The primary focus of this article is dedicated to a thorough investigation of the Fixed Load Transportation Problem (FCTP) and the proposition of an exceedingly efficient resolution method, with a specific emphasis on the achievement of optimal transportation plans within practical time constraints. The FCTP, recognized for its intricate nature, falls into the NP-complete category, notorious for its exponential growth in solution time as the problem's size escalates. Within the realm of combinatorial optimization, metaheuristic techniques like the Dragonfly algorithm and genetic algorithms have garnered substantial acclaim due to their remarkable capacity to deliver high-quality solutions to the challenging FCTP. These techniques demonstrate substantial potential in accelerating the resolution of this formidable problem. The central goal revolves around the exploration of groundbreaking solutions for the Fixed Load Transportation Problem, all while concurrently minimizing the time investment required to attain these optimal solutions. This undertaking necessitates the adept utilization of the Dragonfly algorithm, an algorithm inspired by natural processes, known for its adaptability and robustness in solving complex problems. The FCTP, functioning as an optimization problem, grapples with the multifaceted task of formulating distribution plans for products originating from multiple sources and destined for various endpoints. The overarching aspiration is to minimize overall transportation costs, a challenge that mandates meticulous considerations, including product availability at source locations and demand projections at destination points. The proposed methodology introduces an innovative approach tailored explicitly for addressing the Fixed Charge Transport Problem (FCTP) by harnessing the inherent capabilities of the Dragonfly algorithm. This adaptation of the algorithm's underlying processes is precisely engineered to handle large-scale FCTP instances, with the ultimate objective of unveiling solutions that have hitherto remained elusive. The numerical results stemming from our rigorous experiments unequivocally underscore the remarkable prowess of the Dragonfly algorithm in discovering novel and exceptionally efficient solutions. This demonstration unequivocally reaffirms its effectiveness in overcoming the inherent challenges posed by substantial FCTP instances. In summary, the research represents a significant leap forward in the domain of FCTP solution methodologies by seamlessly integrating the formidable capabilities of the Dragonfly algorithm into the problem-solving process. The insights and solutions presented in this article hold immense promise for significantly enhancing the efficiency and effectiveness of FCTP resolution, ultimately benefiting a broad spectrum of industries and logistics systems, and promising advancements in the optimization of transportation processes.
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