This paper proposes a novel optimization method inspired by radar technology: wave search algorithm (WSA). The WSA algorithm not only draws on radar technology for its unique algorithmic design for the first time but also uses a new initialization method and boundary restriction rules, adopts various improved greedy mechanisms, and makes use of the gradient information of the problem to be optimized. As a result, the WSA algorithm is characterized by accuracy, efficiency, and adaptability. The superiority of the WSA algorithm is experimentally demonstrated by testing it with a rich set of test functions (23 benchmark test functions and 30 CEC-2017 test functions) and comparing it with state-of-the-art and highly cited algorithms. Finally, the WSA algorithm is applied to six common engineering problems and mobile robot path planning problems. The experimental results demonstrate that the optimization ability of the WSA algorithm is better than other state-of-the-art optimization algorithms, and it can efficiently solve practical engineering problems. The MATLAB code for WSA is available at https://github.com/haobinzhang123/A-heuristic-algorithm.git.