LLM Driven Design of Continuous Optimization Problems with Controllable High-level Properties

TL;DR

The paper tackles the limited landscape diversity of continuous optimization benchmarks by automatically generating optimization problems with predefined high‑level properties. It leverages the LLaMEA framework to integrate large language models into an evolutionary loop that uses Exploratory Landscape Analysis (ELA) features and property predictors to steer problem generation, followed by basin‑of‑attraction verification and t‑SNE visualization to confirm coverage of the landscape space. A central methodological advance is an adaptive ELA‑space fitness‑sharing mechanism that promotes diversity across generated landscapes, together with explicit verification procedures for properties like multimodality, separability, basin‑size homogeneity, and global–local optima contrast. The results show that the generated problems expand the BBOB instance space, are verifiable in their target properties, and are released as an open Python library to support benchmarking, landscape analysis, and automated algorithm selection.

Abstract

Benchmarking in continuous black-box optimisation is hindered by the limited structural diversity of existing test suites such as BBOB. We explore whether large language models embedded in an evolutionary loop can be used to design optimisation problems with clearly defined high-level landscape characteristics. Using the LLaMEA framework, we guide an LLM to generate problem code from natural-language descriptions of target properties, including multimodality, separability, basin-size homogeneity, search-space homogeneity and globallocal optima contrast. Inside the loop we score candidates through ELA-based property predictors. We introduce an ELA-space fitness-sharing mechanism that increases population diversity and steers the generator away from redundant landscapes. A complementary basin-of-attraction analysis, statistical testing and visual inspection, verifies that many of the generated functions indeed exhibit the intended structural traits. In addition, a t-SNE embedding shows that they expand the BBOB instance space rather than forming an unrelated cluster. The resulting library provides a broad, interpretable, and reproducible set of benchmark problems for landscape analysis and downstream tasks such as automated algorithm selection.

Figures (7)

• Figure 1: Overview of the three-step LLaMEA process for generating interpretable optimization problems: (1) define problem properties and train machine-learning models to predict them from ELA features; (2) use the prediction models with an LLM-based generator to create problems exhibiting the properties; (3) validate that the generated problems show the desired characteristics.
• Figure 2: Finding different basins of attraction and their approximate sizes using a dense grid on a $2d$ problem landscape. Each point is attributed to an attractor by iteratively searching for an improving path.
• Figure 3: Performance of different LLMs in generating landscapes with certain high‑level properties. Left: results for landscapes optimized for basin‑size homogeneity and separability; Right: multimodal landscapes with a global structure.
• Figure 4: Distribution of nearest-neighbor (Manhattan) distances between normalized ELA feature vectors of landscapes generated with and without fitness sharing. Results are shown for qwen2.5-coder_14b (left) and gpt5-nano (right); larger distances indicate greater landscape diversity.
• Figure 5: A selection of diverse generated landscapes. With high-level features from left to right, for the top row; Basin-size homogeneity, global to local optima contrast, search space homogeneity, multimodality. For the bottom row: Non-homogenous basin sizes, Non-homogeneous basins with separability, Non-homogenous search space, and separable with homogenous search space. More can be found in the supplementary material.