Multi-Objective Transportation Problems in Fuzzy Environments Solved by Combining the Geometric Mean Method with the Ant Colony Optimization Algorithm

Abstract

An optimisation hotspot and a common headache for entrepreneurs everywhere is the transportation issue (TP). Saving money on transportation is the main objective when it comes to getting materials from where they are to where they need to go. The literature shows that many methods have been established with just one objective in mind, even if TPs aren't always made with two objectives in mind. Addressing transportation challenges while juggling many goals is a typical undertaking. An innovative geometric approach to solving multi-criteria TP and a fresh take on the Ant Colony Optimisation algorithm (ACO) for solving multi-objective TP in a fuzzy setting are both highlighted in this work. Several fields have found practical applications for fuzzy numbers, such as optimisation and operations research. For quite some time, the ACO Algorithm has been known as an alternate approach to optimisation issues. This research aims to improve the ACO algorithm for solving the Multi-Objective TP model and to provide a novel method for organising fuzzy numbers. According to the objective values, our technique, which is called Geometric Mean Ant Colony Optimisation Algorithm (GMACOA), is superior to other methods. To show how the approach compares to other methods that are currently in use, numerical examples are given.