Efficiency and fractal behaviour of optimisation methods on multiple-optima surfaces

Given a validated, non-trivial agricultural simulation model, optimisation of profitability for any given scenario is a logical but difficult goal. Of the available techniques, only the hill-climbing algorithms can be recommended. Using known multiple-optima mathematical functions with two optimisation routines, simulations indicate reasons for convergence to local rather than global optima. These include choice of initial values, and fractal patterns displayed in this plane. It is shown that the Simplex direct-search method searches the feasible hyperspace far more thoroughly than the quasi-Newton gradient method, and is thus more likely to find the global optimum. These data help reinforce and explain previous results of optimisations with a 14-dimensional dairy farm model. It is concluded that multiple starting values are essential, and that the direct-search methods are preferable to gradient methods with complex multiple-optima surfaces