Evolutionary Techniques for the Solution of Bio-Heat Equation Arising in Human Dermal Region Model
Iftikhar Ahmad, Hira Ilyas, Syed Ibrar Hussain, Muhammad Asif Zahoor Raja
Abstract
Abstract The proposed research work analyzes the bio-inspired problem through artificial neural networks with a feed-forward approach utilized to approximate the numerical results for singular nonlinear bio-heat equation (BHE) with boundary conditions based on four different scenarios created on the variation of environmental temperature to illustrate the effects of temperature on the human dermal region. The log-sigmoid function is used to construct the fitness function, while the optimization solvers: pattern search and genetic algorithm, are then hybridized with the active set technique, interior point technique, sequential quadratic programming for accurate and reliable results of the proposed BHE with various scenarios where the convergence of the numerical results is also analyzed. Moreover, a comparison of the proposed technique is expressed through residual error that reveals the nature of the numerical results and their efficiency. Additionally, a comprehensive statistical analysis is presented for the designed technique to better illustrate the accuracy, reliability, and efficiency of the obtained results.