With the expanding scope of human activities in marine environments, the efficient detection and tracking of mobile targets on the ocean's surface have become increasingly crucial. Synthetic aperture radar (SAR) constellation can obtain ground observation data based on user requests and subject to visibility conditions. Now it is an indispensable tool in sea surface moving target search tasks. Satellite constellation resources are scarce and limited, and user demands are diverse. How to rationally dispatch satellite constellation resources to meet user needs to the maximum extent and improve the application efficiency of satellite resources is an urgent scientific problem that needs to be solved. This article mainly expounds two respects of work. First, modeling SAR constellation scheduling problem for sea surface moving target search tasks to establish the objective function. Second, a novel multistrategy discrete constrained differential evolution algorithm denoted as MSDCDE is proposed in the article. The proposed MSDCDE algorithm integrates cross strategy based on discrete variables, constraint handling techniques, population restart strategy, and left-shift local strategy, which can effectively avoid falling into local optimality, thereby achieving global optimality and improving search and rescue performances. Six sets of experiments, totaling 215 runs, have been conducted to validate the effectiveness of the proposed resolution process framework and the MSDCDE algorithm. The proposed method demonstrated an over 48.98% performance improvement compared with some state-of-the-art algorithms and significantly reduced task completion time.