A framework for optimization using approximate functions

Population-based, stochastic, zero-order optimization methods (e.g. genetic and evolutionary algorithms) are a popular choice in solving intractable, real-life optimization problems. These methods are particularly attractive as they are easy to use and do not require assumptions about functional and slope continuities unlike some of its gradient-based counterparts. Despite their advantages, these methods require the evaluation of numerous candidate solutions, which is often computationally expensive and practically prohibitive. We introduce a framework for optimization using approximate functions. The optimization algorithm is a population-based, stochastic, zero-order, elite-preserving algorithm that makes use of approximate function evaluations in lieu of actual function evaluations. The approximate function is constructed using a radial basis function (RBF) network and the network is periodically retrained after a few generations unlike other models which create and use the same approximate model repeatedly without retraining. A scheme for controlled elitism is incorporated within the optimization framework to ensure convergence in the actual function space. The computational accuracy and efficiency of the proposed optimization framework is assessed using a set of five mathematical test functions. The results clearly indicate that the optimization framework using approximations is able to arrive at reasonably accurate results using only a fraction of actual functions evaluations.