Adaptive Evolutionary Framework for Safe, Efficient, and Cooperative Autonomous Vehicle Interactions

1. Problem Statement

Modern transportation systems face critical challenges in ensuring road safety and efficiency, particularly with the rapid proliferation of Autonomous Vehicles (AVs). While AVs promise to reduce human-error accidents, their decentralized nature creates complex interaction challenges. Existing decision-making frameworks suffer from specific limitations:

• Rule-based methods: Lack adaptability and generalization in complex, dynamic scenarios.
• Optimization-based methods (e.g., MPC): Often require high computational resources, making real-time deployment difficult.
• Game-theoretic approaches (Nash and Stackelberg):
  • Nash Games: Tend to prioritize self-interest, leading to collective inefficiency (e.g., congestion due to over-caution).
  • Stackelberg Games: Rely on a leader-follower hierarchy and accurate prediction of driving styles, which often fails in real-world unpredictability and lacks flexibility.

There is a critical need for a decentralized, adaptive framework that balances passenger demands (safety, comfort, efficiency) with overall traffic flow without relying on centralized control or rigid hierarchies.

2. Methodology

The authors propose a Causal Evaluation-based Evolutionary Game Theory (CEGT) framework. This approach combines Evolutionary Game Theory (EGT) with a novel causal inference mechanism to dynamically adjust strategy evolution.

A. Core Framework Structure

The system operates through a multi-step loop:

1. Initialization: Kinematic parameters and vehicle states are configured.
2. Causal Inference Mechanism: A module evaluates the relationship between historical vehicle positions and current rewards to determine "causal influence."
3. Evolutionary Game Framework: Vehicles adapt strategies via Imitation (copying successful neighbors) and Mutation (exploring new strategies).
4. Strategy Implementation: Vehicles execute lane changes using Quintic Polynomial Path Planning for smooth transitions.
5. Collision Detection & Evaluation: Safety is monitored via Time-to-Collision (TTC) and collision penalties.

B. Key Technical Components

• Causal Inference Mechanism:
  • Calculates a Causal Effectiveness ($E_{causal}$) metric based on the correlation between historical position vectors and reward vectors.
  • Uses a Causal Mask ($c_m$) to introduce controlled stochasticity, preventing over-exploitation of historical patterns.
  • Computes a Causal Adjustment ($A_{causal}$) which dynamically influences the probability of mutation vs. imitation.
• Evolutionary Strategy Selection:
  • Imitation Probability ($P_{imitation}$): Determined by a sigmoid function of the causal adjustment. Vehicles imitate neighbors with high rewards.
  • Mutation Probability ($P_{mutation}$): $1 - P_{imitation}$. Vehicles explore new speeds within a defined range ($v_{current} \pm 2$ m/s) if the causal signal suggests current strategies are suboptimal.
• Reward Function:
  The total reward ($R$) is a vector sum of:
  • Safety Reward: Inversely proportional to inter-vehicle distance.
  • Efficiency Reward: Based on individual velocity relative to the average system velocity.
  • Cooperation Reward: Penalizes historical collision statistics.
  • Causal Adjustment: Integrates the learned causal influence into the decision-making process.
• Lane Changing: Utilizes quintic polynomials to ensure continuous position, velocity, and acceleration, guaranteeing passenger comfort and stability.

3. Key Contributions

1. Decentralized Adaptive Framework: Proposes an EGT-based system that eliminates the need for leader-follower relationships (unlike Stackelberg) and purely self-interested optimization (unlike Nash), allowing all AVs to operate on equal footing.
2. Causal Evaluation Module (CEGT): Introduces a novel module that dynamically adjusts the evolutionary rate (mutation vs. imitation) by learning from historical interactions. This addresses the critical challenge of defining an appropriate evolutionary rate in standard EGT.
3. Superior Performance: Demonstrates that CEGT outperforms standard EGT, Nash, and Stackelberg games in diverse scenarios, achieving lower collision rates, higher safety distances, and better overall traffic efficiency.

4. Simulation Results

The framework was tested in MATLAB 2024b across two scenarios:

• Case 1: Single-lane highway with four AVs (random speeds 10–20 m/s).
• Case 2: Double-lane highway with four AVs, including lane-changing intentions.

Key Findings:

• Collision Reduction:
  • In Case 1, CEGT achieved an average of ~1.5 collisions per 100 runs, significantly lower than EGT (2.8), Stackelberg (3.6), and Nash (4.5).
  • In Case 2 (lane changing), CEGT reduced collisions to ~0.4, compared to ~2.5 for EGT and ~3.0 for Nash.
• Safety (Time-to-Collision - TTC):
  • CEGT maintained TTC values consistently above the 4-second safety threshold.
  • Nash and Stackelberg frequently dropped below the safety threshold (even reaching negative values, indicating imminent collisions), particularly around $t=2$ seconds.
• Efficiency and Speed:
  • CEGT maintained higher average speeds (10–15 m/s) compared to Nash (often <5 m/s) and Stackelberg (5–10 m/s).
  • CEGT showed faster convergence to optimal rewards and higher total cumulative rewards (e.g., ~162,388 vs. -176,039 for Stackelberg in Case 1).
• Stability: CEGT exhibited narrower confidence bounds and less volatility in performance across different initial conditions and collision penalty settings (-100 to -300) compared to benchmark algorithms.

5. Significance

This research provides a robust solution for cooperative, decentralized autonomous driving. By integrating causal inference into evolutionary game theory, the framework successfully balances the trade-off between individual vehicle goals and collective traffic safety.

• Practical Impact: It offers a computationally feasible alternative to heavy optimization methods and a more adaptive alternative to rigid rule-based or hierarchical game-theoretic models.
• Scalability: The decentralized nature of CEGT makes it suitable for large-scale AV deployments where centralized control is impractical.
• Future Direction: The authors suggest future work will focus on scaling the framework to high-density traffic and integrating advanced predictive models for highly dynamic environments.