Abstract
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 4-th 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.
Supported by the National Nature Science Foundation of China [grant numbers 61472143, 61773410, 61673403].
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Tang, L., Zhou, Y., Chen, Z. (2018). A Dominance-Based Constrained Optimization Evolutionary Algorithm for the 4-th Tensor Power Problem of Matrix Multiplication. In: Sun, X., Pan, Z., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2018. Lecture Notes in Computer Science(), vol 11066. Springer, Cham. https://doi.org/10.1007/978-3-030-00015-8_49
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