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.

中文翻译：

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基于进化算法的链矩阵乘法最优序列

链矩阵乘法问题（CMMP）是一个优化问题，有助于找到链矩阵乘法（CMM）的最佳括号法。在诸如电子学，机器人学，数学编程和密码学的各种科学应用中会出现此问题。对于CMMP，研究人员提出了各种技术，例如动态方法，算术方法和顺序乘法。但是，这些技术在计算时间和大量标量乘法方面不足以为CMMP提供最佳结果。在本文中，我们提出了一种基于小组咨询优化器（GCO）的最小化链矩阵乘法（CMM）操作的新模型。我们的实验结果和他们的分析表明，与顺序链矩阵乘法方法相比，所提出的GCO模型以有效的速度显着减少了时间。与顺序乘法相比，所提出的模型提供了良好的性能，并将乘法运算的范围从45％减少到96％。此外，我们使用最著名的动态编程和算术乘法方法来评估我们的结果，这些方法清楚地证明了所提出的模型在计算时间和空间复杂度方面的表现均优于其他模型。