Geometric Mean Method Combined With Ant Colony Optimization Algorithm to Solve Multi-Objective Transportation Problems in Fuzzy Environments

The Transportation Problem (TP) is a well-known subject in the field of optimization and a very prevalent challenge for businesspeople. The goal is to reduce the total transportation cost, time, and distance of delivering resources from several sources to a large number of destinations. The literature demonstrates that various approaches have been designed with a single goal in mind, although TPs are not always developed with a bi-goal in mind. Solving transportation difficulties with several objectives is a common task. In this study, a new method for addressing multi-criteria TP using geometric means, along with a novel approach of the Ant Colony Optimization algorithm (ACO) for solving multi-objective TP in a fuzzy environment. Fuzzy numbers have been used to solve real-world problems in various domains, including operations research and optimization. The ACO Algorithm has long been recognized as a viable alternative strategy for solving optimization problems. The purpose of this study is to provide a unique approach for organizing fuzzy numbers as well as enhancements to the ACO algorithm for solving the Multi-Objective TP model. Furthermore, the suggested method is quite simple, and it finds the best solution for both the balanced and unbalanced TPs. Our method, such as Geometric Mean Ant Colony Optimization Algorithm (GMACOA), outperforms other methods in terms of objective values. Numerical examples are provided to demonstrate the method in comparison to various current methods.