Illuminating search spaces by mapping elites (1504.04909v1)

Abstract: 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.

• The paper introduces MAP-Elites, a technique that explores user-defined feature dimensions to map diverse, high-performing solutions.
• The algorithm is validated across domains like neural networks, simulated soft robots, and a real robot arm, showing superior coverage and efficiency.
• MAP-Elites emphasizes solution diversity and phenotypic mapping, offering actionable insights for optimizing complex, high-dimensional systems.

Overview of "Illuminating Search Spaces by Mapping Elites"

The paper "Illuminating Search Spaces by Mapping Elites" presents the Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm, a novel approach to understanding how high-performing solutions are distributed across search spaces. This approach is presented as an enhancement over traditional search algorithms, which typically aim to identify a single optimal solution.

Key Contribution

MAP-Elites is designed to traverse and map high-performing solutions across a space defined by user-selected dimensions of variation. The primary benefit of this method is its ability to provide a comprehensive map, or "illumination," of the search space, revealing the dynamics between different attributes and performance outcomes.

Methodology

1. Search Space Exploration: The algorithm searches a high-dimensional space and records the best performance at each point in a lower-dimensional feature space.
2. Feature Space Definition: Users specify dimensions of interest, deciding on the granularity of the exploration based on available computational resources.
3. Diversity of Solutions: Unlike conventional methods that converge on a single solution, MAP-Elites generates a spectrum of high-performing solutions, potentially leading to better global optima and offering insights into solution diversity.

Experimental Validation

The benefits of MAP-Elites are demonstrated in three problem domains:

1. Neural Networks: The algorithm effectively maps the relationship between network modularity, connection costs, and performance, outperforming traditional evolutionary algorithms and other illumination methods.
2. Simulated Soft Robots: MAP-Elites not only revealed a broader range of morphological designs but also identified how material properties influence performance.
3. Real Soft Robot Arm: Conducted with a physical robot, this experiment highlighted MAP-Elites' capacity to efficiently navigate complex, real-world environments where evaluations are costly.

Comparative Analysis

The algorithm was benchmarked against several control methods, including traditional evolutionary algorithms, grid search, and novelty-based approaches. In most cases, MAP-Elites demonstrated superior coverage, reliability, and overall performance in mapping solution diversity.

Implications

MAP-Elites provides a significant shift in how search problems are approached, moving beyond the pursuit of a singular "best" solution towards a more comprehensive understanding of the solution landscape. This has implications across numerous scientific and engineering fields, especially those engaging with complex, high-dimensional search spaces.

Future Developments

Potential enhancements to the algorithm include adaptive feature space resolution, the integration of crossover mechanisms, and real-time exploration, which could further optimize performance and expand its applicability.

Conclusion

MAP-Elites stands as a powerful tool, both as an optimization algorithm and a method for illuminating the intricate relationships within solution spaces. Its capability to visualise the phenotype-fitness map offers researchers a versatile framework for examining multi-dimensional relationships in optimization problems.