Dogfight is a tactical behavior of cooperation between fighters. Inspired by this, this paper proposes a novel metaphor-free metaheuristic algorithm called Dogfight Search (DoS). Unlike traditional algorithms, DoS draws algorithmic framework from the inspiration, but its search mechanism is constructed based on the displacement integration equations in kinematics. Through experimental validation on CEC2017 and CEC2022 benchmark test functions, 10 real-world constrained optimization problems and mountainous terrain path planning tasks, DoS significantly outperforms 7 advanced competitors in overall performance and ranks first in the Friedman ranking. Furthermore, this paper compares the performance of DoS with 3 SOTA algorithms on the CEC2017 and CEC2022 benchmark test functions. The results show that DoS continues to maintain its lead, demonstrating strong competitiveness. The source code of DoS is available at https://ww2.mathworks.cn/matlabcentral/fileexchange/183519-dogfight-search.