ARES-LSHADE: Autoresearch-Enhanced LSHADE with Memetic Polish for the GNBG Benchmark
Authors: Abdullah Naeem, Md Wasi Ul kabir, Manish Bhatt, Ayon Dey, Anav Katwal, Md Tamjidul Hoque
Organizations: University of New Orleans · Amazon†
Abstract
We present ARES-LSHADE, a memetic differential-evolution variant submitted to the GECCO 2026 competition on LLM-designed evolutionary algorithms for the Generalized Numerical Benchmark Generator (GNBG). The algorithm builds on the LLM-LSHADE 2025 winner, contributing two new components: (a) a scout-augmented mutation operator with adaptive CMA-ES integration, produced by an autonomous research loop across approximately thirty LLM-driven design experiments, and (b) a multi-start L-BFGS-B polish phase that respects strict blackbox treatment of the benchmark. On the official 31-run-per-function evaluation with the competition-specified function-evaluation budgets, ARES-LSHADE obtains 510 of 744 wins (per-function gap below 1e-8), reaching machine precision on 18 of 24 functions. The remaining six functions exhibit characteristic plateau signatures consistent with GNBG's compositional structure, and were independently identified by the autoresearch loop as the hardest of the suite. Beyond the result itself, this report documents two methodological observations: (i) an LLM-driven research loop with operator-only edit surface and fitness-only observation space converges to a characteristic plateau on this benchmark; (ii) when we initially widened the observation space to include the benchmark's compositional metadata, the resulting algorithm trivially solved all 24 functions but violated the competition's blackbox rule, which we identified before submission. We discuss this tension between LLM capability and benchmark integrity as a design consideration for future LLM-driven optimization-algorithm research. Code and reproducibility artifacts are available at https://github.com/anaeem1/ARES-LSHADE.
Optimization benchmarks play a fundamental role in assessing algorithm performance; however, existing artificial benchmarks often fail to capture the diversity and irregularity of real-world problem structures, while benchmarks derived from real-world problems are costly and difficult to construct. To address these challenges, we propose an evolutionary automatic benchmark generation framework that leverages a large language model (LLM) as a generative operator, termed the LLM-driven evolutionary benchmark generator (LLM-EBG). In this framework, the LLM serves as an evolutionary operator that generates and evolves benchmark problems within a flexible, expressive representation space. As a case study, we generate unconstrained single-objective continuous minimization problems represented as mathematical expressions designed to induce significant performance differences between a genetic algorithm (GA) and differential evolution (DE). Experimental results show that LLM-EBG successfully produces benchmark problems in which the designated target algorithm consistently outperforms the comparative algorithm in more than 80% of trials. Furthermore, exploratory landscape analysis reveals that benchmarks favoring GA are highly sensitive to variable scaling, demonstrating that the proposed framework can generate problems with distinct geometric characteristics that reflect the intrinsic search behaviors of different optimization algorithms.
LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4%.
Alexey Kravatskiy, Valentin Khrulkov, Ivan Oseledets
AI-Driven Research Systems (ADRS) -- systems coupling LLMs with automated evaluation to discover algorithms, proofs, and designs -- are being optimized and adopted across domains, but the tools to analyze them have not kept pace. ADRS performance depends on component interactions that are poorly understood, expensive to explore, and (as we show) not well captured by standard convergence guarantees. These guarantees rely on structural assumptions that do not hold under the ADRS process we formalize. We introduce GAMBLe, a framework that decomposes ADRS behavior into four parameters (generator G, assessor A, discovery mechanism M, budget B) and one compositional object, the effective landscape Leff=A∘G, which reveals that distinct generator-assessor pairs induce structurally different per-problem optimization landscapes. We exercise the framework on 760+ replicated runs (>46,000 iterations) spanning generators from single LLMs to dynamically-adaptive ensembles, mechanisms from greedy selection to co-evolutionary meta-search, and three NP-hard problems whose assessors range from continuous scoring to cliff functions. The experiments reveal no total ordering of generators or mechanisms: frontier models can underperform open-source alternatives and the simplest mechanism sometimes outperforms state-of-the-art meta-search. Results show that even under limited budgets (60 iterations per run), the right component choices can improve performance by 13-67% and search efficiency by 6-39x.