MAPO Gaming: LLM-First Quality-Diversity Optimization for Automated PCB Layout Through Adversarial Co-Evolution

MAPO Gaming: LLM-First Quality-Diversity Optimization for Automated PCB Layout Through Adversarial Co-Evolution

Abstract

We present MAPO Gaming (Multi-Agent Pareto Optimization with Gaming AI), a novel framework for automated PCB layout optimization that synthesizes three complementary algorithmic paradigms: MAP-Elites quality-diversity optimization, Red Queen adversarial co-evolution, and Ralph Wiggum persistent iteration. Unlike conventional approaches that require extensive neural network training on domain-specific datasets, MAPO Gaming operates in an LLM-first mode where Large Language Models serve as first-class optimization operators---replacing the state encoder, value network, policy network, and dynamics model typically implemented as trained neural networks. We introduce a 10-dimensional behavioral descriptor space specifically designed for PCB layouts, capturing characteristics from routing density to thermal distribution. Our 8-domain validation framework simultaneously optimizes against DRC, ERC, IPC-2221 compliance, signal integrity, thermal performance, manufacturability, best practices, and testability. Experimental evaluation on a complex 10-layer, 164-component FOC motor controller demonstrates 63% reduction in DRC violations and 95% reduction in unconnected items compared to baseline automated tools. The framework achieves these results without any training data, model fine-tuning, or GPU infrastructure---requiring only API access to a capable LLM. We provide comprehensive analysis of convergent evolution dynamics, demonstrating that adversarial co-evolution produces solutions that are not merely locally optimal but robust across diverse constraint landscapes. This work establishes a new paradigm for applying evolutionary computation to electronic design automation through LLM-mediated intelligence.

1. Introduction

The design of printed circuit boards (PCBs) represents one of the most challenging optimization problems in modern engineering. A typical PCB layout must simultaneously satisfy hundreds of design rules while optimizing for signal integrity, thermal management, manufacturability, and cost. Traditional electronic design automation (EDA) tools rely on rule-based algorithms and constraint solvers that, while effective for simple designs, struggle with the exponentially growing complexity of modern electronics.

Recent advances in deep reinforcement learning have demonstrated promising results for PCB placement and routing. Wang et al. proposed hierarchical reinforcement learning for power electronics PCB layout, achieving significant reductions in critical current loop lengths. FanoutNet introduced neuralized PCB fanout automation using deep reinforcement learning with CNN and attention-based architectures. However, these approaches share a common limitation: they require extensive training on domain-specific datasets, limiting their applicability to novel design categories.

We observe that the PCB layout optimization problem exhibits characteristics that make it particularly amenable to a different class of algorithms: quality-diversity optimization. Unlike single-objective optimization that converges to a single best solution, quality-diversity algorithms maintain an archive of diverse, high-performing solutions across a behavioral space. This diversity provides two critical advantages: (1) it enables discovery of novel solutions through "stepping stones" in behavioral space, and (2) it produces a portfolio of design options from which engineers can select based on secondary criteria.

1.1 Contributions

This paper makes the following contributions:

1. LLM-First Architecture: We demonstrate that Large Language Models can serve as effective replacements for trained neural networks in evolutionary PCB optimization, eliminating the need for training data, GPU infrastructure, and domain-specific model development.

2. MAP-Elites for PCB Layout: We introduce a 10-dimensional behavioral descriptor space specifically designed for PCB characteristics, enabling quality-diversity optimization in the electronic design domain for the first time.

3. Red Queen Adversarial Co-Evolution: We adapt the Digital Red Queen paradigm from code evolution to circuit design, where PCB layouts must beat all historical champions across accumulating constraint sets.

4. Ralph Wiggum Persistent Iteration: We implement file-based state persistence with stagnation detection and escalation strategies, enabling indefinite optimization until success criteria are met.

5. 8-Domain Validation Framework: We present a unified fitness function spanning DRC, ERC, IPC-2221 compliance, signal integrity, thermal analysis, DFM, best practices, and testability.

6. Multi-Agent Tournament Architecture: We introduce a 5-agent tournament system where specialized agents (Signal Integrity, Thermal/Power, Manufacturing, etc.) compete and evolve through Elo-ranked matches.

1.2 Paper Organization

Section 2 reviews related work in PCB automation, quality-diversity optimization, and LLM-based evolutionary algorithms. Section 3 presents the system architecture and LLM-first design philosophy. Section 4 details the MAP-Elites implementation with PCB-specific behavioral descriptors. Section 5 describes the Red Queen adversarial co-evolution mechanism. Section 6 covers the Ralph Wiggum persistent iteration framework. Section 7 presents the multi-agent tournament system. Section 8 describes the 8-domain validation framework. Section 9 provides experimental evaluation. Section 10 discusses implications and limitations, and Section 11 concludes.

2. Related Work

2.1 PCB Layout Automation

The automation of PCB layout has been an active research area for decades. Early approaches relied on rule-based systems and simulated annealing. More recently, deep learning approaches have shown promise.

Wang et al. proposed a hierarchical reinforcement learning approach for power electronics PCB design, where a high-level agent oversees sub-circuit placement while low-level agents optimize individual placements. Their method achieved significant reductions in critical current loop lengths but required extensive training on power electronics datasets.

Liao et al. introduced FanoutNet, the first automation method for PCB fanout using deep reinforcement learning. Their approach combines convolutional neural networks with attention mechanisms, trained using Proximal Policy Optimization (PPO). While effective for fanout specifically, the method does not address the broader layout optimization problem.

Recent work by InstaDeep demonstrated that AI-driven optimization could reduce PCB design time from weeks to hours---a medium-sized board that previously took two engineers four weeks was 80-90% completed by their system in 24 hours. However, their approach requires significant training infrastructure and domain adaptation.

2.2 Quality-Diversity Optimization

Quality-diversity (QD) algorithms represent a paradigm shift from traditional optimization. Rather than seeking a single optimal solution, QD algorithms maintain an archive of diverse, high-performing solutions across a behavioral space.

MAP-Elites, introduced by Mouret and Clune (2015), discretizes the behavioral space into a grid where each cell stores the highest-performing solution discovered for that behavioral niche. This simple yet powerful approach has demonstrated remarkable success in robotics, enabling damage recovery through behavioral repertoires.

Recent extensions include CMA-ME (Fontaine et al., 2020) which uses Covariance Matrix Adaptation within MAP-Elites, and differentiable quality-diversity approaches. However, to our knowledge, no prior work has applied MAP-Elites or related QD algorithms to electronic design automation.

2.3 Adversarial Co-Evolution

The Red Queen hypothesis, named after the character in Lewis Carroll's "Through the Looking-Glass" who must run constantly just to stay in place, describes evolutionary dynamics where competing species must continually evolve to maintain relative fitness.

Sakana AI's Digital Red Queen (2026) demonstrated this principle in the domain of Core War, where assembly programs evolved through adversarial competition using LLM-based mutation operators. Their work showed that Red Queen dynamics could produce solutions that generalize across diverse opponents---a form of robustness that single-objective optimization cannot achieve.

We adapt this paradigm to circuit design, where the "opponents" are not competing programs but rather accumulating sets of design constraints and validation criteria.

2.4 LLM-Based Evolutionary Algorithms

The integration of Large Language Models with evolutionary computation represents an emerging research direction. LLMatic (Nasir et al., 2023) demonstrated that LLMs could serve as mutation operators in neural architecture search, achieving competitive results with significantly less computational overhead than traditional NAS methods.

Lehman et al. (2022) introduced Evolution through Large Models (ELM), showing that LLMs could generate novel code solutions through mutation and crossover operations guided by natural language. Their work established that LLMs possess sufficient domain knowledge to serve as intelligent variation operators.

CircuitLM (2025) presented a multi-agent LLM pipeline for circuit schematic generation, using specialized agents for different design aspects. While focused on schematic generation rather than layout optimization, their work demonstrates the viability of LLM-based approaches in the EDA domain.

2.5 Positioning of Our Work

MAPO Gaming synthesizes insights from all four areas above into a unified framework. Unlike prior PCB automation work, we require no training data or neural network infrastructure. Unlike standard QD optimization, we incorporate adversarial dynamics that encourage robust, generalizable solutions. Unlike prior LLM-evolutionary work, we target the specific domain of physical electronic design with a comprehensive multi-domain fitness function.

3. System Architecture

3.1 Design Philosophy: LLM-First

The central architectural decision in MAPO Gaming is to use Large Language Models as the primary intelligence layer, rather than as a fallback or augmentation to trained neural networks. This "LLM-first" philosophy offers several advantages:

No Training Required: Traditional RL-based PCB optimization requires extensive training on domain-specific datasets. MAPO Gaming requires only API access to a capable LLM (e.g., Claude, GPT-4), eliminating the need for training infrastructure, dataset curation, and model maintenance.

Zero-Shot Generalization: LLMs encode broad knowledge about electronic design principles, enabling effective optimization even on novel design categories not seen during any training process.

Interpretable Reasoning: LLM-generated mutations come with natural language explanations, providing insight into optimization decisions that opaque neural networks cannot offer.

Rapid Iteration: Without training cycles, new validation criteria or design rules can be incorporated immediately through prompt modification.

3.2 LLM Backend Architecture

We replace four traditional neural network components with LLM-based alternatives:

3.2.1 State Encoder (Replaces GNN/CNN)

Traditional approaches use Graph Neural Networks or Convolutional Neural Networks to encode PCB state. We replace this with a deterministic hash function combined with semantic analysis:

StateEncoding = Hash(ComponentPositions, TraceRoutes, Zones)
              + LLM_Summarize(DesignContext, ViolationTypes)

The hash provides a unique identifier for the design state, while LLM summarization extracts semantic understanding of the current design quality.

3.2.2 Value Network (Replaces MLP)

Instead of a trained Multi-Layer Perceptron predicting design quality, we prompt the LLM with the current design state and violation summary:

YAML
3 lines
Copy
Prompt: "Given a PCB with {component_count} components, {layer_count} layers,
        current violations: {violation_summary}, estimate the design quality
        score from 0.0 to 1.0 and identify the most impactful improvement areas."

3.2.3 Policy Network (Replaces Softmax Action Selection)

The policy network traditionally outputs a probability distribution over possible modifications. Our LLM-based policy generates structured modification suggestions:

YAML
6 lines
Copy
Prompt: "Suggest a modification to improve this PCB layout.
        Current state: {state_summary}
        Top violations: {top_violations}
        Round {round_number} - must beat {champion_count} previous champions.

        Respond with JSON: {modification_type, target_component, parameters}"

3.2.4 Dynamics Model (Replaces World Model)

For planning and look-ahead, we use LLM-based outcome simulation:

YAML
3 lines
Copy
Prompt: "If we apply {modification} to the current design,
        predict the resulting violation count and which violations
        would be resolved vs. introduced."

3.3 Configuration

The system supports both LLM-first and hybrid modes:

Python
7 lines
Copy
@dataclass
class GamingAIConfig:
    use_llm: bool = True              # Primary intelligence layer
    use_neural_networks: bool = False  # Optional GPU acceleration
    llm_model: str = "anthropic/claude-sonnet-4-20250514"
    llm_temperature: float = 0.7
    llm_max_tokens: int = 2048

When use_neural_networks=True, optional neural components can accelerate evaluation, but the LLM remains the primary decision-maker for mutations.

4. Quality-Diversity with MAP-Elites

4.1 Behavioral Descriptor Space

The effectiveness of MAP-Elites depends critically on the choice of behavioral descriptors---dimensions that capture meaningful variation in solution behavior. For PCB layouts, we define a 10-dimensional behavioral space:

4.2 Behavioral Discretization

The continuous behavioral space is discretized into a grid archive. For 10 dimensions with 10 bins each, the theoretical archive size is 10^10 cells. In practice, the archive remains sparse---typically only 3-5% of cells are occupied---as evolution explores promising regions.

Python
5 lines
Copy
def discretize(descriptor: BehavioralDescriptor, bins: int = 10) -> Tuple[int, ...]:
    """Convert continuous descriptor to discrete grid coordinates."""
    vector = descriptor.to_vector()  # [0, 1]^10
    indices = tuple(min(int(v * bins), bins - 1) for v in vector)
    return indices

4.3 Archive Operations

The MAP-Elites archive supports three key operations:

Add: When a new solution is generated, compute its behavioral descriptor, discretize to grid coordinates, and compare against the existing occupant (if any). If the new solution has higher fitness, it replaces the occupant.

Sample: Two sampling strategies are supported:

• Fitness-weighted: Sample cells proportional to their fitness, encouraging exploitation of high-quality regions.
• Curiosity-weighted: Sample cells inversely proportional to their visitation count, encouraging exploration of under-explored regions.

Statistics: Track archive coverage, average fitness, diversity metrics, and improvement trajectory over iterations.

4.4 Quality-Diversity Dynamics

The power of MAP-Elites lies in its ability to maintain diverse solutions that serve as "stepping stones" to novel high-quality regions. A solution that appears suboptimal in isolation may occupy a critical cell in behavioral space, enabling subsequent mutations to reach otherwise inaccessible regions.

In PCB optimization, this manifests as maintaining design variants with different trade-off profiles. A thermally-focused design (low thermal spread, high zone coverage) and a signal integrity-focused design (low signal length variance, high power path directness) both occupy the archive, even if neither achieves the absolute best fitness.

5. Red Queen Adversarial Co-Evolution

5.1 Motivation

Standard evolutionary optimization converges toward solutions that perform well on a fixed fitness function. However, real-world PCB designs must be robust across diverse manufacturing conditions, component variations, and operating environments. The Red Queen mechanism addresses this by continuously raising the bar for solution quality.

5.2 Round-Based Evolution

Evolution proceeds in discrete rounds. Each round maintains its own MAP-Elites archive and extracts champions---the top-performing solutions---at completion. Critically, solutions in subsequent rounds are evaluated not only on base fitness but also on their ability to beat all previous champions.

Round 1: Optimize for base fitness (DRC, ERC, etc.)
         → Extract 5 champions

Round 2: Optimize for base fitness + beat Round 1 champions
         → Extract 5 champions (now 10 total in history)

Round 3: Optimize for base fitness + beat all 10 historical champions
         → Extract 5 champions (now 15 total)

...continuing until convergence or termination

5.3 Generality Scoring

The generality score measures how well a solution performs against historical champions:

Python
23 lines
Copy
def evaluate_generality(solution, champions_history) -> GeneralityScore:
    wins, ties, losses = 0, 0, 0
    win_margins = []

    for round_champions in champions_history:
        for champion in round_champions:
            margin = solution.fitness - champion.fitness
            if margin > WIN_THRESHOLD:
                wins += 1
                win_margins.append(margin)
            elif margin > -TIE_THRESHOLD:
                ties += 1
            else:
                losses += 1

    total = wins + ties + losses
    generality = (wins + ties * 0.5) / max(1, total)

    return GeneralityScore(
        wins=wins, ties=ties, losses=losses,
        generality=generality,
        win_margin=np.mean(win_margins) if win_margins else 0.0
    )

5.4 Combined Fitness

The combined fitness balances base design quality with generality across historical champions:

Python
6 lines
Copy
def combined_fitness(base_fitness, generality, round_number):
    # Adaptive weighting: generality importance increases over rounds
    gen_weight = min(0.7, 0.3 + round_number * 0.05)
    fit_weight = 1.0 - gen_weight

    return fit_weight * base_fitness + gen_weight * generality.generality

In early rounds (round 1-2), base fitness dominates. By round 8-10, generality accounts for up to 70% of combined fitness, strongly encouraging robust solutions.

5.5 Convergent Evolution Tracking

A key insight from biological evolution is that different evolutionary paths can converge on similar solutions (phenotypes) through different mechanisms (genotypes). We track this phenomenon:

Phenotype Hash: Hash of the behavioral descriptor vector (what the design does) Genotype Hash: Hash of the design parameters (how the design is implemented)

When phenotype variance decreases while genotype diversity remains high, we observe convergent evolution---different design approaches arriving at similar behavioral profiles. This indicates the evolutionary process has discovered robust behavioral targets.

6. Ralph Wiggum Persistent Iteration

6.1 Philosophy

Named after the Simpsons character known for never giving up despite setbacks, the Ralph Wiggum technique implements persistent, file-based iteration that continues until explicit success criteria are met. Unlike traditional optimization that runs for a fixed number of iterations, Ralph Wiggum optimizers "never say die."

Core principle: "Iteration beats perfection when you have clear goals and automatic verification."

6.2 Completion Criteria

Optimization success is defined by configurable criteria:

Python
13 lines
Copy
@dataclass
class CompletionCriteria:
    target_violations: int = 50      # Maximum acceptable DRC violations
    target_fitness: float = 0.9      # Minimum fitness score
    target_generality: float = 0.8   # Required generality vs. champions
    max_iterations: int = 1000       # Safety limit
    max_stagnation: int = 15         # Iterations without improvement
    max_duration_hours: float = 24.0 # Time limit

    def is_success(self, violations, fitness, generality):
        return (violations <= self.target_violations and
                fitness >= self.target_fitness and
                generality >= self.target_generality)

6.3 File-Based Persistence

All optimization state persists to disk, enabling:

• Resume from interruption: Power failures, system updates, or manual stops don't lose progress
• Parallel optimization: Multiple instances can checkpoint independently
• Audit trail: Complete history of optimization decisions

State files include:

• .kicad_pcb: Current best PCB design
• .mapos_state.json: Iteration count, fitness history, current champions
• .mapos_history.json: Complete violation and fitness trajectory
• Git commits: Versioned design history with meaningful messages

6.4 Stagnation Detection and Escalation

When optimization stalls (no improvement for max_stagnation iterations), escalation strategies activate:

Python
6 lines
Copy
class EscalationStrategy(Enum):
    INCREASE_MUTATION = auto()   # Raise mutation rate from 0.8 to 0.95
    RESET_POPULATION = auto()    # Clear archive, keep only champions
    SWITCH_AGENTS = auto()       # Rotate agent priorities
    EXPAND_SEARCH = auto()       # Increase behavioral space granularity
    CALL_FOR_HELP = auto()       # Flag for human review

Escalation proceeds through strategies in sequence. If all strategies are exhausted without breaking stagnation, the system flags for human intervention while continuing to explore.

6.5 Atomic Operations

All file operations use atomic writes to prevent corruption:

Python
10 lines
Copy
def atomic_write_json(filepath: Path, data: Dict):
    """Write JSON atomically via temp file + rename."""
    fd, temp_path = tempfile.mkstemp(dir=filepath.parent)
    try:
        with os.fdopen(fd, 'w') as f:
            json.dump(data, f, indent=2)
        os.replace(temp_path, filepath)  # Atomic on POSIX
    except:
        os.unlink(temp_path)
        raise

File locking prevents race conditions in multi-instance deployments.

7. Multi-Agent Tournament System

7.1 Specialized Optimization Agents

MAPO Gaming employs five specialized agents, each focusing on different PCB quality aspects:

7.2 Tournament Structure

Agents compete in round-robin tournaments where each agent's proposed modifications are evaluated against the current best design:

Tournament Round:
  1. Each agent proposes a modification given current state
  2. All modifications are applied and evaluated independently
  3. Solutions are ranked by combined fitness
  4. Winner's modification is accepted; Elo ratings updated

7.3 Elo Rating System

Agent performance is tracked using the Elo rating system, originally developed for chess:

Python
5 lines
Copy
def update_elo(winner_rating, loser_rating, k=32):
    expected_win = 1 / (1 + 10 ** ((loser_rating - winner_rating) / 400))
    winner_new = winner_rating + k * (1 - expected_win)
    loser_new = loser_rating + k * (0 - (1 - expected_win))
    return winner_new, loser_new

Agents with higher Elo ratings receive more opportunities to propose modifications, creating a meritocratic selection pressure.

7.4 Agent Collaboration Dynamics

Despite competition, agents implicitly collaborate through the shared archive. A Signal Integrity Agent's modification might create opportunities for the Thermal Agent to optimize in subsequent iterations. The tournament structure ensures that modifications benefiting overall design quality are selected, regardless of which agent proposed them.

8. Eight-Domain Validation Framework

8.1 Unified Fitness Function

PCB quality cannot be captured by a single metric. Our 8-domain validation framework provides comprehensive assessment:

Cypher
11 lines
Copy
Fitness = Σ(weight_i × domain_score_i) for i in [1..8]

Where domains and weights are:
  DRC Score:           20%
  ERC Score:           15%
  IPC-2221 Compliance: 15%
  Signal Integrity:    15%
  Thermal Score:       15%
  DFM Score:           10%
  Best Practices:       5%
  Testing Score:        5%

8.2 Domain Descriptions

8.2.1 DRC Score (20%)

Design Rule Checking validates physical manufacturability:

• Minimum trace width and spacing
• Via drill sizes and annular rings
• Copper-to-edge clearances
• Silkscreen overlaps

8.2.2 ERC Score (15%)

Electrical Rule Checking validates connectivity:

• Unconnected pins and nets
• Short circuits
• Missing net connections
• Power/ground continuity

8.2.3 IPC-2221 Compliance (15%)

Industry standard compliance per IPC-2221:

• Trace width for current capacity: I = 0.048 × ΔT^0.44 × A^0.725 (external)
• Via current capacity based on barrel plating
• Voltage clearance requirements
• Thermal relief specifications

8.2.4 Signal Integrity (15%)

High-speed signal quality metrics:

• Impedance matching (±10% target)
• Crosstalk coupling coefficients
• Length matching for differential pairs
• Return path continuity

8.2.5 Thermal Score (15%)

Heat management assessment:

• Thermal via coverage under power components
• Copper spreading for heat dissipation
• Junction temperature estimates
• Thermal relief for assembly

8.2.6 DFM Score (10%)

Design for Manufacturing validation:

• Solder mask dam requirements
• Silkscreen legibility
• Panel utilization efficiency
• Assembly clearances

8.2.7 Best Practices (5%)

Industry best practice adherence:

• Decoupling capacitor placement
• Power plane splits
• Test point accessibility
• Reference designator conventions

8.2.8 Testing Score (5%)

Test coverage and accessibility:

• Test point coverage per net class
• Probe accessibility analysis
• Boundary scan compliance
• In-circuit test feasibility

8.3 Actionable Feedback

Each domain validator produces not just a score but actionable feedback for the optimization loop:

Python
13 lines
Copy
@dataclass
class ValidationResult:
    domain: str
    score: float  # 0.0 to 1.0
    violations: List[Violation]
    suggestions: List[Suggestion]

@dataclass
class Suggestion:
    priority: int  # 1=critical, 2=important, 3=recommended
    description: str
    affected_items: List[str]  # Component refs or net names
    modification_hint: Dict  # Structured hint for LLM policy

This structured feedback enables the LLM policy network to make informed modification decisions.

9. Experimental Evaluation

9.1 Benchmark Design

We evaluate MAPO Gaming on a complex reference design: a 10-layer Field-Oriented Control (FOC) motor controller for heavy-lift drone applications. This design presents significant optimization challenges:

9.2 Baseline Comparison

We compare MAPO Gaming against:

1. KiCad Autorouter: Built-in automatic routing
2. Freerouting: Open-source Java-based autorouter
3. Manual Expert Design: Professional layout engineer (20+ years experience)

9.3 Optimization Pipeline

MAPO Gaming operates as phase 7 of a 7-phase optimization pipeline:

9.4 Results

9.4.1 Violation Reduction

9.4.2 Quality Metrics

| Overall Fitness | 0.78 | 0.91 | +17% |
| Signal Integrity Score | 0.82 | 0.89 | +9% |
| Thermal Score | 0.71 | 0.85 | +20% |
| DFM Score | 0.85 | 0.92 | +8% |
| IPC-2221 Compliance | 0.79 | 0.94 | +19% |

9.4.3 Optimization Dynamics

Evolution typically proceeds through distinct phases:

Phase A (Iterations 1-100): Rapid improvement as obvious violations are addressed. Fitness increases from ~0.4 to ~0.7.

Phase B (Iterations 100-300): Slower improvement as archive diversifies. Multiple behavioral niches are explored.

Phase C (Iterations 300-500): Red Queen dynamics dominate. Solutions must beat accumulating champions.

Phase D (Iterations 500+): Convergent evolution observed. Phenotype variance decreases while genotype diversity maintains.

9.5 Convergent Evolution Analysis

A key finding is the emergence of convergent evolution---different optimization paths arriving at similar behavioral profiles. By round 8, phenotype variance (measured as standard deviation of behavioral descriptors among champions) decreased by 67% compared to round 1, while genotype diversity (unique parameter configurations) remained high.

This indicates that the adversarial pressure of beating historical champions drives solutions toward robust behavioral targets that represent genuinely good design trade-offs, not merely local optima.

9.6 Ablation Studies

We conducted ablation studies to assess component contributions:

*Neural network configuration required 48 hours of training before optimization.

Key observations:

• Red Queen contributes +7% to final fitness by encouraging robust solutions
• MAP-Elites reduces time-to-quality by 32% through diverse exploration
• Tournament system improves fitness by +9% over single-agent
• LLM-first achieves comparable quality to neural networks without training overhead

9.7 Computational Requirements

LLM-first mode trades slightly longer optimization time for dramatically reduced total cost and eliminated training requirements.

10. Discussion

10.1 LLM as First-Class Optimization Operator

Our results demonstrate that LLMs can serve effectively as optimization operators in domain-specific applications without fine-tuning. The key insight is that LLMs encode sufficient general knowledge about electronic design principles to make reasonable modification suggestions when provided with structured context about the current design state and violation patterns.

This has significant implications for EDA tool development. Rather than investing months in training domain-specific neural networks, tool developers can leverage existing LLM capabilities through careful prompt engineering and structured feedback.

10.2 Quality-Diversity for Physical Design

The success of MAP-Elites in PCB optimization suggests broader applicability of quality-diversity algorithms to physical design problems. The 10-dimensional behavioral space we define captures meaningful variation in PCB characteristics, but similar spaces could be defined for IC layout, mechanical enclosure design, or antenna geometry optimization.

10.3 Adversarial Robustness Through Evolution

The Red Queen mechanism produces solutions that are not merely locally optimal but robust across diverse constraint landscapes. This robustness is particularly valuable for PCB designs that must function across manufacturing variations, temperature ranges, and component tolerances.

10.4 Limitations

Several limitations warrant discussion:

LLM Dependency: The current implementation depends on API access to capable LLMs. API availability, pricing changes, or capability regressions could impact system performance.

Evaluation Speed: Each design modification requires DRC/ERC evaluation, which takes 2-5 seconds in KiCad. This limits iteration speed compared to purely simulated environments.

Behavioral Space Design: Our 10-dimensional behavioral space, while effective, was designed through domain expertise. Automated behavioral space discovery could improve generalization.

Scalability: The current implementation has been validated on boards up to 200 components. Scaling to 1000+ component designs may require architectural modifications.

10.5 Future Directions

Several directions merit future investigation:

Hierarchical Optimization: For large designs, hierarchical decomposition into sub-circuits optimized independently before global integration could improve scalability.

Transfer Learning: Champions from one design could seed optimization for similar designs, reducing iteration requirements.

Human-in-the-Loop: Integration of designer preferences and feedback could guide optimization toward solutions that better match implicit design requirements.

Multi-Board Optimization: Extending the framework to optimize multiple interconnected boards (e.g., motherboard + daughter cards) presents interesting challenges in cross-board constraint management.

11. Conclusion

We have presented MAPO Gaming, a novel framework for automated PCB layout optimization that synthesizes MAP-Elites quality-diversity optimization, Red Queen adversarial co-evolution, and Ralph Wiggum persistent iteration. Our LLM-first architecture demonstrates that Large Language Models can serve as effective optimization operators without neural network training, achieving 63% reduction in DRC violations on a complex 10-layer reference design.

The framework's three algorithmic pillars contribute complementary benefits: MAP-Elites maintains diverse solutions enabling stepping-stone discoveries; Red Queen dynamics encourage robust, generalizable designs; and Ralph Wiggum persistence ensures optimization continues until explicit success criteria are met.

Our 8-domain validation framework provides comprehensive PCB quality assessment spanning DRC, ERC, IPC-2221 compliance, signal integrity, thermal management, manufacturability, best practices, and testability. The multi-agent tournament system leverages specialized agents with Elo-ranked competition to balance exploration and exploitation.

Beyond immediate practical applications, MAPO Gaming establishes a new paradigm for applying evolutionary computation to electronic design automation. The synthesis of quality-diversity optimization with adversarial co-evolution, mediated by LLM intelligence, offers a template for tackling complex engineering optimization problems where traditional approaches require extensive training data and domain-specific model development.

The complete implementation is available as part of the Adverant EE Design Partner platform, enabling immediate application to real-world PCB design challenges.

References

1. Mouret, J.B. and Clune, J. (2015). Illuminating search spaces by mapping elites. arXiv:1504.04909.

2. Sakana AI. (2026). Digital Red Queen: Adversarial Program Evolution in Core War with LLMs. arXiv:2601.03335.

3. Wang, Y. (2024). Research on PCB Module Automatic Layout Algorithm based on Deep Reinforcement Learning. Archives Des Sciences, 74(S1).

4. Liao, W. et al. (2023). FanoutNet: A Neuralized PCB Fanout Automation Method Using Deep Reinforcement Learning. AAAI Conference on Artificial Intelligence.

5. Nasir, M. et al. (2023). LLMatic: Neural Architecture Search via Large Language Models and Quality Diversity Optimization. arXiv:2306.01102.

6. Lehman, J. et al. (2022). Evolution through Large Models. arXiv:2206.08896.

7. IPC-2221B. (2012). Generic Standard on Printed Board Design. Association Connecting Electronics Industries.

8. Fontaine, M. et al. (2020). Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space. GECCO.

9. Vassallo, L. (2024). Learning Circuit Placement Techniques through Reinforcement Learning with Adaptive Rewards.

10. Pugh, J.K., Soros, L.B., and Stanley, K.O. (2016). Quality Diversity: A New Frontier for Evolutionary Computation. Frontiers in Robotics and AI.

11. CircuitLM. (2025). A Multi-Agent LLM-Aided Design Framework for Generating Circuit Schematics from Natural Language Prompts. arXiv:2601.04505.

12. Huang, Z. et al. (2024). Fast ML-driven Analog Circuit Layout using Reinforcement Learning and Steiner Trees. arXiv:2405.16951.

13. Asai, A. et al. (2023). Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection. arXiv:2310.11511.

14. Stanley, K.O. and Miikkulainen, R. (2002). Evolving Neural Networks through Augmenting Topologies. Evolutionary Computation.

15. Cully, A. et al. (2015). Robots that can adapt like animals. Nature, 521(7553).

16. Ha, D. and Schmidhuber, J. (2018). World Models. arXiv:1803.10122.

17. Silver, D. et al. (2017). Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm. arXiv:1712.01815.

18. Schrittwieser, J. et al. (2020). Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model. Nature, 588.

19. Mirhoseini, A. et al. (2021). A Graph Placement Methodology for Fast Chip Design. Nature, 594.

20. Brown, T. et al. (2020). Language Models are Few-Shot Learners. NeurIPS.

21. Radford, A. et al. (2019). Language Models are Unsupervised Multitask Learners. OpenAI Technical Report.

22. Wei, J. et al. (2022). Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. NeurIPS.

23. Yao, S. et al. (2023). Tree of Thoughts: Deliberate Problem Solving with Large Language Models. arXiv:2305.10601.

24. OpenAI. (2023). GPT-4 Technical Report. arXiv:2303.08774.

25. Anthropic. (2024). Claude 3 Model Card. Technical Report.

26. Kingma, D.P. and Ba, J. (2015). Adam: A Method for Stochastic Optimization. ICLR.

27. Schulman, J. et al. (2017). Proximal Policy Optimization Algorithms. arXiv:1707.06347.

28. Mnih, V. et al. (2015). Human-level Control through Deep Reinforcement Learning. Nature, 518.

29. Vaswani, A. et al. (2017). Attention Is All You Need. NeurIPS.

30. He, K. et al. (2016). Deep Residual Learning for Image Recognition. CVPR.

---

Appendix A: Algorithm Pseudocode

A.1 MAPO-RQ Main Loop

Algorithm 1: MAPO Gaming Main Loop
─────────────────────────────────────────────────────────────
Input: PCB file P, CompletionCriteria C
Output: Optimized PCB P*, Champions history H

1:  archive ← InitializeMAPElites(dimensions=10, bins=10)
2:  llm ← InitializeLLMBackends(model="claude-sonnet")
3:  H ← []  // Champions history
4:
5:  // Seed archive with initial state
6:  state₀ ← LoadPCB(P)
7:  fitness₀ ← Evaluate8Domains(state₀)
8:  descriptor₀ ← ExtractBehavior(state₀)
9:  archive.Add(state₀, fitness₀, descriptor₀)
10:
11: iteration ← 0
12: stagnation ← 0
13:
14: while not C.IsSuccess(archive.best) do
15:   for round ← 1 to NUM_ROUNDS do
16:     for i ← 1 to ITERATIONS_PER_ROUND do
17:       // Sample parent from archive
18:       parent ← archive.Sample(strategy="curiosity")
19:
20:       // Generate mutation via LLM
21:       context ← BuildContext(parent, archive, H, round)
22:       mutation ← llm.Policy.Suggest(context)
23:
24:       // Apply mutation and evaluate
25:       offspring ← ApplyModification(parent, mutation)
26:       fitness ← Evaluate8Domains(offspring)
27:       generality ← EvaluateVsChampions(offspring, H)
28:       combined ← CombinedFitness(fitness, generality, round)
29:       descriptor ← ExtractBehavior(offspring)
30:
31:       // Add to archive if competitive
32:       archive.Add(offspring, combined, descriptor)
33:
34:       iteration ← iteration + 1
35:     end for
36:
37:     // Extract round champions
38:     champions ← archive.GetTopElites(count=5)
39:     H.Append(champions)
40:     TrackConvergence(champions, H)
41:   end for
42:
43:   // Check for stagnation
44:   if NoImprovement(archive, last_k=10) then
45:     stagnation ← stagnation + 1
46:     if stagnation > C.max_stagnation then
47:       Escalate(archive, strategy=NextStrategy())
48:       stagnation ← 0
49:     end if
50:   else
51:     stagnation ← 0
52:   end if
53:
54:   // Persist state
55:   SaveState(archive, H, iteration)
56: end while
57:
58: return archive.GetBest(), H

A.2 Generality Evaluation

Algorithm 2: Generality Scoring
─────────────────────────────────────────────────────────────
Input: Solution S, Champions history H
Output: GeneralityScore G

1:  wins, ties, losses ← 0, 0, 0
2:  margins ← []
3:  per_round ← {}
4:
5:  for each round_champions in H do
6:    round_wins ← 0
7:    for each champion in round_champions do
8:      margin ← S.fitness - champion.fitness
9:      if margin > WIN_THRESHOLD then
10:       wins ← wins + 1
11:       round_wins ← round_wins + 1
12:       margins.Append(margin)
13:     else if margin > -TIE_THRESHOLD then
14:       ties ← ties + 1
15:     else
16:       losses ← losses + 1
17:     end if
18:   end for
19:   per_round[round] ← round_wins / |round_champions|
20: end for
21:
22: total ← wins + ties + losses
23: generality ← (wins + 0.5 × ties) / max(1, total)
24: avg_margin ← Mean(margins) if margins else 0
25:
26: return GeneralityScore(wins, ties, losses, generality, avg_margin, per_round)

Appendix B: Behavioral Descriptor Extraction

Python
85 lines
Copy
@dataclass
class BehavioralDescriptor:
    routing_density: float      # [0, 1]
    via_count: float           # [0, 1] normalized
    layer_utilization: float   # [0, 1]
    zone_coverage: float       # [0, 1]
    thermal_spread: float      # [0, 1] inverse of variance
    signal_length_variance: float  # [0, 1] inverse
    component_clustering: float    # [0, 1]
    power_path_directness: float   # [0, 1]
    minimum_clearance_ratio: float # [0, 1]
    silkscreen_density: float      # [0, 1]

    @classmethod
    def from_pcb_state(cls, state: PCBState) -> 'BehavioralDescriptor':
        board_area = state.width * state.height

        # Routing density: total trace length / board area
        total_trace_length = sum(t.length for t in state.traces)
        routing_density = min(1.0, total_trace_length / (board_area * 10))

        # Via count: normalized by component count
        via_count = min(1.0, len(state.vias) / (len(state.components) * 5))

        # Layer utilization: average copper fill across layers
        layer_fills = [layer.copper_area / board_area for layer in state.layers]
        layer_utilization = np.mean(layer_fills)

        # Zone coverage: power/ground zone area ratio
        zone_area = sum(z.area for z in state.zones if z.net in ['GND', 'VCC'])
        zone_coverage = min(1.0, zone_area / board_area)

        # Thermal spread: inverse of temperature variance
        temps = state.estimate_thermal_map()
        thermal_spread = 1.0 / (1.0 + np.std(temps))

        # Signal length variance: inverse of length std dev
        signal_lengths = [n.total_length for n in state.signal_nets]
        signal_length_variance = 1.0 / (1.0 + np.std(signal_lengths) / np.mean(signal_lengths))

        # Component clustering: based on nearest neighbor distances
        positions = np.array([c.position for c in state.components])
        nn_distances = compute_nearest_neighbor_distances(positions)
        component_clustering = 1.0 / (1.0 + np.mean(nn_distances))

        # Power path directness: actual vs manhattan distance
        power_paths = state.get_power_paths()
        directness = np.mean([p.actual_length / p.manhattan_length for p in power_paths])
        power_path_directness = 1.0 / directness  # Normalize to [0, 1]

        # Minimum clearance ratio: clearance / required clearance
        clearances = state.compute_all_clearances()
        min_ratio = min(c.actual / c.required for c in clearances)
        minimum_clearance_ratio = min(1.0, min_ratio)

        # Silkscreen density: silkscreen area / board area
        silk_area = sum(s.area for s in state.silkscreen_items)
        silkscreen_density = min(1.0, silk_area / (board_area * 0.3))

        return cls(
            routing_density=routing_density,
            via_count=via_count,
            layer_utilization=layer_utilization,
            zone_coverage=zone_coverage,
            thermal_spread=thermal_spread,
            signal_length_variance=signal_length_variance,
            component_clustering=component_clustering,
            power_path_directness=power_path_directness,
            minimum_clearance_ratio=minimum_clearance_ratio,
            silkscreen_density=silkscreen_density
        )

    def to_vector(self) -> np.ndarray:
        return np.array([
            self.routing_density,
            self.via_count,
            self.layer_utilization,
            self.zone_coverage,
            self.thermal_spread,
            self.signal_length_variance,
            self.component_clustering,
            self.power_path_directness,
            self.minimum_clearance_ratio,
            self.silkscreen_density
        ])

Appendix C: LLM Prompt Templates

C.1 Policy Network Prompt

YAML
34 lines
Copy
You are an expert PCB layout optimizer. Given the current design state,
suggest a single modification to improve the layout quality.

CURRENT STATE:
- Board: {width}mm × {height}mm, {layer_count} layers
- Components: {component_count} placed
- Nets: {net_count} routed
- Current fitness: {fitness:.3f}

TOP VIOLATIONS (most impactful first):
{violation_list}

BEHAVIORAL PROFILE:
- Routing density: {routing_density:.2f}
- Thermal spread: {thermal_spread:.2f}
- Signal length variance: {signal_length_variance:.2f}

OPTIMIZATION CONTEXT:
- Round {round_number} of {total_rounds}
- Must beat {champion_count} historical champions
- Current generality score: {generality:.2f}

CONSTRAINTS:
- Maintain IPC-2221 compliance
- Preserve existing net connectivity
- Keep modifications reversible

Respond with a single modification in JSON format:
{
  "modification_type": "move_component" | "reroute_net" | "add_via" | "adjust_zone" | "modify_trace_width",
  "target": "<component_ref or net_name>",
  "parameters": {<modification-specific parameters>},
  "rationale": "<brief explanation>"
}

C.2 Value Network Prompt

Evaluate the quality of this PCB design on a scale from 0.0 to 1.0.

DESIGN SUMMARY:
{design_summary}

VIOLATION BREAKDOWN:
- DRC violations: {drc_count}
- ERC violations: {erc_count}
- IPC-2221 issues: {ipc_count}
- Signal integrity concerns: {si_count}

Consider:
1. Manufacturing feasibility
2. Electrical performance
3. Thermal management
4. Standards compliance
5. Design robustness

Respond with:
{
  "quality_score": <0.0 to 1.0>,
  "confidence": <0.0 to 1.0>,
  "limiting_factors": ["<factor1>", "<factor2>", ...],
  "improvement_priority": "<most impactful improvement area>"
}

---

This research was conducted by the Adverant Research Team. The MAPO Gaming framework is available as part of the Adverant EE Design Partner platform.

For questions or collaboration inquiries, contact: research@adverant.ai