## 1 Introduction  
Multimodal transportation optimization has emerged as a crucial strategy to address the complex challenges faced by nations worldwide, and Iraq is no exception. In the context of Iraq's transportation landscape, multimodal transportation optimization stands as a beacon of hope, promising to alleviate unique challenges while leveraging the nation's geographical advantage for economic growth and development. Strategically positioned in the heart of the Middle East, Iraq holds immense potential for a robust multimodal transportation system, facilitated by vital waterways like the Persian Gulf and an extensive road network linking major cities and neighboring nations. This geographic advantage, when properly harnessed, can elevate Iraq's transportation network to new heights [1; 2; 3]. Multimodal transportation integrates various modes such as road, rail, air, and sea to efficiently move goods and people. Iraq's diverse geography, including mountains, deserts, and a substantial coastline along the Persian Gulf, necessitates a strategic approach to transportation. Recognizing the varying needs of different regions, Iraq embraces multi-modal transportation as a flexible solution [4; 5; 6]. This integrated approach proves vital for economic development and post-conflict reconstruction, ensuring efficient transportation networks for rebuilding infrastructure. The economic backbone of Iraq, particularly its reliance on oil exports, underscores the importance of efficient transportation links from production centers to export terminals. Multimodal transportation facilitates seamless movement, contributing to overall economic resilience and growth. Additionally, Iraq's geographical location, surrounded by neighboring countries, emphasizes the significance of regional connectivity. Adopting multimodal transportation enhances collaboration, cross-border trade, and economic ties, fostering a more interconnected and prosperous region. Efficiency, cost reduction, and security are additional advantages offered by multimodal transportation, especially pertinent in mitigating historical security challenges by diversifying transportation routes [4; 5; 6]. From an environmental perspective, multimodal transportation contributes to sustainability efforts by reducing overall greenhouse gas emissions. By strategically utilizing different modes based on their efficiencies and environmental impacts, Iraq can make strides toward a more sustainable and eco-friendly transportation system. Addressing urban congestion, particularly in major cities like Baghdad, is another benefit. Integrating public transit alongside other modes can alleviate traffic congestion, enhancing the quality of life for urban residents. Moreover, well-developed transportation infrastructure, including air travel and roads, promotes tourism, leading to economic growth, revenue generation, and increased employment opportunities. In times of humanitarian crises, efficient multimodal transportation is indispensable for delivering timely and essential humanitarian aid to affected populations [4; 5; 6]. This comprehensive approach ensures that aid reaches its destination promptly, contributing to the well-being of those in need. In essence, Iraq's adoption of multimodal transportation reflects a holistic strategy that addresses diverse needs, promotes economic development, enhances security, and fosters sustainability across various facets of the nation's progress. In light of these challenges, the integration of various transportation modes through approaches like data envelopment analysis (DEA) and hidden Markov models (HMM) becomes instrumental [7; 8; 9; 10; 11]. These methods offer tailored solutions that can address Iraq's transportation woes and unlock the full potential of its transportation network. In a context where infrastructure quality profoundly influences safety and efficiency, DEA employed for efficiency evaluation utilizes real-time data to assess the efficiency of each transportation arc.