Generation of alternative optima for nonlinear programming problems

Many nonlinear optimization problems are not unimodal, and only local optima can be obtained using gradient algorithms. A heuristic method, Modeling to Generate Alternatives (MGA), is introduced as a method for use in searching for a good local optimum for a highly nonlinear problem. The purpose of the MGA approach in this context is to produce easily a set of points which are feasible and maximally different from each other. By using this set as starting points for a nonlinear programming algorithm, the likelihood of locating more local optima is increased, and thus the likelihood of locating the global optimum or a good local optimum is also increased. Several problems, having multiple local optimum and therefore difficult to optimize globally, were obtained from the literature and were used to demonstrate the approach. Two problems are described here: a wastewater treatment plant design model and a facility location model.