Design of stochastic solvers based on genetic algorithms for solving nonlinear equations
In the present study, a novel intelligent computing approach is developed for solving nonlinear equations using evolutionary computational technique mainly based on variants of genetic algorithms (GA). The mathematical model of the equation is formulated by defining an error function. Optimization of fitness function is carried out with the competency of GA used as a tool for viable global search methodology. Comprehensive numerical experimentation has been performed on number of benchmark nonlinear algebraic and transcendental equations to validate the accuracy, convergence and robustness of the designed scheme. Comparative studies have also been made with available standard solution to establish the correctness of the proposed scheme. Reliability and effectiveness of the design approaches are validated based on results of statistical parameters.
We consider in this work a variant of the Steiner Problem in Graphs (SPG) with the additional restriction that terminal nodes must have degree 1. We customize the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic, testing its performance on a large problem set obtained by modifying 182 SPG instances from the SteinLib repository. The GRASP obtained good results, with low average gaps with respect to known lower bounds in most of the problem classes, and attaining the optimum in 44 cases (24% of the problem set).