<abstract xmlns="http://www.w3.org/1999/xhtml">Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local optima or does not factually represent a constantly changing solution. Hence the need for evolutionary algorithms becomes evident. However, evolutionary algorithms are compute-intensive since they scan the entire solution space for an optimal solution. Larger populations and smaller step sizes allow for improved quality solution but results in an increase in the complexity of the optimization process. In this research a population-distributed implementation for differential evolution algorithm is presented for solving systems of 2<italic>nd</italic>-order, 2-point boundary value problems (BVPs). In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraint boundary conditions and is then solved using differential evolution in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Four benchmark BVPs are solved using the proposed parallel framework for differential evolution to observe the speedup in the execution time. Meanwhile, the statistical analysis is provided to discover the effect of parametric changes such as an increase in population individuals and nodes representing features on the quality and behavior of the solutions found by differential evolution. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving 2<italic>nd</italic>-order, 2-point BVPs.</abstract>

Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local optima or does not factually represent a constantly changing solution. Hence the need for evolutionary algorithms becomes evident. However, evolutionary algorithms are compute-intensive since they scan the entire solution space for an optimal solution. Larger populations and smaller step sizes allow for improved quality solution but results in an increase in the complexity of the optimization process. In this research a population-distributed implementation for differential evolution algorithm is presented for solving systems of 2nd-order, 2-point boundary value problems (BVPs). In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraint boundary conditions and is then solved using differential evolution in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Four benchmark BVPs are solved using the proposed parallel framework for differential evolution to observe the speedup in the execution time. Meanwhile, the statistical analysis is provided to discover the effect of parametric changes such as an increase in population individuals and nodes representing features on the quality and behavior of the solutions found by differential evolution. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving 2nd-order, 2-point BVPs.

Solution of Linear and Non-Linear Boundary Value Problems Using Population-Distributed Parallel Differential Evolution

Department of Information Engineering (DII)

Department of Computer and Information Sciences (DCIS), Pakistan Institute of Engineering and Applied Sciences

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local...

Solution of Linear and Non-Linear Boundary Value Problems Using Population-Distributed Parallel Differential Evolution

Published Online: May 09, 2019

Page range: 205 - 218

Received: Oct 18, 2018

Accepted: Jan 20, 2019

DOI: https://doi.org/10.2478/jaiscr-2019-0004

Keywords
parallel evolutionary algorithms, differential evolution, boundary value problems, optimization

© 2019 Amnah Nasim et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Solution of Linear and Non-Linear Boundary Value Problems Using Population-Distributed Parallel Differential Evolution

Published Online: May 09, 2019

Page range: 205 - 218

Received: Oct 18, 2018

Accepted: Jan 20, 2019

DOI: https://doi.org/10.2478/jaiscr-2019-0004

Keywordsparallel evolutionary algorithms, differential evolution, boundary value problems, optimization

© 2019 Amnah Nasim et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
parallel evolutionary algorithms, differential evolution, boundary value problems, optimization