Solving Banana (Rosenbrock) Function Based on Fitness Function
Lubna Zaghlul Bashir, Rajaa Salih Mohammed Hasan · World Scientific News · 2015
When solving real optimization problems numerically, the solution process typically involves the phases of modelling, simulation and optimization. A simulated model of a real life problem is often complex, and the objective function to be minimized may be non convex and have several local minima. Then, global optimization methods are needed to prevent the stagnation to a local minimum. Therefore, in the recent years, there has been a great deal of interest in developing methods for solving global optimization problems [1, 2, 3] and references therein). Genetic algorithms [4, 5, 6] are meta heuristics used for solving problems with both discrete and continuous variables. The population is the main element of genetic algorithms, and the genetic operations like crossover and mutation are just instruments for manipulating the population so that it evolves towards the final population including a “close to optimal” solution. The requirements set on the population also change during the execution of the algorithm [7]. In this work we test the function known as the “banana function” because of its shape; f(x) = 100. (x2 x1 2 ) 2 + (1x1) 2 . In this problem, there are two design variables with lower and upper limits of [-5 , 5].we use genetic algorithm for solving this problem, Basic philosophy of genetic algorithm and its flowchart are described. Step by step numerical computation of genetic algorithm for solving the banana function will be briefly explained. The results shows that The Rosenbrock function has a known global minimum at [1 , 1] with an optimal function value of zero.