Solving and Optimization of Cobb–Douglas Function by Genetic Algorithm: A Step-by-Step Implementation

Abstract

This study presents an innovative application of genetic algorithms (GAs) for optimizing the Cobb–Douglas production function, a cornerstone of economic modeling that examines the relationship between production output and the inputs of labor and capital. This research integrates traditional optimization methods, such as partial derivatives, with evolutionary computation techniques to address complex economic constraints. The methodology demonstrates how GAs outperform classical techniques in solving constrained optimization problems, offering superior robustness, adaptability, and efficiency. Key results highlight the alignment between GA solutions and traditional Lagrangian methods while underscoring the computational advantages of GAs in navigating non-linear and multi-modal landscapes. This work serves as a valuable resource for both educators and practitioners, offering insights into the potential of GAs to enhance optimization processes in engineering, economics, and interdisciplinary applications. Visual aids and pedagogical recommendations further illustrate the algorithm’s utility, making this study a significant contribution to the computational optimization literature. Additionally, the optimization process using genetic algorithms is presented in a step-by-step manner, with accompanying visual graphs that enhance comprehension and demonstrate the method’s effectiveness in solving mathematical problems, as validated by the study’s results.

Keywords

• genetic algorithms (GAs)
• optimization
• mathematical economics
• Cobb–Douglas production function
• computational methods
• evolutionary computation