Optimal sequence for chain matrix multiplication using evolutionary algorithm

Abstract

The Chain Matrix Multiplication Problem (CMMP) is an optimization problem that helps to find the optimal way of parenthesization for Chain Matrix Multiplication (CMM). This problem arises in various scientific applications such as in electronics, robotics, mathematical programing, and cryptography. For CMMP the researchers have proposed various techniques such as dynamic approach, arithmetic approach, and sequential multiplication. However, these techniques are deficient for providing optimal results for CMMP in terms of computational time and significant amount of scalar multiplication. In this article, we proposed a new model to minimize the Chain Matrix Multiplication (CMM) operations based on group counseling optimizer (GCO). Our experimental results and their analysis show that the proposed GCO model has achieved significant reduction of time with efficient speed when compared with sequential chain matrix multiplication approach. The proposed model provides good performance and reduces the multiplication operations varying from 45% to 96% when compared with sequential multiplication. Moreover, we evaluate our results with the best known dynamic programing and arithmetic multiplication approaches, which clearly demonstrate that proposed model outperforms in terms of computational time and space complexity.

Keywords

• Chain matrix multiplication
• Evolutionary algorithm