Optimal sequence for chain matrix multiplication using evolutionary algorithm.

Area of Science:

• Computer Science
• Optimization Algorithms
• Computational Mathematics

Background:

• The Chain Matrix Multiplication Problem (CMMP) is crucial for optimizing matrix operations in scientific applications.
• Existing methods like dynamic programming and sequential multiplication often fall short in efficiency.
• These deficiencies include high computational time and excessive scalar multiplications.

Purpose of the Study:

• To propose a novel Group Counseling Optimizer (GCO) model for minimizing Chain Matrix Multiplication (CMM) operations.
• To enhance the efficiency and reduce the computational complexity of solving CMMP.
• To provide a superior alternative to existing optimization techniques for CMMP.

Main Methods:

• Development of a new optimization model based on the Group Counseling Optimizer (GCO).
• Implementation and testing of the GCO model for Chain Matrix Multiplication (CMM).
• Comparative analysis against sequential, dynamic programming, and arithmetic multiplication approaches.

Main Results:

• The proposed GCO model demonstrated significant reductions in computational time and scalar multiplications.
• Performance improvements ranged from 45% to 96% compared to sequential multiplication.
• The GCO model outperformed dynamic programming and arithmetic approaches in time and space complexity.

Conclusions:

• The Group Counseling Optimizer (GCO) model offers a highly efficient solution for the Chain Matrix Multiplication Problem (CMMP).
• This approach significantly reduces computational overhead and improves speed.
• The GCO model presents a promising advancement for optimizing matrix computations in various scientific domains.