TITLE:
Lagrangian Relaxation Method for Multiobjective Optimization Methods: Solution Approaches
AUTHORS:
H. S. Faruque Alam
KEYWORDS:
Multiobjective Optimization Problem, Lagrangian Relaxation, Lagrange Multipliers, Scalarization Method
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
25,
2022
ABSTRACT: This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation method that leads to finding the optimal solution to the problem. Our analysis aims to find a suitable technique to generate Lagrangian multipliers, and later these multipliers are used in the relaxation method to solve Multiobjective optimization problems. We propose a search-based technique to generate Lagrange multipliers. In our paper, we choose a suitable and well-known scalarization method that transforms the original multiobjective into a scalar objective optimization problem. Later, we solve this scalar objective problem using Lagrangian relaxation techniques. We use Brute force techniques to sort optimum solutions. Finally, we analyze the results, and efficient methods are recommended.