A Novel Discrete Filled Function Algorithm in Solving Discrete Optimization Problems (S/O: 12408)

• Main Authors: Woon, Siew Fang, Karim, Sharmila, Mohamad, Mohd Saiful Adli
• Format: Monograph
• Language: English
• Published: UUM 2016
• Subjects: QA Mathematics
• Online Access: https://repo.uum.edu.my/id/eprint/31728/1/12408.pdf; https://repo.uum.edu.my/id/eprint/31728/
• Institution: Universiti Utara Malaysia

Most practical discrete and mixed discrete optimization problems are nonlinear and known to have more than one locally optimal solution. This suggests the need for global optimization techniques which seek the best solution amongst multiple local optima. The challenge in global optimization is to avoid being trapped in the basins surrounding local minimizers. Several global methods have been proposed for solving discrete optimization problems. We focus our study on a recently developed method known as discrete filled function method. At the initial stage, an auxiliary function is introduced in discrete filled function method which turns the local minimizer of the original function to be a local maximizer. Then, an improved local minimizer is found by minimizing the filled function, otherwise the boundary of the feasible region is reached. Based on a discrete filled function method from the literature, we proposed a modification particularly on the neighbourhood search to enhance its computational efficiency. Then, we tested the proposed method on several benchmark test problems, such as Colvilles function, Goldstein and Prices function, Beales function, Powells function, and Rosenbrocks function. Numerical results suggest that the proposed algorithm is efficient in solving large scale complex discrete optimization problems, thus could be extended into solving real life application mixed discrete optimization problem in the future