Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as "black boxes", ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via a Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-ofthe-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Quality-Diversity algorithms have transformed optimization by prioritizing the discovery of diverse, high-performing solutions over a single optimal result. However, traditional Quality-Diversity methods, such as MAP-Elites, rely heavily on predefined behavior descriptors and complete prior knowledge of the task to define the behavior space grid, limiting their flexibility and applicability. In this work, we introduce Vector Quantized-Elites (VQ-Elites), a novel Quality-Diversity algorithm that autonomously constructs a structured behavior space grid using unsupervised learning, eliminating the need for prior task-specific knowledge. At the core of VQ-Elites is the integration of Vector Quantized Variational Autoencoders, which enables the dynamic learning of behavior descriptors and the generation of a structured, rather than unstructured, behavior space grid -- a significant advancement over existing unsupervised Quality-Diversity approaches. This design establishes VQ-Elites as a flexible, robust, and task-agnostic optimization framework. To further enhance the performance of unsupervised Quality-Diversity algorithms, we introduce behavior space bounding and cooperation mechanisms, which significantly improve convergence and performance, as well as the Effective Diversity Ratio and Coverage Diversity Score, two novel metrics that quantify the actual diversity in the unsupervised setting. We validate VQ-Elites on robotic arm pose-reaching, mobile robot space-covering, and MiniGrid exploration tasks. The results demonstrate its ability to efficiently generate diverse, high-quality solutions, emphasizing its adaptability, scalability, robustness to hyperparameters, and potential to extend Quality-Diversity optimization to complex, previously inaccessible domains.

Developmental changes in body morphology profoundly shape locomotion in animals, yet artificial agents and robots are typically trained under static physical parameters. Inspired by ontogenetic scaling of muscle power in biology, we propose Scaling Mechanical Output over Lifetime (SMOL), a novel curriculum that dynamically modulates robot actuator strength to mimic natural variations in power-to-weight ratio during growth and ageing. Integrating SMOL into the MAP-Elites quality-diversity framework, we vary the torque in standard robotics tasks to mimic the evolution of strength in animals as they grow up and as their body changes. Through comprehensive empirical evaluation, we show that the SMOL schedule consistently elevates both performance and diversity of locomotion behaviours across varied control scenarios, which we hypothesise to be thanks to agents leveraging advantageous physics early on to discover skills that act as stepping stones when they reach their final standard body properties. Based on studies of the total power output in humans, we also implement the SMOL-Human schedule that models isometric body variations due to non-linear changes like puberty, and study its impact on robotics locomotion.

Brain-body co-optimization remains a challenging problem, despite increasing interest from the community in recent years. To understand and overcome the challenges, we propose exhaustively mapping a morphology-fitness landscape to study it. To this end, we train controllers for each feasible morphology in a design space of 1,305,840 distinct morphologies, constrained by a computational budget. First, we show that this design space constitutes a good model for studying the brain-body co-optimization problem, and our attempt to exhaustively map it roughly captures the landscape. We then proceed to analyze how evolutionary brain-body co-optimization algorithms work in this design space. The complete knowledge of the morphology-fitness landscape facilitates a better understanding of the results of evolutionary brain-body co-optimization algorithms and how they unfold over evolutionary time in the morphology space. This investigation shows that the experimented algorithms cannot consistently find near-optimal solutions. The search, at times, gets stuck on morphologies that are sometimes one mutation away from better morphologies, and the algorithms cannot efficiently track the fitness gradient in the morphology-fitness landscape. We provide evidence that experimented algorithms regularly undervalue the fitness of individuals with newly mutated bodies and, as a result, eliminate promising morphologies throughout evolution. Our work provides the most concrete demonstration of the challenges of evolutionary brain-body co-optimization. Our findings ground the trends in the literature and provide valuable insights for future work.

We address the problem of game level repair, which consists of taking a designed but non-functional game level and making it functional. This might consist of ensuring the completeness of the level, reachability of objects, or other performance characteristics. The repair problem may also be constrained in that it can only make a small number of changes to the level. We investigate search-based solutions to the level repair problem, particularly using evolutionary and quality-diversity algorithms, with good results. This level repair method is applied to levels generated using a machine learning-based procedural content generation (PCGML) method that generates stylistically appropriate but frequently broken levels. This combination of PCGML for generation and search-based methods for repair shows great promise as a hybrid procedural content generation (PCG) method.

Personal use of this material is permitted. Abstract --Prompt engineering is essential for optimizing large language models (LLMs), yet the link between prompt structures and task performance remains underexplored. This work introduces an evolutionary approach that combines context-free grammar (CFG) with the MAP-Elites algorithm to systematically explore the prompt space. Our method prioritizes quality and diversity, generating high-performing and structurally varied prompts while analyzing their alignment with diverse tasks by varying traits such as the number of examples (shots) and reasoning depth. By systematically mapping the phenotypic space, we reveal how structural variations influence LLM performance, offering actionable insights for task-specific and adaptable prompt design. Evaluated on seven BigBench Lite tasks across multiple LLMs, our results underscore the critical interplay of quality and diversity, advancing the effectiveness and versatility of LLMs. The rapid advancement of Generative Pre-Trained Transformer (GPT)-based Large Language Models (LLMs), such as ChatGPT, has revolutionized the field of Natural Language Processing (NLP) [1]. These models excel across domains, emphasizing the importance of prompt engineering to optimize performance and bridge user intent with model output [2], [3].

Brain-body co-optimization suffers from fragile co-adaptation where brains become over-specialized for particular bodies, hindering their ability to transfer well to others. Evolutionary algorithms tend to discard such low-performing solutions, eliminating promising morphologies. Previous work considered applying MAP-Elites, where niche descriptors are based on morphological features, to promote better search over morphology space. In this work, we show that this approach still suffers from fragile co-adaptation: where a core mechanism of MAP-Elites, creating stepping stones through solutions that migrate from one niche to another, is disrupted. We suggest that this disruption occurs because the body mutations that move an offspring to a new morphological niche break the robots' fragile brain-body co-adaptation and thus significantly decrease the performance of those potential solutions -- reducing their likelihood of outcompeting an existing elite in that new niche. We utilize a technique, we call Pollination, that periodically replaces the controllers of certain solutions with a distilled controller with better generalization across morphologies to reduce fragile brain-body co-adaptation and thus promote MAP-Elites migrations. Pollination increases the success of body mutations and the number of migrations, resulting in better quality-diversity metrics. We believe we develop important insights that could apply to other domains where MAP-Elites is used.

Quality-Diversity is a family of evolutionary algorithms that generate diverse, high-performing solutions through local competition principles inspired by natural evolution. While research has focused on improving specific aspects of Quality-Diversity algorithms, surprisingly little attention has been paid to investigating alternative formulations of local competition itself -- the core mechanism distinguishing Quality-Diversity from traditional evolutionary algorithms. Most approaches implement local competition through explicit collection mechanisms like fixed grids or unstructured archives, imposing artificial constraints that require predefined bounds or hard-to-tune parameters. We show that Quality-Diversity methods can be reformulated as Genetic Algorithms where local competition occurs through fitness transformations rather than explicit collection mechanisms. Building on this insight, we introduce Dominated Novelty Search, a Quality-Diversity algorithm that implements local competition through dynamic fitness transformations, eliminating the need for predefined bounds or parameters. Our experiments show that Dominated Novelty Search significantly outperforms existing approaches across standard Quality-Diversity benchmarks, while maintaining its advantage in challenging scenarios like high-dimensional and unsupervised spaces.

Two fundamental challenges face generative models in engineering applications: the acquisition of high-performing, diverse datasets, and the adherence to precise constraints in generated designs. We propose a novel approach combining optimization, constraint satisfaction, and language models to tackle these challenges in architectural design. Our method uses Quality-Diversity (QD) to generate a diverse, high-performing dataset. We then fine-tune a language model with this dataset to generate high-level designs. These designs are then refined into detailed, constraint-compliant layouts using the Wave Function Collapse algorithm. Our system demonstrates reliable adherence to textual guidance, enabling the generation of layouts with targeted architectural and performance features. Crucially, our results indicate that data synthesized through the evolutionary search of QD not only improves overall model performance but is essential for the model's ability to closely adhere to textual guidance. This improvement underscores the pivotal role evolutionary computation can play in creating the datasets key to training generative models for design. Web article at https://tilegpt.github.io