In human social systems, debates are often seen as a means to resolve differences of opinion. However, in reality, debates frequently incur significant communication costs, especially when dealing with stubborn opponents. Inspired by this phenomenon, this paper examines the impact of malicious agents on the evolution of normal agents' opinions from the perspective of opinion evolution cost, and proposes corresponding solutions for the scenario in which malicious agents hold different opinions in multi-agent systems(MASs). First, this paper analyzes the negative impact of malicious agents on the opinion evolution process, reveals the additional evolution cost it brings, and provides a theoretical basis for the subsequent solutions. Secondly, based on the characteristics of opinion evolution, the malicious agent isolation algorithm based on opinion evolution direction vector is proposed, which does not strongly restrict the proportion of malicious agents. Additionally, an evolution rate adjustment mechanism is introduced, allowing the system to flexibly regulate the evolution process in complex situations, effectively achieving the trade-off between opinion evolution rate and cost. Extensive numerical simulations demonstrate that the algorithm can effectively eliminate the negative influence of malicious agents and achieve a balance between opinion evolution costs and convergence speed.

翻译：在人类社交系统中，辩论常被视为解决观点分歧的一种方式。然而现实中，辩论往往会产生显著的沟通成本，尤其在面对固执的对手时。受此现象启发，本文从观点演化成本的角度，研究恶意智能体对正常智能体观点演化的影响，并针对多智能体系统中恶意智能体持有不同观点的场景提出相应解决方案。首先，本文分析了恶意智能体对观点演化过程的负面影响，揭示了其带来的额外演化成本，为后续解决方案提供了理论依据。其次，基于观点演化的特性，提出了基于观点演化方向向量的恶意智能体隔离算法，该算法不强硬限制恶意智能体的比例。此外，引入了演化速率调节机制，使系统能够在复杂情况下灵活调控演化过程，有效实现观点演化速率与成本之间的权衡。大量数值模拟表明，该算法能有效消除恶意智能体的负面影响，并在观点演化成本与收敛速度之间取得平衡。