A PARTITIONING GRADIENT-BASED (PGB) ALGORITHM FOR SOLVING NONLINEAR GOAL PROGRAMMING-PROBLEMS

This paper presents an efficient and reliable method called the partit ioning gradient based (PGB) algorithm for solving nonlinear goal progr amming (NLGP) problems. The PGB algorithm uses the partitioning techni que developed for linear GP problems and the generalized reduced gradi ent (GRG) method to solve nonlinear programming problems. The PGB algo rithm is tested against the modified pattern search (MPS) method, curr ently available for solving NLGP problems. The results indicate that t he PGB algorithm always outperforms the MPS method except for some sma ll problems. In addition, the PGB method found the optimal solution fo r 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.