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GA-Agent: Large Language Models as Hyperparameter Optimizers for Evolutionary Controller Synthesis

Mohammad Narimani, Seyyed Ali Emami

arXiv:2609.27725v1eess.SYcs.SY

TL;DR

PID tuning must balance competing control objectives, while GA performance depends on configuration choices that are difficult to set manually or through costly nested optimization. GA-Agent pairs GA-based gain search with an LLM that adapts the GA configuration from run outcomes. It reports 100% success across its case studies and robustness to prompt surface format.

  • Problem

    PID tuning must balance competing objectives, while GA performance depends on meta-level settings commonly chosen through manual trial-and-error or costly optimization.

    Source: §1 · p. 3

  • Method

    GA-Agent uses a GA to optimize PID gains and an LLM to diagnose completed runs and propose updated GA configurations.

    Source: §1 · p. 4

  • Results

    GA-Agent achieves 100% success across eight case studies, outperforming fixed-hyperparameter GA in solution quality and sample efficiency and matching or surpassing Cascade-GA.

    Source: §1 · p. 5

  • Takeaways & Limitations

    Performance is largely robust to prompt surface format, with results driven primarily by the semantic content of feedback rather than markup conventions.

    Source: §4.3 · p. 26

    Evaluation is limited to SISO PID synthesis in closed-loop simulation with nominal plant models; robustness to practical perturbations remains open.

    Source: §5 · p. 28

Abstract

from arXiv · show

Tuning PID controllers to satisfy competing objectives - low tracking error, fast settling, limited overshoot, and moderate control effort - is labor-intensive and requires expertise. Genetic algorithms (GAs) offer gradient-free optimization of controller gains against a weighted fitness function, but success depends on meta-level choices: population size, generation budget, gain bounds, and fitness weights. These are usually set by manual trial-and-error or costly bilevel optimization, exposing a tension: GAs excel at dense numerical search, but configuring them needs high-level, context-dependent semantic reasoning. We propose GA-Agent, which decouples these modes. A standard GA handles low-level PID gain optimization. A large language model (LLM) agent operates at the meta-level: it observes completed GA runs, diagnoses gaps versus user control objectives, and proposes updated GA configurations. The architecture uses structured memory, quantitative goal translation, resource-aware termination, and outcome-driven routing. We evaluate GA-Agent on eight control case studies with diverse dynamics (DC motor, inverted pendulum, aircraft pitch, autonomous underwater vehicle, and others). GA-Agent achieves 100% success on all benchmarks, outperforming a Regular GA with fixed hyperparameters in solution quality and sample efficiency. It matches or surpasses a Cascade-GA baseline while reducing function evaluations by one to two orders of magnitude, typically converging in one to three optimization attempts. Sensitivity analysis shows robustness across LLM backbones and memory configurations. A compact memory buffer (size 2-3) and cost-effective models (DeepSeek-V4-Flash at about $0.002 per run) achieve superior performance.

1. Introduction

GA-Agent assigns numerical PID-gain search to a genetic algorithm and semantic, goal-directed configuration to an LLM agent. Across the reported case studies, it achieves 100% success and improves on a fixed-hyperparameter GA while matching or surpassing Cascade-GA.

1. Introduction

  • GA-Agent addresses the expertise and effort required to tune PID gains for competing objectives such as tracking error, settling time, overshoot, and control effort.Classical methods can provide starting points but seldom satisfy all metrics simultaneously, especially for nonlinear or poorly modeled plants.Source: §1 · p. 3
  • GA success depends on meta-level choices—population size, generation budget, gain bounds, and fitness weights—typically set through trial-and-error or costly cascade optimization.Cascade optimization can require one to two orders of magnitude more function evaluations than a single well-configured GA run.Source: §1 · pp. 3–4
  • GA-Agent separates dense numerical gain search by a GA from an LLM that diagnoses completed runs and proposes updated GA configurations.The agent adjusts population size, generation count, gain bounds, and fitness weights based on user objectives and previous outcomes.Source: §1 · p. 4
  • Memory, quantitative goal translation, budget-aware termination, and routing support the iterative optimization loop, which typically converges within one to three attempts.A WarmUp-Agent first translates the task specification into a structured configuration.Source: §1 · pp. 4–5
  • 100% success across eight case studies; GA-Agent outperforms fixed-hyperparameter GA in solution quality and sample efficiency, and matches or surpasses Cascade-GA.The reported average NFE reduction versus Regular GA is 33%.Source: §1 · p. 5

2. Related Work

Related work spans evolutionary control design, agentic AI patterns, and LLM-based optimization and control. GA-Agent is positioned as a control-specialized approach that reserves the LLM for meta-level decisions while a GA searches controller gains.

2.1. Machine Learning and Evolutionary Methods in Control

  • Evolutionary methods, including GAs, suit nonconvex and multimodal control objectives, but their effectiveness depends on costly manual tuning or nested optimization of GA hyperparameters.These costs motivate automated, sample-efficient alternatives for controller design.Source: §2.1 · p. 6

2.2. From Large Language Models to Agentic AI

  • Agentic AI design patterns include memory, routing, tool use, goal setting, and resource-aware optimization; LLM-enhanced RL work also frames LLMs as reward designers and decision-makers.GA-Agent adjusts fitness weights and proposes GA configurations based on textual and numerical feedback.Source: §2.2 · pp. 6–7

2.3. LLMs in Optimization and Control Design

  • Unlike reward-code systems such as Text2Reward and Eureka, GA-Agent refines scalar fitness weights within a fixed cost structure, trading generality for reliability in safety-relevant control.It also specializes AgentHPO’s closed-loop approach to control metrics and evaluates against fixed-hyperparameter and cascade-GA baselines.Source: §2.2 · p. 7, §2.3 · p. 8
  • LLM-based optimization includes AgentHPO’s iterative hyperparameter refinement and direct numerical approaches such as ProPS and AgenticControl, which propose policy parameters or PID gains.GA-Agent instead assigns gain search to a GA and meta-level configuration to the LLM.Source: §2.3 · pp. 7–8
  • GA-Agent targets offline, design-time controller optimization rather than online adaptation used by other LLM-in-the-loop control approaches.Figure 1 depicts the iterative pipeline from task configuration through GA search and simulation feedback to routing or final controller output.Source: §2.3 · p. 9, Figure 1 · p. 9

3. Methodology

The methodology formulates PID tuning as a SISO regulation problem with competing performance metrics, then separates gain optimization from the selection of GA hyperparameters. GA-Agent uses LLM-guided, history-aware updates to configure successive GA attempts under fixed targets and resource limits.

3.1. Problem Formulation

  • The SISO regulation task targets a setpoint while meeting transient and steady-state specifications, using PID gains over potentially nonlinear plant dynamics.The simulated controller uses backward finite differences for the derivative term and hard-clips control to actuator limits; no derivative filter or anti-windup is applied.Source: §3.1 · p. 10

3.2.1. Low-Level GA

  • The low-level GA searches PID gains using a weighted fitness over four closed-loop metrics: MSE, settling time, percent overshoot, and normalized control effort.Because raw metric scales differ, the LLM uses achieved values and target deviations to adjust relative weights across attempts.Source: §3.2.1 · p. 11, §3.1 · p. 11

3.2.2. Baseline Cost

  • A weight-independent baseline cost supports fair comparison across configurations, while the success score separately records whether each metric meets its fixed target.The baseline cost measures summed relative deviations, whereas the success score awards each of four metrics 25% for passing its target.Source: §3.2.2 · pp. 11–12

3.2.3. The Hyperparameter Tuning Problem

  • The outer tuning problem spans mixed discrete and continuous choices, and GA-Agent proposes one informed configuration per attempt rather than evaluating an outer population.The choices include population size, generation budget, fitness weights, and gain bounds; unlike Cascade GA's population-based search, the LLM reasons sequentially from accumulated evidence.Source: §3.2.3 · pp. 12, 14, Figure 2 · p. 13
  • GA-Agent separates PID-gain search by a standard GA from LLM decisions that update GA hyperparameters between attempts.The LLM conditions proposals on prior outcomes, control goals, and available budgets.Source: §3.2.3 · p. 14

3.3. GA-Agent Architecture

  • The architecture combines a rolling attempt history, fixed goal targets, tunable fitness weights, and time and monetary budgets to guide updates and termination.History includes gains, metrics, fitness and baseline costs, population statistics, reasoning, and resource use; routing halts at a limit or when all targets are met, returning the attempt with the lowest baseline cost.Source: §3.3 · pp. 14–17

3.4. Prompt Design

  • The prompt assembles context from the architecture modules, and its exploration-first guideline is a design choice rather than a systematically varied strategy.The study varies prompt wording while leaving systematic variation of the underlying strategy guidelines for future work.Source: §3.3 · p. 16, §3.4 · p. 17

1. A system prompt

The prompt combines structured goal, memory, and budget information to guide the LLM’s next GA configuration. The evaluation covers eight control case studies using nonlinear plant models.

1. A system prompt

  • The LLM receives a system prompt, goal specification, per-attempt memory, and budget status, then returns updated weights, GA settings, gain ranges, and a reasoning trace.Outputs are validated against a JSON schema; malformed or out-of-range responses can trigger up to three re-queries.Source: §1 · p. 17, Figure 4 · p. 18

3.5. Pre-Processing

  • The WarmUp-Agent is described as translating user problems into plant and simulation configurations, but experiments use manually specified configurations for reproducibility.Initial hyperparameters are either a shared general-purpose default or a memory-free LLM proposal.Source: §3.5 · p. 18

3.6. Implementation Details

  • The implementation uses Python 3.11.10, LangGraph for workflow orchestration, and the OpenAI Python SDK for LLM inference.The experiments use DeepSeek-V4-Flash at temperature 0; alternative backbones are evaluated in sensitivity analysis.Source: §3.6 · pp. 18–19
  • GA fitness evaluations use PyGAD, while closed-loop dynamics are simulated with a custom fixed-step forward Euler integrator implemented in NumPy.GA evaluations run sequentially on a single CPU core, without GPU acceleration or population parallelization.Source: §3.6 · p. 19

3.7. Case Studies and Evaluation Protocol

  • The eight case studies span aerial, underwater, robotic, and process-control domains, including AUV, aircraft pitch, CSTR, DC motor, cart–pole, helicopter, and manipulator control.The plant models are nonlinear and are used without linearization.Source: §3.7 · pp. 19–20, Figure 5 · p. 20
  • Each case study specifies its plant, control objective, actuator constraints, simulation parameters, and fixed performance targets.Detailed configurations are provided in Appendix A.Source: §3.7 · p. 20
  • The evaluation compares a fixed-hyperparameter GA, a bilevel GA, and GA-Agent under shared resource budgets.The protocol also evaluates methods using baseline cost, success score, and cumulative function evaluations.Source: §3.7 · p. 20

• Regular GA:

The Regular GA uses a standard low-level genetic algorithm with fixed, manually set hyperparameters across attempts.

• Regular GA:

  • A standard low-level GA uses fixed, manually set hyperparameters θ throughout its attempts.Source: • Regular GA · p. 20

• Cascade GA:

The Cascade GA uses an outer evolutionary loop to optimize the hyperparameters of an inner GA, while GA-Agent uses LLM-driven adaptation under shared resource constraints.

• Cascade GA:

  • The Cascade GA uses an outer evolutionary loop to optimize θ while an inner GA optimizes controller parameters p.Source: • Cascade GA · p. 20
  • GA-Agent pairs the low-level GA with LLM-driven hyperparameter adaptation.Source: • Cascade GA · p. 20
  • All three methods share a maximum of 12 attempts, a 1,000-second limit, and a $0.05 API-cost cap per experiment.The Regular GA uses a single attempt rather than repeating its allocation across all 12 possible attempts.Source: • Cascade GA · p. 20
  • Each case-study/method pair is evaluated in five independent runs using distinct seeds, with results reported as mean ± standard deviation.The same seed is used across methods within each trial.Source: • Cascade GA · p. 21
  • Evaluation measures baseline cost, success score, and cumulative function evaluations.Source: • Cascade GA · p. 21

4. Results

GA-Agent reaches 100% success on all eight case studies, compared with a mean of 81.3% for the fixed-hyperparameter Regular GA. Against Cascade-GA, GA-Agent+ has comparable success rates and uses fewer evaluations on average.

4.1. Performance of GA-Agent vs. Regular GA

  • 2,135 versus 3,210 NFE on average for GA-Agent and Regular GA, respectively, alongside an 18.7 percentage-point success-score improvement.GA-Agent uses fewer NFE on six of eight case studies, with one tie; DC Motor is an exception, requiring 6,911 versus 4,518 NFE while achieving 100% versus 55.0 ± 41.1% success.Source: §4.1 · p. 22
  • 100% success on all eight case studies for GA-Agent, versus 81.3% mean success for Regular GA.Regular GA reaches 100% only on 2DoF Helicopter and Two-Link Manipulator; the largest deficits are DC Motor at 55.0±41.1% and Aircraft Pitch at 65.0 ± 13.7%.Source: §4.1 · p. 22, Table 2 · p. 23

4.2. Comparison with Cascade-GA

  • 70 versus 2,306 NFE on AUV for GA-Agent+ (LLM Init) and Cascade-GA, respectively, at identical 100% success.Other reported reductions include 35 versus 411 NFE on 2DoF Helicopter and 275 versus 1,559 NFE on Ball & Beam.Source: §4.2 · p. 24
  • 1,147 NFE per run for GA-Agent+ (LLM Init), versus 1,813 for Cascade-GA, a 37% reduction while matching or improving its success rates.Across benchmarks, mean success rates are 96.9% for GA-Agent+ (Manual Init), 96.3% for Cascade-GA, and 95.0% for GA-Agent+ (LLM Init).Source: §4.2 · pp. 23–24
  • The lowest baseline cost L does not always correspond to the highest success score, because L aggregates relative errors while success measures joint satisfaction of all targets.The passage identifies success score as the more informative practical metric for controller-synthesis evaluation.Source: §4.2 · p. 24
  • Numerical feedback alone is generally sufficient for comparable performance between GA-Agent and GA-Agent+, with system context improving Aircraft Pitch cost and variance.On Aircraft Pitch, system context yields −2.02 ± 0.15 versus −1.86 ± 0.28.Source: §4.2 · p. 24

Effect of System Context (GA-Agent vs. GA-Agent+)..

System context can help or hinder GA-Agent depending on a plant’s gain requirements. Prompt-format tests show that success is largely robust to surface format, while normalized baseline cost varies across variants.

Effect of System Context (GA-Agent vs. GA-Agent+)..

  • On DC Motor, GA-Agent+ (Manual Init) records a baseline cost of 4.64 ± 17.72, while GA-Agent achieves −3.33 ± 0.53.The reported contrast indicates sharply reversed effects of adding system context on this plant.Source: Effect of System Context (GA-Agent vs.… · p. 25

4.3. Sensitivity Analysis Summary

  • The Original prompt attains the lowest normalized baseline cost (0.288±0.309), while Variation 2 records the highest (0.425±0.148), a 47% relative spread.Original and Variation 1 both attain 100% success, while Variation 2 has the lowest success rate and highest variance.Source: §4.3 · p. 26
  • GA-Agent is largely robust to prompt surface format, with performance driven primarily by feedback structure’s semantic content rather than markup conventions.The comparison covers four prompt formulations on AUV and Aircraft Pitch.Source: §4.3 · p. 26

Effect of Buffer Size..

The sensitivity results do not support simply increasing memory size: performance peaks at different buffer sizes across models and declines at larger sizes. DeepSeek-V4-Flash offers the best reported cost-success combination among the evaluated backbones.

Effect of Buffer Size..

  • Grok-4.1-Fast peaks at 82.5% success at B = 5, while Grok-3-Mini-Beta peaks at 80.0% at B = 2.Across buffer sizes, overall success falls from 73.8% at B = 1 to 65.0% at B = 7.Source: Effect of Buffer Size · p. 26
  • The recommended default buffer is B = 2 for lightweight models and B = 3 for heavier models, balancing recent history against prompt length and token cost.Neither evaluated model benefits monotonically from a larger buffer.Source: Effect of Buffer Size · p. 26
  • DeepSeek-V4-Flash and Gemini-2.5-Flash both achieve 100% success; DeepSeek-V4-Flash costs $0.0026 ± 0.0014 per run, the lowest of seven models.Claude-Haiku-4.5 is the most expensive at $0.0976 ± 0.0242 per run; DeepSeek-V4-Flash is identified as Pareto-optimal.Source: Effect of Buffer Size · p. 26

5. Discussion and Remarks

GA-Agent variants reduce evaluation counts relative to the reported baselines, with the discussion attributing the efficiency difference to LLM-guided configuration rather than an outer evolutionary search. The discussion also identifies practical and theoretical boundaries and several extensions.

5. Discussion and Remarks

  • System-blind GA-Agent achieves 100% success on all eight benchmarks, while system context can accelerate or degrade performance depending on plant gain requirements.LLM Init reaches 365 NFE on DC Motor but yields 75% success and high variance on Aircraft Pitch, where it underestimates large Kp needs.Source: §5 · pp. 26–27
  • Running Manual Init and LLM Init in parallel for the first one to two attempts is proposed as a hedge against their complementary failure modes.The proposed strategy would continue from whichever start yields lower baseline cost or higher success; its marginal overhead is described as negligible relative to the GA evaluation budget.Source: §5 · p. 27
  • Lightweight backbones perform best at B = 2, while heavier models are more robust across buffer sizes and are recommended at B = 3.Grok-4.1-Fast peaks empirically at B = 5.Source: §5 · pp. 27–28
  • DeepSeek-V4-Flash is reported as Pareto-optimal, achieving 100% success at the lowest per-run cost; model cost does not reliably predict optimization performance.The correlation between cost and success across the seven evaluated models is negative.Source: §5 · p. 28
  • GA-Agent reduces average NFE by 33% versus Regular GA (2,135 vs. 3,210) while improving average success by 18.7 percentage points; GA-Agent+ (LLM Init) reduces NFE by 37% versus Cascade-GA (1,147 vs. 1,813) at comparable success (95.0% vs. 96.3%).On individual benchmarks, the reported gains reach ≈33× on AUV, ≈12× on 2DoF Helicopter, and ≈6× on Ball & Beam.Source: §5 · p. 28
  • Cascade-GA evaluates a full population of hyperparameter configurations at each outer generation, whereas the LLM reasons over accumulated outcomes and typically converges within one to three attempts.The discussion frames this as replacing blind outer-loop evolutionary search with goal-directed, outcome-conditioned reasoning.Source: §5 · p. 28
  • The evaluation is limited to SISO PID synthesis in closed-loop simulation with nominal plant models; robustness to disturbances, noise, unmodeled dynamics, and actuator nonlinearities remains open.The listed actuator effects include saturation, hysteresis, and dead zones, unlike the hard-clipping saturation used in simulation.Source: §5 · p. 28
  • The LLM currently receives only completed-run summary statistics, while buffer size and prompt structure are selected offline and theoretical convergence and sample-complexity guarantees remain underdeveloped.The discussion also identifies multi-loop cascade control, joint controller-structure adaptation, and adaptive Pareto-frontier weights as future directions.Source: §5 · pp. 28–29

Appendix A. Case Study Descriptions

The appendix describes eight control case studies and traces a four-attempt AUV run in which the agent progressively adjusts the search and ultimately meets all targets.

Appendix A. Case Study Descriptions

  • The eight cases include transport-aircraft pitch, AUV depth regulation, ball position, reactor temperature, DC-motor speed, inverted-pendulum stabilization, helicopter yaw, and manipulator joint position.The cases span distinct plant dynamics and include both SISO and MIMO examples.Source: Appendix A · p. 33
  • The helicopter and manipulator cases apply PID control to one channel of a MIMO plant while holding the other input at trim.The helicopter regulates yaw; the manipulator regulates its first joint angle.Source: Appendix A · p. 33

Attempt 4 — Scaling Up Within the Identified Region

  • Across attempts 1–3, the gain bounds and fitness weights shift toward lower-effort solutions, and attempt 4 scales up the GA within the identified region.The full-run figure shows population and generation budgets increasing from (10, 10) in attempt 1 to (30, 40) in attempt 4.Source: Figure B.9 · p. 34

Appendix B. Inside a Full Run — What the Agent Actually Does

  • The appendix traces a complete four-attempt AUV run with DeepSeek-V4-Flash and uses a panel overview to map changes in configuration, weights, budgets, scores, and gain bounds.The run is presented as a detailed account of configuration decisions, search-space dynamics, and convergence behavior.Source: Appendix B · p. 34

Attempt 1 — Manual Initialization

  • The manual-initialization attempt starts with Npop=10 and Ngen=10 over broad gain bounds, satisfying three targets but leaving control effort at 0.95 against a 0.1 target.Its success score is 75/100, with Kd and Kp near their upper bounds.Source: Attempt 1 — Manual Initialization · pp. 34–35

Attempt 2 — Diagnosing a Boundary-Constrained Local Minimum

  • After diagnosing high gains and insufficient effort penalty, attempt 2 narrows Kp and Kd ranges and increases the control-effort weight; effort falls to 0.291, still 2.9× the target.The best cost drops from 6.78 to 0.61, while the success score remains 75/100.Source: Attempt 2 — Diagnosing a… · p. 35

Attempt 3 — Progressive Tightening of the Search Space

  • By attempt 3’s end, bounds had been tightened for the second consecutive time; best cost reached −0.28, exceeding the initial baseline, while effort was 0.212 and success remained 75/100 because effort exceeded the 0.1 target.Source: Attempt 3 — Progressive Tightening of… · p. 36

Attempt 4 — Scaling Up Within the Identified Region

  • By attempt 4, control effort falls to 0.092, below the 0.1 target, and the success score reaches 100/100.The LLM treats the absence of boundary violations as confirmation of the search region and increases the GA budget without changing parameter ranges.Source: Attempt 4 — Scaling Up Within the… · p. 36

Convergence Analysis and Comparison with Regular GA

GA-Agent improves the final cost over a fixed-configuration Regular GA, with the clearest differences in control effort and the gain-search trajectory. Its attempt-boundary changes redirect the search toward lower gains.

Overall cost

Individual metrics

Interpretation

  • GA-Agent’s advantage comes from diagnosing failure modes and changing configurations between runs, rather than from any single GA run being superior.The Regular GA remains in a high-gain attractor, whereas GA-Agent explicitly escapes it after attempt 1.Source: Convergence Analysis and Comparison… · pp. 36–37

PID gain trajectories

Appendix C. Sensitivity Analysis

The sensitivity studies vary the LLM backbone, memory buffer, and prompt format across AUV and Aircraft Pitch. Performance depends on these choices, but the study identifies practical defaults and cost-effective model options.

LLM backbone comparison

  • Gemini-2.5-Flash and DeepSeek-V4-Flash both achieve 100.0±0.0% success; DeepSeek-V4-Flash is the most attempt-efficient, requiring 3.8±1.5 attempts on average, versus GPT-4.1-Mini’s 8.2 ± 3.5.Source: Appendix C · pp. 38–39

Wall-clock time and budget use

  • Gemini-2.5-Flash and Claude-Haiku-4.5 complete in 25.7 and 26.8 seconds on average, using 2.6% and 2.7% of the 1000-second budget.All tested models finish within the time constraint; the passage identifies GA function evaluations, not LLM inference or overhead, as the dominant cost.Source: Figure C.13 · p. 39, Appendix C · p. 40

Per-case-study performance

  • Model rankings differ by plant: Grok-3-Mini-Beta has the lowest normalized cost on AUV (0.20), while GPT-4.1-Mini leads on Aircraft Pitch (0.02).The findings indicate that no single model dominates across both case studies.Source: Figure C.13 · p. 39, Appendix C · p. 40

Overall assessment

  • The tested models tolerate a range of backbone choices, with meaningful success-rate degradation concentrated in the weakest tested model.The authors report that strong performance does not require top-tier reasoning capacity, creating an opportunity to reduce model cost without sacrificing controller quality.Source: Appendix C · pp. 38, 40

Memory buffer size

  • Grok-4.1-Fast peaks at 82.5 ± 18.2% success with B = 5, while Grok-3-Mini-Beta peaks at 80.0 ± 21.8% with B = 2.For both models, success does not rise monotonically with buffer size; the cited practical defaults are B = 3 for stronger models and B = 2 for lightweight models.Source: Figure C.14 · p. 41, Appendix C · pp. 41–42
  • Normalized baseline cost falls as buffers grow, but this does not imply more targets are jointly satisfied.The study distinguishes the continuous aggregate cost from success score, which measures joint target satisfaction.Source: Appendix C · p. 42

Appendix C.3. Ablation Study

The ablation compares four prompt formats with identical semantic content on AUV and Aircraft Pitch. Results show broadly similar success, with differences in cost, token use, and variation across runs.

Success score

  • Original and Prose prompts each achieve 100.0 ± 0.0% success, while XML achieves 92.5± 16.9% and Enumerated reaches 97.5 ± 7.9%.The four variants differ in presentation only; the reported success spread is 7.5 percentage points.Source: Appendix C.3 · pp. 42–43, Figure C.15 · p. 43

Baseline cost

  • The Original prompt has the lowest mean normalized baseline cost (0.288), although Prose is lower on AUV (0.438 versus 0.504).XML has the highest normalized cost on Aircraft Pitch (0.320) and AUV (0.530).Source: Appendix C.3 · p. 43, Figure C.15 · p. 43

Token consumption

  • Prose uses 15,410 total tokens, compared with 34,629 for XML, which consumes 2.2× more.The passage treats lower token use as an indirect sign of earlier convergence, not a shorter prompt.Source: Appendix C.3 · pp. 43–44, Figure C.15 · p. 43

Overall assessment

  • The authors recommend the Original Markdown prompt for its perfect success, lowest baseline cost, and moderate token efficiency; Prose is a viable alternative.XML is least recommended because of its higher variance and elevated token cost.Source: Appendix C.3 · pp. 43–44

Appendix C.3.1. Effect of System Context: GA-Agent vs. GA-Agent+

Across the three variants, initialization trades prior plant knowledge against robustness: LLM Init can be efficient when its proposed gain ranges fit the plant, while Manual Init handles atypical gain requirements better. The appendices also specify the fixed Regular GA baseline, the Cascade GA’s bilevel search, and the simulation and software setup.

Appendix C.3.1. Effect of System Context: GA-Agent vs. GA-Agent+

  • GA-Agent (system-blind) achieves 100% success on all eight benchmarks; LLM Init has the highest NFE efficiency on three but misses 100% on Aircraft Pitch and CSTR.Manual Init reaches 100% on six of eight benchmarks, with DC Motor at 80%.Source: Appendix C.3.1 · p. 45
  • LLM Init excels when its initial gain ranges suit the plant but can fail on atypical requirements; Manual Init’s broad bounds defer specialization to later adaptation.Aircraft Pitch favors Manual Init (−2.02±0.15, 100% success at 896 NFE) over LLM Init (2.70 ± 5.75, 75% success at 4,264 NFE); DC Motor shows the reverse, with LLM Init at −3.38 ± 0.49 and 100% success at 1,426 NFE, versus Manual Init at 4.64±17.72 and 80.0±32.6% success at 11,660 NFE. On easy 2DoF Helicopter, LLM Init uses 3,953 NFE versus 46 NFE for both alternatives, all at 100% success.Source: Appendix C.3.1 · pp. 44–45, Table C.4 · p. 45

Appendix D.1. Regular GA

  • The Regular GA uses fixed operator parameters across case studies and seeds, and stops at 500 generations, when all targets are met, or at a 1,000-second wall-clock limit.CSTR and Aircraft Pitch use fewer than the maximum NFE under the Regular GA; the text attributes this to the wall-clock limit or early target satisfaction in some seeds.Source: Appendix D.1 · pp. 45–46

Appendix D.2. Cascade GA

  • Cascade GA searches hyperparameters with an outer GA whose seven-gene chromosomes encode four fitness weights and three PID gain upper bounds for the inner GA.Memoized evaluations avoid rerunning an inner GA for previously evaluated chromosome keys; chromosome-specific seeds make distinct configurations reproducible and give them different inner-GA initializations.Source: Appendix D.2 · pp. 46–48

Appendix D.3. ODE Solver and Simulation

  • All simulations use fixed-step forward Euler with zero-order hold, and no implicit or stiff solver is used; results retain first-order truncation error, O(∆t).For the stiff CSTR, ∆t = 0.001 s was selected conservatively to ensure Euler stability while keeping fitness evaluations cheap and deterministic.Source: Appendix D.3 · pp. 49–50

Appendix D.4. Implementation Details

  • The implementation uses LangGraph for workflow orchestration, the OpenAI SDK for model calls, NumPy for simulation, and PyGAD for GA operators and population management.The appendix describes the software stack and execution environment used for the experiments.Source: Appendix D.4 · p. 50, Appendix D.4.1 · pp. 50–51

Appendix D.4.2. Hardware Configuration

This appendix section documents GA-Agent’s evaluation and configuration setup, including its CPU-only sequential workflow, prompt templates, and decision rules. It also describes XML, enumerated, and prose prompt formats that preserve semantic content while varying its presentation.

Appendix D.4.2. Hardware Configuration

  • LLM inference latency and API round-trip time, rather than fitness evaluations, are the main GA-Agent workflow bottleneck.Experiments use no GPU acceleration, and candidates within each generation are evaluated sequentially on a single CPU core.Source: Appendix D.4.2 · p. 51

Appendix E. Full Prompts Used

  • Each LLM call combines a fixed system prompt with a runtime user prompt assembled from the goal, memory, and budget modules.Four prompt variants were evaluated; the original Markdown-rich heuristic prompt was used in the main experiments and as the ablation reference.Source: Appendix E · p. 54

• Variation 1 (Prose):

• Variation 2 (XML):

  • The XML variant expresses hierarchy through semantic tags such as parameter, rule, and resource-strategy elements.Source: • Variation 2 (XML) · p. 54

• Variation 3 (Enumerated):

  • The enumerated variant uses decimal-numbered hierarchy to make instructions addressable, while all prompt variants retain the same semantic content and output schema.The formatting comparison isolates presentation from information content; context variants separately determine whether system name and physical description are supplied.Source: • Variation 3 (Enumerated) · pp. 54–55

Appendix E.1.2. User Prompt Templates

  • User templates distinguish the initial attempt from subsequent attempts and provide GA-Agent+ with system context, while GA-Agent uses a generic problem-context preamble.The templates include fixed targets and simulation parameters, attempt information, and instructions to return a resource-aware GA configuration in JSON.Source: Appendix E.1.2 · pp. 57–58

Appendix E.2.2. System Prompt (Variation 1 – Prose)

  • The prose system prompt directs the agent to tune objective weights, GA population and generations, and PID gain ranges under separate cost and time budgets.Boundary rules expand ranges when performance improves, restrict them when it stagnates or worsens, and reverse repeated restrictions if the parameter keeps reaching the new ceiling; persistent target failures despite weight increases call for structural range changes.Source: Appendix E.2.2 · pp. 60–61

Appendix E.2.3. User Prompt Templates

  • Variation 1 user templates retain the same placeholders and GA-Agent/GA-Agent+ context split but remove Markdown formatting in favor of plain declarative text.The closing instruction is also changed from Markdown bold to a plain imperative sentence.Source: Appendix E.2.3 · p. 62

Appendix E.3.2. System Prompt (Variation 2 – XML)

  • The XML system prompt encodes the same objective-weight tradeoffs and gain-boundary rules, including expansion after repeated ceiling hits and tightening ranges when parameters cluster away from boundaries.It frames GA fitness as the weighted sum of squared achieved objectives and baseline cost as normalized distance from fixed targets.Source: Appendix E.3.2 · p. 63
  • The XML system prompt adjusts metric weights and gain ranges in response to failures while adapting GA size and iteration strategy to cost and time budgets.It recommends early weight exploration, scaling up during refinement if time allows, and a larger final run; simulation parameters remain fixed.Source: Appendix E.3.2 · pp. 64–65

Appendix E.3.3. User Prompt Templates

  • The XML user templates wrap prompt fields in corresponding elements, with subsequent attempts adding current weights, GA configuration, and an XML-encoded attempt counter.The GA-Agent+ template includes system information, while the no-context template uses a task preamble; placeholders match the Original.Source: Appendix E.3.3 · p. 65

Appendix E.4.2. System Prompt (Variation 3 – Enumerated)

  • The enumerated system prompt specifies weight, population, generation, and gain-range rules, including boundary-hit diagnosis, a ceiling-chasing exception, and resource-aware phases.Its decision guidelines also prescribe responses to stagnating costs and repeated target failures, while keeping simulation parameters fixed.Source: Appendix E.4.2 · pp. 66–67

Appendix E.4.3. User Prompt Templates

  • The enumerated user templates organize system information, targets, attempt status, feedback, and task instructions, adding current weights and GA configuration on later attempts.The no-context template substitutes problem context, and numbered instructions support references in the agent’s reasoning.Source: Appendix E.4.3 · pp. 67–68
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