<p>In response to the failure of most metaheuristic algorithms in dealing with the high-dimensional and ultra-high dimensional optimization problems, this paper proposes a multidimensional search algorithm (MDA) by analyzing and serially computing each parameter of the optimization problem. MDA consists of three key components: starting position determination, multidimensional serial search, and position mutation. The algorithm analyzes every influencing parameter of the optimization problem and is suitable for solving high-dimensional and ultra-high dimensional optimization problems. By using anchor points to mutate the position, it addresses the problem of particles easily getting stuck in local optimal positions during the evolution process. MDA was benchmarked using CEC2022 test suite and selected benchmark functions from CEC2005, and compared with various metaheuristic algorithms. Experimental results demonstrate that MDA provides highly competitive results across low- to high-dimensional problems, exhibiting good optimization accuracy and stability. Finally, the proposed algorithm was applied to optimize 3060 parameters within an Extreme Learning Machine (ELM) for fault diagnosis. Bearing fault classification experiments demonstrated excellent classification performance, indicating the algorithm's suitability for ultra-high-dimensional engineering optimization problems.</p>