# The Evolution and Optimization Strategies of a PBFT Consensus Algorithm for Consortium Blockchains
## 4 Analysis of the Improved PBFT Consensus Algorithm
### Improvements to Multi-Leader Consensus Algorithms  
In the conventional PBFT consensus algorithm, the primary node is chosen by applying the modulus operation of the view number against the overall count of nodes. Nevertheless, should the primary node experience a failure, it can lead to a frequent switching of views, which may adversely affect the efficiency of consensus. To address this issue, researchers worldwide have proposed various multi-primary-node consensus algorithm improvements. [PERSON] et al. [104] proposed an approach that introduces an optimized Practical Byzantine Fault Tolerance (PBFT) consensus algorithm that leverages the concepts of Vague sets and credit ratings to effectively tackle existing challenges within the consensus mechanism. By incorporating Vague sets, this algorithm significantly improves the efficiency of the voting process that is essential for achieving consensus among nodes. It achieves this enhancement by carefully balancing the influences of both positive and negative votes, thereby offering a more nuanced and rational framework for evaluating the behavior of individual nodes. This advanced evaluation criterion not only facilitates more informed decision-making within the network but also contributes to the overall reliability and robustness of the consensus protocol. This serves as the basis for primary node selection. Additionally, the algorithm quantifies node attributes and optimizes the selection of consensus nodes to improve the overall consensus efficiency. [PERSON] et al. [105] proposed a Byzantine fault-tolerant architecture that employs multiple primary replicas in parallel, enhancing system robustness through redundancy. Their protocol follows an N \(\geq\) 3f + 1 node configuration to tolerate up to \(f\) Byzantine node failures. The core mechanism establishes a collaborative oversight system between a Primary Instance (responsible for request ordering and execution authorization) and Backup Instances (which validate ordering correctness and monitor the primary node). When an anomaly is detected in the primary node, a dynamic view-switching mechanism is employed to rapidly replace the faulty instance. [PERSON] et al. [106] introduced a multi-leader mechanism to overcome the communication bottleneck in single-leader Byzantine Fault Tolerant (BFT) protocols. Their approach optimizes the communication complexity to O(N), ensuring stability even when proposal voting and coordination phases overlap. The BigBFT protocol achieves block ordering in two rounds of communication while leveraging pipelining techniques \begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **Reward and Punishment Mechanism** & **Number of Consensus Nodes** & **Network Model** \\ \hline QIPBFT [98] & QoS-aware global evaluation mechanism for trust services & N \(-\) [(n - 1)/3] & Semi-Synchronous Network \\ \hline SC-PBFT [99] & Reputation-based scoring mechanism & N/2 & Semi-Synchronous Network \\ \hline T-PBFT [100] & EigenTrust-based evaluation mechanism & N \(\times\) d/100 & Semi-Synchronous Network \\ \hline
5C-PBFT [101] & Node reputation model & N/2 & Semi-Synchronous Network \\ \hline APBFT [102] & Reputation credit mechanism & N/3 & Semi-Synchronous Network \\ \hline \end{tabular}
\end{table} 
Table 11: A comparison of reward and penalty mechanisms across different algorithms. to transmit blocks from the same or different rounds, ultimately reaching consensus efficiently. [PERSON] et al. [107] proposed a parallel-leading Byzantine Fault Tolerant state machine replication protocol designed for partially synchronous models with theoretical performance guarantees. Their FnF-BFT algorithm enables all replicas to act as leaders and propose requests independently, allowing for parallel request execution. By distributing the workload across the entire network, leader parallelization mitigates the bottleneck of a single leader, significantly enhancing system throughput. Table 12 provides a comparative analysis of multi-leader selection mechanisms across different algorithms.