Abstract: As a basic operation in computer science and mathematics, matrix multiplication is widely used in scientific research and engineering calculation. Determining the minimum number of multipliers required for computing the product of two matrices is one of the most important problems that have not been solved in computer algebra. In this paper, the matrix multiplication problem is modeled as a combinational optimization problem, and then the matrix multiplication problem is solved by the artificial bee colony heuristic search algorithm. An improved artificial bee colony algorithm with a circle traversal method is proposed to avoid repeated searches for the same neighborhood of a solution. The effectiveness of the proposed algorithm is verified by numerical experiments on the 2×2 matrix multiplication problem. Experimental results show that the proposed algorithm can quickly find the product method of 2×2 matrix decomposition.

Key words: fast matrix multiplication algorithm, Strassen algorithm, artificial bee colony algorithm, inferior solution, circle traversal