A Partitioning Gradient Based (PGB) algorithm for solving nonlinear goal programming problems

This paper presents an efficient and reliable method called the partitioning gradient based (PGB) algorithm for solving nonlinear goal programming (NLGP) problems. The PGB algorithm uses the partitioning technique developed for linear GP problems and the generalized reduced gradient (GRG) method to solve nonlinear programming problems. The PGB algorithm is tested against the modified pattern search (MPS) method, currently available for solving NLGP problems. The results indicate that the PGB algorithm always outperforms the MPS method except for some small problems. In addition, the PGB method found the optimal solution for all test problems proving its robustness and reliability, while the MPS method failed in more than half of the test problems by converging to a nonoptimal point.