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

Agentic workflows are increasingly used across domains such as technology, finance, and enterprise operations. As these agents become more widely deployed, continually improving them becomes increasingly important. This raises an immediate challenge: How should the agent evolve? This evolution requires effective evaluation that can assess outcomes and provide useful feedback for optimization. As the agent evolves, its behaviors and failure modes may also change, making a fixed evaluator increasingly inadequate. Another fundamental question: How should we evaluate an evolving agent? These two challenges are inherently coupled; changes in agent behavior can expose limitations of the current evaluator, while a stronger evaluator provides more informative feedback for improving the agent. Motivated by this interaction, we introduce DUET, a framework that jointly optimizes a solver agent and a grader agent to improve both. DUET iteratively selects training tasks, executes them with the solver, evaluates the resulting outcomes with the grader, and uses a tool-using update module to revise the solver and the grader, alternating between the two across rounds. By updating the grader within the optimization loop, DUET turns evaluation from a fixed source of feedback into a first-class optimization objective that adapts alongside the solver. Experiments across four agent benchmarks show that DUET improves both solver and grader performance and consistently outperforms baselines that optimize the solver with a fixed grader.

2026 has brought an explosion of interest in LLM-guided evolution of agentic artifacts, with systems like GEPA and Autoresearch demonstrating that LLMs can iteratively improve prompts, code, and agent architectures across diverse domains. As adoption accelerates, a central question emerges: given the same information, the same seed agent, and the same objective, which optimization algorithm yields the best results under the same evaluation budget? This question becomes critical when evaluations are expensive, such as when they require human judgment or multiple LLM calls. We present the first systematic comparison of three optimization paradigms -- Elo tournament selection (RoboPhD), Pareto-based selection (GEPA), and greedy hill-climbing (Autoresearch) -- across four benchmarks spanning abstract reasoning, cloud scheduling, SQL generation, and financial QA, all under a fixed budget of 1,500 evaluations. RoboPhD introduces validation-free evolution: instead of splitting the budget between training and validation, it uses Elo competition on training data to simultaneously evaluate agents and drive evolution. All three systems receive seed agents with diagnostic print() statements that evolution can grow, enabling self-instrumenting agents that develop increasingly informative diagnostics for the benefit of their evolutionary successors. Using a single default configuration, RoboPhD outperforms both GEPA and Autoresearch on three of four benchmarks, losing only on the simplest task, where the winning solution (from our Autoresearch adaptation) required under 90 lines of code. On ARC-AGI, RoboPhD evolves a 22-line seed agent into a 1,013-line multi-strategy system, improving accuracy from 27.8% to 65.8% using Gemini 3.1 Flash Lite as the solver. We release RoboPhD as a versatile toolkit under the MIT license with a simple optimize_anything() API for evolving diverse complex agents.

Black-box optimization (BBO) arises in many scientific and engineering problems where objective evaluations are expensive and limited. Recent large language model (LLM) agents offer a new way to approach BBO by combining task semantics, computation, optimization tools, and feedback-driven decision making, showing great potential due to the integration with mathematically rigorous tools. However, existing agentic BBO studies use different task domains and system configurations, making their results difficult to compare and the effects of individual design choices hard to isolate. We therefore introduce AgenticBBO-Bench, a cross-domain benchmark for agentic BBO spanning synthetic functions, hyperparameter optimization, database tuning, chip design, and molecular design under a unified finite-budget evaluation protocol. In our experiments, agentic BBO achieves higher family-averaged scores than direct LLM-based methods in all five domains and outperforms the best numerical optimizers in four. We further study three factors shaping agent performance: optimization tools, task information and prior knowledge, and the role of the LLM during search. Our results show that additional numerical tools do not consistently improve performance, task semantics are broadly useful while more specific priors are less reliable, and numerical optimizers can effectively absorb gains from search trajectories established by the agent. Finally, we introduce a five-task frontier challenge within AgenticBBO-Bench and evaluate seven LLMs under the Codex agent harness, where GPT-6 Astra and DeepSeek-V4.1-Flash lie on the Pareto frontier of performance and cost among the evaluated models. Our code is available at https://github.com/lamda-bbo/agentic-bbo.