Raja Muhammad Asif Zahoor, Kiani Adiqa Kausar, Shehzad Azam, Zameer Aneela
Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan.
Department of Economics, Federal Urdu University of Arts Science and Technology, Islamabad, Pakistan.
Springerplus. 2016 Dec 1;5(1):2063. doi: 10.1186/s40064-016-3750-8. eCollection 2016.
In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm.
Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes.
Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.
在本研究中，利用受生物启发的计算方法，通过遗传算法（GA）的变体来求解非线性方程组，将其作为全局搜索方法的工具，并与序列二次规划（SQP）相结合进行高效的局部搜索。通过在均方意义上定义非线性方程组的误差函数来构建适应度函数。利用遗传算法的能力对数学模型的设计参数进行训练，并通过可行的SQP算法进行优化。
通过在优化过程中采用不同的繁殖例程，设计了12种混合方法GA-SQP。在所提出的变体的性能在六个数值问题上进行了评估，这些问题包括区间算术基准模型、运动学、神经生理学、燃烧和化学平衡中出现的非线性方程组。借助统计性能指标，对所提出结果在准确性、收敛性和复杂性方面进行了比较研究，以确定这些方案的价值。
在模拟研究的每种情况下，都发现混合计算GA-SQP的准确性和收敛性更好，并且通过基于不同性能指标的准确性和复杂性的统计结果进一步确定了该方案的有效性。
