This paper presents an efficient and reliable partitioning Gradient Based (PGB) algorithm for solving Nonlinear Goal Programming (NLGP) Problems. The PGB algorithm uses the partitioning technique development for linear GP problems, to decompose the NLGP problem into a series of single objective nonlinear problems. It begins by considering only those constraints associated with the first priority, and uses the Generalized Reduced Gradient (GRG) method to solve the first subproblem. If a unique optimal solution is reached, the algorithm terminates with the current point as the optimal solution to the entire NLGP; otherwise, the second subproblem is solved by adding the second priority goal constraints and a linear constraint to retain the first priority and minimizing the second priority objective. This procedure is continued until all the subproblems are solved or unique optimal solution is detected at any subproblem. A sufficient test is developed to detect unique solutions for nonlinear 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 more 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.
All Science Journal Classification (ASJC) codes
- Information Systems and Management
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics