolution to capture open-endedness, the idea is to simply search for behavioral novelty. Even in an objective-based problem, such novelty search ignores the objective. Because many points in the search space collapse to a single behavior, the search for novelty is often feasible. Furthermore, because there are only so many simple behaviors, the search for novelty leads to increasing complexity. By decoupling open-ended search from artificial life worlds, the search for novelty is applicable to real world problems. Counterintuitively, in the maze navigation and biped walking tasks in this paper, novelty search significantly outperforms objective-based search, suggesting the strange conclusion that some problems are best solved by methods that ignore the objective. The main lesson is the inherent limitation of the objective-based paradigm and the unexploited opportunity to guide search through other means.


source code : http://eplex.cs.ucf.edu/software/NoveltySearchC++.zip


title={Abandoning objectives: Evolution through the search for novelty alone},
  author={Lehman, Joel and Stanley, Kenneth O},
  journal={Evolutionary computation},
  publisher={MIT Press}	}



We introduce DeLeNoX (Deep Learning Novelty Explorer), a system that autonomously creates artifacts in constrained spaces according to its own evolving interestingness criterion. DeLeNoX proceeds in alternating phases of exploration and transformation. In the exploration phases, a version of novelty search augmented with constraint handling searches for maximally diverse artifacts using a given distance function. In the transformation phases, a deep learning autoencoder learns to compress the variation between the found artifacts into a lower-dimensional space. The newly trained encoder is then used as the basis for a new distance function, transforming the criteria for the next exploration phase. In the current paper, we apply DeLeNoX to the creation of spaceships suitable for use in two-dimensional arcade-style computer games, a representative problem in procedural content generation in games. We also situate DeLeNoX in relation to the distinction between exploratory and transformational creativity, and in relation to Schmidhuber’s theory of creativity through the drive for compression progress.



  title={Transforming exploratory creativity with DeLeNoX},
  author={Liapis, Antonios and Mart{\i}nez, H{\'e}ctor P and Togelius, Julian and Yannakakis, Georgios N},
  booktitle={Proceedings of the Fourth International Conference on Computational Creativity},
  organization={AAAI Press}

Curiosity Search


Natural animals are renowned for their ability to acquire a diverse and general skill set over the course of their lifetime. However, research in artificial intelligence has yet to produce agents that acquire all or even most of the available skills in non-trivial environments. One candidate algorithm for encouraging the production of such individuals is Novelty Search, which pressures organisms to exhibit different behaviors from other individuals. However, we hypothesized that Novelty Search would produce sub-populations of specialists, in which each individual possesses a subset of skills, but no one organism acquires all or most of the skills. In this paper, we propose a new algorithm called Curiosity Search, which is designed to produce individuals that acquire as many skills as possible during their lifetime. We show that in a multiple-skill maze environment, Curiosity Search does produce individuals that explore their entire domain, while a traditional implementation of Novelty Search produces specialists. However, we reveal that when modified to encourage intra-life behavioral diversity, Novelty Search can produce organisms that explore almost as much of their environment as Curiosity Search, although Curiosity Search retains a significant performance edge. Finally, we show that Curiosity Search is a useful helper objective when combined with Novelty Search, producing individuals that acquire significantly more skills than either algorithm alone.


  title={Curiosity search: producing generalists by encouraging individuals to continually explore and acquire skills throughout their lifetime},
  author={Stanton, Christopher and Clune, Jeff},
  journal={PloS one},
  publisher={Public Library of Science}

Surprise Search


Grounded in the divergent search paradigm and inspired by the principle of surprise for unconventional discovery in computational creativity, this paper introduces surprise search as a new method of evolutionary divergent search. Surprise search is tested in two robot navigation tasks and compared against objective-based evolutionary search and novelty search. The key findings of this paper reveal that surprise search is advantageous compared to the other two search processes. It outperforms objective search and it is as efficient as novelty search in both tasks examined. Most importantly, surprise search is, on average, faster and more robust in solving the navigation problem compared to objective and novelty search. Our analysis reveals that surprise search explores the behavioral space more extensively and yields higher population diversity compared to novelty search.


source code : http://www.autogamedesign.eu/software


  title={Surprise search: Beyond objectives and novelty},
  author={Gravina, Daniele and Liapis, Antonios and Yannakakis, Georgios},
  booktitle={Proceedings of the 2016 on Genetic and Evolutionary Computation Conference},

Coupling Novelty and Surprise for Evolutionary Divergence


Divergent search techniques applied to evolutionary computation, such as novelty search and surprise search, have demonstrated their efficacy in highly deceptive problems compared to traditional objective-based fittness evolutionary processes. While novelty search rewards unseen solutions, surprise search rewards unexpected solutions. As a result these two algorithms perform a different form of search since an expected solution can be novel while an already seen solution can be surprising. As novelty and surprise search have already shown much promise individually, the hypothesis is that an evolutionary process that rewards both novel and surprising solutions will be able to handle deception in a better fashion and lead to more successful solutions faster. In this paper we introduce an algorithm that realises both novelty and surprise search and we compare it against the two algorithms that compose it in a number of robot navigation tasks. The key findings of this paper suggest that coupling novelty and surprise is advantageous compared to each search approach on its own. The introduced algorithm breaks new ground in divergent search as it outperforms both novelty and surprise in terms of efficiency and robustness, and it explores the behavioural space more extensively.


source code : http://www.autogamedesign.eu/software

  title={Coupling Novelty and Surprise for Evolutionary Divergence},
  author={Gravina, Daniele and Liapis, Antonios and Yannakakis, Georgios N},
  booktitle={Proceedings of the Genetic and Evolutionary Computation Conference},

Minimal Criterion Coevolution


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.


  title={Minimal Criterion Coevolution},
  author={Brant, Jonathan C and  Stanley, Kenneth O},
  booktitle={Proceedings of the 2017 on Genetic and Evolutionary Computation Conference},

Source code: https://github.com/jbrant/MinimalCriterionCoevolution/releases/



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


  title={Rapid phenotypic landscape exploration through hierarchical spatial partitioning},
  author={Smith, Davy and Tokarchuk, Laurissa and Wiggins, Geraint},
  booktitle={International conference on parallel problem solving from nature},

Quality Diversity algorithms

Novelty Search Multiobjectivation


Novelty search is a recent and promising approach to evolve neurocontrollers, especially to drive robots. The main idea is to maximize the novelty of behaviors instead of the efficiency. However, abandoning the efficiency objective(s) may be too radical in many contexts. In this paper, a Pareto-based multi-objective evolutionary algorithmis employed to reconcile novelty search with objective-based optimization by following a multiobjectivization process. Several multiobjectivizations based on behavioral novelty and on behavioral diversity are compared on a maze navigation task. Results show that the bi-objective variant “Novelty + Fitness” is better at fine-tuning behaviors than basic novelty search, while keeping a comparable number of iterations to converge.


  title={Novelty-based multiobjectivization},
  author={Mouret, Jean-Baptiste},
  booktitle={New horizons in evolutionary robotics},

Novelty Search with Local Competition


An ambitious challenge in artificial life is to craft an evolutionary process that discovers a wide diversity of welladapted 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.


  title={Evolving a diversity of virtual creatures through novelty search and local competition},
  author={Lehman, Joel and Stanley, Kenneth O},
  booktitle={Proceedings of the 13th annual conference on Genetic and evolutionary computation},



Nearly all science and engineering 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 highestperforming 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 highperforming 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 costto-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 MAPElites (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 the state-of-the-art for finding a single, best solution, it will catalyze advances throughout all science and engineering fields.


  title={Illuminating search spaces by mapping elites},
  author={Mouret, Jean-Baptiste and Clune, Jeff},
  journal={arXiv preprint arXiv:1504.04909},

source code: https://github.com/sferes2/map_elites

Quality Diversity


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.


  title={Quality diversity: A new frontier for evolutionary computation},
  author={Pugh, Justin K and Soros, Lisa B and Stanley, Kenneth O},
  journal={Frontiers in Robotics and AI},

Constrained Novelty Search


Novelty search is a recent algorithm geared towards exploring search spaces without regard to objectives. When the presence of constraints divides a search space into feasible space and infeasible space, interesting implications arise regarding how novelty search explores such spaces. This paper elaborates on the problem of constrained novelty search and proposes two novelty search algorithms which search within both the feasible and the infeasible space. Inspired by the FI-2pop genetic algorithm, both algorithms maintain and evolve two separate populations, one with feasible and one with infeasible individuals, while each population can use its own selection method. The proposed algorithms are applied to the problem of generating diverse but playable game levels, which is representative of the larger problem of procedural game content generation. Results show that the two-population constrained novelty search methods can create, under certain conditions, larger and more diverse sets of feasible game levels than current methods of novelty search, whether constrained or unconstrained. However, the best algorithm is contingent on the particularities of the search space and the genetic operators used. Additionally, the proposed enhancement of offspring boosting is shown to enhance performance in all cases of two-population novelty search.



  title={Constrained novelty search: A study on game content generation},
  author={Liapis, Antonios and Yannakakis, Georgios N and Togelius, Julian},
  journal={Evolutionary computation},
  publisher={MIT Press}

Quality and Diversity Optimization: A Unifying Modular Framework


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


  title={Quality and Diversity Optimization: A Unifying Modular Framework},
  author={Cully, Antoine and  Demiris, Yiannis},
  journal={IEEE transactions on evolutionary computation},

Source code: https://github.com/sferes2/modular_QD

Surrogate-Assisted Illumination (SAIL)


The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique to ’illuminate’ the problem space through the lens of chosen features has the potential to be a powerful tool for exploring design spaces, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination (SAIL) algorithm, introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites. The ability of SAIL to efficiently produce both accurate models and diverse high-performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMAES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.


  title={Data-efficient exploration, optimization, and modeling of diverse designs through surrogate-assisted illumination},
  author={Gaier, Adam and Asteroth, Alexander and Mouret, Jean-Baptiste},
  booktitle={Proceedings of the Genetic and Evolutionary Computation Conference},

Quality Diversity Through Surprise


Quality diversity is a recent evolutionary computation paradigm which maintains an appropriate balance between divergence and convergence and has achieved promising results in complex problems. There is, however, limited exploration on how different paradigms of divergent search may impact the solutions found by quality diversity algorithms. Inspired by the notion of surprise as an effective driver of divergent search and its orthogonal nature to novelty this paper investigates the impact of the former to quality diversity performance. For that purpose we introduce three new quality diversity algorithms which use surprise as a diversity measure, either on its own or combined with novelty, and compare their performance against novelty search with local competition, the state of the art quality diversity algorithm. The algorithms are tested in a robot maze navigation task, in a challenging set of 60 deceptive mazes. Our findings suggest that allowing surprise and novelty to operate synergistically for divergence and in combination with local competition leads to quality diversity algorithms of significantly higher efficiency, speed and robustness.


  title={Quality Diversity Through Surprise},
  author={Gravina, Daniele and Liapis, Antonios and Yannakakis, Georgios N},
  journal={arXiv preprint arXiv:1807.02397},

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Divergence and Quality Diversity is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.