We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases.

Quality Diversity (QD) is an emerging field in which collections of high performing, behaviorally diverse solutions are trained.

Quality-Diversity (QD) algorithms constitute a branch of optimization that is concerned with discovering a diverse and high-quality set of solutions to an optimization problem. Current QD methods commonly maintain diversity by dividing the behavior space into discrete regions, ensuring that solutions are distributed across different parts of the space. The QD problem is then solved by searching for the best solution in each region. This approach to QD optimization poses challenges in large solution spaces, where storing many solutions is impractical, and in high-dimensional behavior spaces, where discretization becomes ineffective due to the curse of dimensionality. We present an alternative framing of the QD problem, called \emph{Soft QD}, that sidesteps the need for discretizations. We validate this formulation by demonstrating its desirable properties, such as monotonicity, and by relating its limiting behavior to the widely used QD Score metric. Furthermore, we leverage it to derive a novel differentiable QD algorithm, \emph{Soft QD Using Approximated Diversity (SQUAD)}, and demonstrate empirically that it is competitive with current state of the art methods on standard benchmarks while offering better scalability to higher dimensional problems.

Automated algorithm design is entering a new phase: Large Language Models can now generate full optimisation (meta)heuristics, explore vast design spaces and adapt through iterative feedback. Yet this rapid progress is largely performance-driven and opaque. Current LLM-based approaches rarely reveal why a generated algorithm works, which components matter or how design choices relate to underlying problem structures. This paper argues that the next breakthrough will come not from more automation, but from coupling automation with understanding from systematic benchmarking. We outline a vision for explainable automated algorithm design, built on three pillars: (i) LLM-driven discovery of algorithmic variants, (ii) explainable benchmarking that attributes performance to components and hyperparameters and (iii) problem-class descriptors that connect algorithm behaviour to landscape structure. Together, these elements form a closed knowledge loop in which discovery, explanation and generalisation reinforce each other. We argue that this integration will shift the field from blind search to interpretable, class-specific algorithm design, accelerating progress while producing reusable scientific insight into when and why optimisation strategies succeed.

Bayesian optimisation (BO) is a surrogate-based optimisation technique that efficiently solves expensive black-box functions with small evaluation budgets. Recent studies consider trust regions to improve the scalability of BO approaches when the problem space scales to more dimensions. Motivated by this research, we explore the effectiveness of trust region-based BO algorithms for diversity optimisation in different dimensional black box problems. We propose diversity optimisation approaches extending TuRBO1, which is the first BO method that uses a trust region-based approach for scalability. We extend TuRBO1 as divTuRBO1, which finds an optimal solution while maintaining a given distance threshold relative to a reference solution set. We propose two approaches to find diverse solutions for black-box functions by combining divTuRBO1 runs in a sequential and an interleaving fashion. We conduct experimental investigations on the proposed algorithms and compare their performance with that of the baseline method, ROBOT (rank-ordered Bayesian optimisation with trust regions). We evaluate proposed algorithms on benchmark functions with dimensions 2 to 20. Experimental investigations demonstrate that the proposed methods perform well, particularly in larger dimensions, even with a limited evaluation budget.

We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases.