Evaluating MAP-Elites on Constrained Optimization Problems

Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. While some constraints are hard and as such must be satisfied with zero-tolerance, others may be soft, such that non-zero violations are acceptable. Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. On the one hand, MAP-Elites implicitly preserves diversity, thus allowing a good exploration of the search space. On the other hand, it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms that use gradient information or advanced constraint handling techniques. Nevertheless, it has a higher potential at finding constraint violations vs. objectives trade-offs and providing new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms

Learning the Designer's Preferences to Drive Evolution

This paper presents the Designer Preference Model, a data-driven solution that pursues to learn from user generated data in a Quality-Diversity Mixed-Initiative Co-Creativity (QD MI-CC) tool, with the aims of modelling the user's design style to better assess the tool's procedurally generated content with respect to that user's preferences. Through this approach, we aim for increasing the user's agency over the generated content in a way that neither stalls the user-tool reciprocal stimuli loop nor fatigues the user with periodical suggestion handpicking. We describe the details of this novel solution, as well as its implementation in the MI-CC tool the Evolutionary Dungeon Designer. We present and discuss our findings out of the initial tests carried out, spotting the open challenges for this combined line of research that integrates MI-CC with Procedural Content Generation through Machine Learning.Comment: 16 pages, Accepted and to appear in proceedings of the 23rd European Conference on the Applications of Evolutionary and bio-inspired Computation, EvoApplications 202

Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate a diverse range of solutions, these algorithms require a large number of evaluations for exploration of continuous spaces. Meanwhile, variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are among the best-performing derivative-free optimizers in single-objective continuous domains. This paper proposes a new QD algorithm called Covariance Matrix Adaptation MAP-Elites (CMA-ME). Our new algorithm combines the self-adaptation techniques of CMA-ES with archiving and mapping techniques for maintaining diversity in QD. Results from experiments based on standard continuous optimization benchmarks show that CMA-ME finds better-quality solutions than MAP-Elites; similarly, results on the strategic game Hearthstone show that CMA-ME finds both a higher overall quality and broader diversity of strategies than both CMA-ES and MAP-Elites. Overall, CMA-ME more than doubles the performance of MAP-Elites using standard QD performance metrics. These results suggest that QD algorithms augmented by operators from state-of-the-art optimization algorithms can yield high-performing methods for simultaneously exploring and optimizing continuous search spaces, with significant applications to design, testing, and reinforcement learning among other domains.Comment: Accepted to GECCO 202

Generating Levels That Teach Mechanics

The automatic generation of game tutorials is a challenging AI problem. While it is possible to generate annotations and instructions that explain to the player how the game is played, this paper focuses on generating a gameplay experience that introduces the player to a game mechanic. It evolves small levels for the Mario AI Framework that can only be beaten by an agent that knows how to perform specific actions in the game. It uses variations of a perfect A* agent that are limited in various ways, such as not being able to jump high or see enemies, to test how failing to do certain actions can stop the player from beating the level.Comment: 8 pages, 7 figures, PCG Workshop at FDG 2018, 9th International Workshop on Procedural Content Generation (PCG2018