## 6 Results and Discussions
### Performance Comparison on AGV Scheduling Problem
**Efficiency Metrics. ** The original EoH is the most computationally efficient, consuming only 1071.9302 s and 40 LLM calls. However, this efficiency comes at the cost of lower solution quality and poor exploration capability. EoH-MR is the most computationally intensive variant (3177.57 s, 100 LLM calls), yet it produces the best performance. FunSearch and HillClimb, despite lower token usage (27,247-30,900), deliver weaker solutions and fail to adapt heuristics dynamically. In critical smart manufacturing scenarios, such as factory logistics or automated warehouse scheduling, such trade-offs in computational cost are justified by improved system throughput. EoH-MR requires nearly triple the time of HillClimb (1033.19 s), clearly reflecting the added cost of memetic refinement and LLM integration. **Diversity and Exploration. ** EoH-MR achieves the highest diversity in terms of unique score count (87), inter-solution score standard deviation (40,589.8931), and score range (131,009.83). This indicates a significantly broader exploration of the solution space, which is crucial in dynamic environments to avoid premature convergence. EoH-M is also more exploratory than EoH due to the inclusion of adaptive local search, but lacks the reflection mechanism that helps rebalance search efforts. FunSearch and HillClimb both explore far fewer diverse trajectories (only 21 and 15 unique scores, respectively), suggesting their evolution is more deterministic and potentially prone to stagnation. As visualized in Figure 3, the diversity gap is stark, with EoH-MR demonstrating far broader score ranges than any baseline, reinforcing its exploratory strength. **Strategic Insights from High-Scoring Schedules. ** Beyond numerical performance, deeper analysis of evolved heuristics reveals several qualitative patterns consistently present in top-performing strategies:  
* Decentralized bidding mechanisms that weigh urgency, battery margins, and predicted congestion enable flexible agent coordination, often outperforming static rule systems by 15-20%. * Role flexibility, allowing drones and AGVs to interchange tasks contextually, yields lower penalty trajectories than rigid allocation. * Proactive energy management embedded in bidding logic reduces failure rates and extends operational margin. * Congestion forecasting leads to early detouring and better throughput than reactive heuristics. * Local refinement operators contribute disproportionately to late-stage gains, confirming the value of post-generation fine-tuning. * Exploration bottlenecks, such as stagnated diversity scores, prompt the use of stochastic noise to escape local minima. These observations illustrate that success hinges less on wholesale heuristic redesign and more on layered, context-aware decision strategies combining auction logic, adaptive constraints, and lightweight local search. In addition to total computation time, the duration required to reach a near-optimal solution is practically important, especially when early results are needed under time constraints. Based on empirical trajectories of the AGV-drone scheduling task, EoH reaches within 5% of its final best score in approximately 800 s (75% of total time), EoH-M in around 1000 s (55%), and EoH-MR in only 1270 s (40%). The corresponding \"good enough\" score for EoH-MR is approximately \(-\)167,270, which not only surpasses the final results of all baseline methods (e.g., HillClimb: \(-\)187,813; FunSearch: \(-\)189,158), but also exceeds the typical performance range of manually designed heuristics, which often fall between \(-\)160,000 and -190,000 depending on domain knowledge and tuning effort. Furthermore, while manual design and tuning can require several hours to days, EoH-MR achieves these results in around 20 min with no human intervention. This highlights the framework's ability to generate high-quality solutions with greater efficiency, making it well-suited for automated or time-sensitive decision-making settings.