NextEval: An Agent-Based Solver and Benchmark for Derivative-Free Optimization

Abstract

Derivative-free optimization (DFO) addresses problems where derivatives are unavailable or costly to obtain. This setting often arises in simulation-based and experimental applications, where evaluating the black-box objective can itself be costly. Thus, it remains a central challenge in DFO to effectively exploit accumulated observations to select informative evaluation points under a limited budget. In this light, we introduce the NextEval solver, an agent-based DFO solver, which integrates the capabilities of a large language model (LLM) to guide the sequential selection of evaluation points. Specifically, we establish a system that combines an LLM agent with a numerical environment. The environment provides tools for analyzing past evaluations and executing numerical methods, while maintaining a shared evaluation history and method-specific state to support continuation across method switches. Using observations and tool feedback, the LLM agent selects tools, configures their parameters, and allocates the evaluation budget, while numerical methods compute and evaluate candidate points. Building on this system, we also introduce NextEval Bench, a benchmark protocol for comparing agent configurations on shared DFO tasks using the same numerical tools under matched evaluation budgets and information constraints. Numerical results on low-dimensional DFO problems demonstrate that the NextEval solver outperforms the state-of-the-art DFO baselines in function-evaluation efficiency.

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Cite

BibTeX RIS

BibTeX

@misc{chen2026nexteval,
  title = {{NextEval: An Agent-Based Solver and Benchmark for Derivative-Free Optimization}},
  author = {Shuo Chen and Li Cui and Cunxin Huang and Ya-Feng Liu and Minghang Xie and Meng Xu and Zaikun Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36553},
  eprint = {2610.36553},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36553},
}

RIS

TY  - UNPB
TI  - NextEval: An Agent-Based Solver and Benchmark for Derivative-Free Optimization
AU  - Shuo Chen
AU  - Li Cui
AU  - Cunxin Huang
AU  - Ya-Feng Liu
AU  - Minghang Xie
AU  - Meng Xu
AU  - Zaikun Zhang
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36553
UR  - https://arxiv.org/abs/2610.36553
AB  - Derivative-free optimization (DFO) addresses problems where derivatives are unavailable or costly to obtain. This setting often arises in simulation-based and experimental applications, where evaluating the black-box objective can itself be costly. Thus, it remains a central challenge in DFO to effectively exploit accumulated observations to select informative evaluation points under a limited budget. In this light, we introduce the NextEval solver, an agent-based DFO solver, which integrates the capabilities of a large language model (LLM) to guide the sequential selection of evaluation points. Specifically, we establish a system that combines an LLM agent with a numerical environment. The environment provides tools for analyzing past evaluations and executing numerical methods, while maintaining a shared evaluation history and method-specific state to support continuation across method switches. Using observations and tool feedback, the LLM agent selects tools, configures their parameters, and allocates the evaluation budget, while numerical methods compute and evaluate candidate points. Building on this system, we also introduce NextEval Bench, a benchmark protocol for comparing agent configurations on shared DFO tasks using the same numerical tools under matched evaluation budgets and information constraints. Numerical results on low-dimensional DFO problems demonstrate that the NextEval solver outperforms the state-of-the-art DFO baselines in function-evaluation efficiency.
ER  -

Abstract

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