Benchmarking Blockchain, Federated Learning, and Quantum Evolutionary Algorithm for Combinatorial Optimization

Fair benchmarking for decentralized Quantum Computing (QC) against equivalent Federated Learning (FL) methods is essential to evaluate the comparative advantages, limitations, and applicability of these emerging paradigms. However, scalable and practical implementations are needed to address this gap. In this work, we deploy a Quantum-inspired Evolutionary Algorithm (QEA) integrated with Blockchain (BC) methods to enable reliable decentralization. Additionally, we adapt a Self-Organizing Maps (SOM) approach for unsupervised FL. Together, these components form the BloQFeL framework, which implements innovative and adaptable BLOckchain-based Quantum computing and Federated Learning techniques to solve combinatorial optimization problems. The goal of BloQFeL is to benchmark BC-based QEA and SOM algorithms against equivalent FL algorithms. We demonstrate its applicability by simultaneously solving equivalent, randomly generated Traveling Salesman Problem (TSP) instances using integrated BC-QEA, FL-SOM, and BC-SOM algorithms. For problem sizes up to 100 cities and 50 optimizer nodes, the results showed significant performance variation among systems. Post-hoc analysis revealed that BC-SOM and FL-SOM significantly outperformed BC-QEA, with BC-SOM offering the most efficient overall performance. Specifically, FL-SOM achieved the lowest CPU Utilization (30.66 ± 21.37%), Latency (0.58 ± 0.23 s), Route Length (5.11&# x 00 D 7; 10 5 ± 4.24&# x 00 D 7; 10 5 ), and Energy Consumption (6.76 ± 3.92 J), while BC-SOM performed best in Memory Utilization (2315.73 ± 7.77 MB) with comparable results on other metrics. In contrast, BC-QEA consistently recorded higher values across all metrics, such as Latency (4.04 ± 3.63 s) and Energy Consumption (169.76 ± 166.53 J), indicating lower efficiency. These results establish BloQFeL as a robust benchmarking framework and a baseline for future research.