## 1 Introduction  
With the continuous growth of ocean resource exploitation and maritime security needs, the sonar for target search tasks has emerged as a pivotal technological way in fields of ocean exploration [1, 2]. With the increasing complexity of maritime tasks, single sonar platform has exposed its limitation in detection capability and efficiency. By multi-sonar collaboration, detection efficiency can be significantly improved, which plays an increasingly important role in maritime tasks such as reconnaissance, surveillance and target searching [3, 4, 5, 6]. The collaborative search efficiency of a multi-sonar system refers to the actual performance of the search capability in specific search tasks. Therefore, evaluating the collaborative search efficiency is an effective way to measure whether a task can be successful, which can provide support for making the collaborative search strategies. It is also of great significance in the optimization of resource allocation and can enhance the situational awareness and response capabilities in the dynamic scenes [7]. The evaluation of the collaborative search efficiency of multi-sonar systems belongs to the research field of efficiency evaluation. Some researchers have made great efforts in solving this problem. [PERSON] et al. analyzed the main indicators and factors that affect the UAV cluster combat efficiency through the OODA (Observe, Orient, Decide, Act) loop, and proposed a comprehensive evaluation method based on AHP-FCE (Analytic Hierarchy Process-Fuzzy Comprehensive Evaluation) to obtain numerical efficiency values [8]. [PERSON] et al. proposed an efficiency evaluation method for UAV cluster combat systems based on system dynamic modeling and conducted model simulation research [9]. [PERSON] et al. proposed a conditional entropy-based weight combination method to evaluate the UAV collaborative combat efficiency, which addresses the problem of excessive index weight coefficients and considers the interrelationships between indicators in traditional entropy-based methods [10]. [PERSON] et al. conducted research on the efficiency evaluation of multiple wake-guided torpedoes carried by UUV based on the ADC model [11]. [PERSON] et al. proposed an improved multi-expert combined weight (MMCW)-fuzzy comprehensive evaluation (FCE) method to address the subjectivity of expert opinions in performance evaluation, and applied it to evaluate the AUV intelligence [12]. [PERSON] et al. proposed a distributed combat efficiency evaluation method for UAV cluster based on DoDAF (Department of Defense Architecture Framework) to address the issues of insufficient completeness and systematicity, as well as strong subjectivity in traditional distributed combat efficiency evaluation of UAV clusters [13]. [PERSON] et al. used the System Effectiveness Analysis (SEA) method to evaluate the reconnaissance effectiveness of UUV systems, and constructed mathematical models for effectiveness evaluation indicators, system mapping, and mission mapping [14]. [PERSON] et al. established a multiple unmanned surface vehicles collaborative efficiency evaluation model based on GA-BP neural network, which improved the efficiency of efficiency evaluation [15]. [PERSON] et al. proposed a collaborative efficiency evaluation method for UUVs based on GAPSO-BP neural network and verified it through simulation analysis [16]. There is relatively little research on the evaluation of sonar search path detection efficiency, and how to evaluate sonar search efficiency in dynamic scenarios is still an open issue. We analyzed the entire process of the multi-sonar collaborative search task, and found there are two issues that urgently need to be studied and resolved. _A.