For collision encounter scenarios between spacecraft and potentially threatening moving objects, this paper proposes the definition of a threat corridor and establishes its mathematical model. Based on neural network pattern recognition, the number of evasive maneuver impulses for spacecraft is determined. Based on this, an improved simulated annealing-genetic algorithm (SA-GA) is proposed to optimize spacecraft evasive maneuvers. Distinct from traditional evasive maneuver methods, this approach adopts the threat corridor as a novel evasion metric, extends evasive actions to multiple impulses, and fully integrates the global exploration capability of genetic algorithms with the local exploitation ability of simulated annealing in the improved SA-GA algorithm, achieving superior optimization results. Simulation results demonstrate that compared with conventional evasive maneuver methods, this approach ensures timeliness, effectiveness, and economy of evasive maneuvers while effectively overcoming the limitations of standalone genetic algorithms. It significantly improves the overall success probability of evasive maneuvers, providing new technical perspectives for spacecraft evasive maneuvers against potential threats.