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Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear

Muhammad Asif Zahoor Raja1, Adiqa Kausar Kiani2, Azam Shehzad3

  • 1Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan.

Springerplus
|December 21, 2016
PubMed
Summary

This study introduces a hybrid Genetic Algorithm-Sequential Quadratic Programming (GA-SQP) approach for solving nonlinear equations. The bio-inspired method demonstrates superior accuracy and convergence compared to other schemes.

Keywords:
Genetic algorithmsHybrid computingNonlinear equationsNonlinear systemsSequential quadratic programming

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Area of Science:

  • Computational Science
  • Applied Mathematics
  • Bio-inspired Computing

Background:

  • Solving systems of nonlinear equations is a fundamental challenge in various scientific domains.
  • Traditional methods may struggle with complex, nonlinear systems, necessitating advanced computational techniques.

Purpose of the Study:

  • To develop and evaluate a novel hybrid optimization algorithm for solving systems of nonlinear equations.
  • To leverage bio-inspired computing, specifically Genetic Algorithms (GAs), combined with Sequential Quadratic Programming (SQP) for enhanced problem-solving capabilities.

Main Methods:

  • A hybrid approach combining Genetic Algorithms (GAs) for global search and Sequential Quadratic Programming (SQP) for local search was developed.
  • The fitness function was defined using the mean square error of the nonlinear system.
  • Twelve variants of the GA-SQP memetic algorithm were created by varying reproduction routines.

Main Results:

  • The performance of the twelve GA-SQP variants was assessed on six diverse numerical problems.
  • Evaluations included systems from interval arithmetic, kinematics, neurophysiology, combustion, and chemical equilibrium.
  • Statistical performance indices were used to compare accuracy, convergence, and complexity.

Conclusions:

  • The memetic computing GA-SQP approach consistently demonstrated superior accuracy and convergence across all tested simulations.
  • Statistical analysis confirmed the effectiveness and efficiency of the proposed GA-SQP schemes for solving nonlinear equations.