Random search algorithm for 2×2 matrices multiplication problem

Since Volker Strassen proposed a recursive matrix multiplication algorithm reducing the time complexity to n2.81 in 1968, many scholars have done a lot of research on this basis. In recent years, researchers have proposed using computer algorithms to solve fast matrix multiplication problem. They have found Strassen´s algorithm or other algorithms that have the same time complexity as Strassen algorithm by using genetic algorithm. In this paper, we used random search algorithm to find the matrix multiplication algorithms that require fewer multiplications. And we used combining Gaussian elimination for the first time to improve calculation speed; meanwhile we improved the local search technology to enhance the local search capability of the algorithm. In the numerical experiments of 2×2 matrices, the results verified the effectiveness of the algorithm. Compared with the existing genetic algorithm, the new method has obvious advantage of quick search, and found some of new matrix multiplication algorithms.