A Dominance-Based Constrained Optimization Evolutionary Algorithm for the 4-th Tensor Power Problem of Matrix Multiplication

作者：Tang, Langping^*; Zhou, Yuren; Chen, Zefeng

来源：4th International Conference on Cloud Computing and Security (ICCCS), 2018-06-08 To 2018-06-10.

DOI：10.1007/978-3-030-00015-8_49

• Matrix multiplication
• Tensor power
• Constrained optimization
• Evolutionary algorithm

As one of the fundamental operations, matrix multiplication plays a significant role in mathematics, computer science and many other science fields. In Williams' research of studying matrix multiplication problem, she put emphasis on studying the even tensor powers of Coppersmith-Winograd approach, and then obtained improved upper bound for the matrix multiplication exponent. In fact, the program for calculating the so-called even tensor power is a constrained optimization problem with complicated constraints. In this paper, we focus on the 4th tensor power problem of matrix multiplication. After converting this practical problem, we design a dominance-based constrained optimization evolutionary algorithm. Empirical results show that this algorithm can effectively solve the 4-th tensor power problem. What is more, the feasible solution obtained by this algorithm is better than the current known solution of the problem.

• 出版日期2018
• 单位中山大学; 华南理工大学