Intelligent search methods for nonlinear goal programming problems

Three methods were developed to solve nonlinear goal programming (NLGP) problems by adapting and extending the Nelder–Mead method, the Complex search method, and the Hook and Jeeves Pattern Search method to account for multiple criteria. These modifications were largely accomplished by using goal programming, lexicographic ordering, and partitioning concepts. The three resulting methods were Lexicographic Nelder–Mead (LNM) method, Partitioning Nelder–Mead-Complex (PNMC) method, and the Partitioning Pattern Search (PPS) method. Each method is analyzed based on results and compared with the other methods. Each of the methods appears to function effectively and generate a good solution. In general the PPS method did well in respect to computational time and number of iterations; however, none of the methods clearly outperformed or was outperformed by the other methods.