<p>The Multiobjective Transportation Problem (MOTP) addresses the optimization of multiple objectives, often conflicting in nature of transportation and logistics systems. Various approaches have been proposed to solve the MOTP, including manual methods as well as the heuristic-based techniques such as local search, gradient descent and genetic algorithms. However, these methods frequently encounter the challenges in handling real-life uncertainties and finding the feasible and variable solutions. This paper proposes a hybrid optimization framework that incorporates the genetic algorithms with Type-1 and Type-2 fuzzy logic and local search to improve solution robustness and variability, where variability is defined as the ability of the algorithm to generate diverse yet feasible solutions across multiple runs, reflecting robustness under uncertainty and preventing premature convergence. Results reveal that the genetic algorithm alone struggles to consistently find feasible, variable solutions, while adding manual search yields limited improvement. Incorporating hybrid local search addresses feasibility and introduces variability but expands the solution search space. Applying Type-1 fuzzy logic with local search further improves feasibility and variability while reducing the search space. Finally, integrating Type-2 fuzzy logic with local search maintains feasibility, enhances variability and significantly narrows the optimal search space, outperforming all previous methods. The proposed hybrid algorithm ‘GT2FLS’ thus demonstrates superior performance in managing uncertainty and delivering more optimal and diverse solutions for MOTP.</p>