Effect Of Numerical Errors On The Performance Of Optimization Method
Real-life chemical engineering systems are often difficult to optimise by conventional mathematical methods. It is hypothesised that this is due not so much to the behaviour of the systems being modelled, as to the way the modellers set up and solve the governing equations. The models are usually solved by some numerical methods which introduce random numerical errors, misleading the search method. To test this hypothesis, a well-behaved algebraic test function (Rosenbrock's valley) is reformulated in such a way that it has to be solved numerically, like a realistic engineering model. It is given alternately the form of an ODE model, a PDE model, as the root of nonlinear equations, and as a Monte Carlo simulation. Two gradient-based optimization methods (Conjugate Gradient and Quasi-Newton), a non-gradient based deterministic method (Nelder Meads), and two stochastic methods (Genetic Algorithm and Simulated Annealing) are tested on these numerical models. It was found that the numerical errors did affect the performance of the methods. The stochastic methods performed best, followed by Nelder-Meads, while the gradient methods usually fail.