International shipping underpins the global economy, transporting approximately 80% of all global trade. However, this critical sector is also a significant contributor to environmental degradation, ranking among the top 10 global emitters of greenhouse gases (GHGs). Recognizing the urgent need to address this issue, members of the International Maritime Organization (IMO) adopted a 2018 plan to reduce GHG emissions from ships, aiming to mitigate the impact of climate change. As a result, ocean carriers and cruise lines operating in IMO-member countries must comply with increasingly stringent emissions policies and regulations.

Among potential solutions, ammonia (NH 3 ) stands out as a promising non-fossil fuel alternative for reducing CO 2 emissions in shipping. According to a recent Clean Air Task Force report, ammonia-fueled vessels retrofitted for this purpose could offer lower operating costs than traditional fossil fuel ships (1). Key advantages of ammonia include high power-to-fuel-topower efficiency, a high-octane rating of 110-130, and a narrow flammability range, which enhances safety by reducing explosion risks (2). Despite these benefits, ammonia's adoption as a shipping fuel presents significant challenges, particularly its lower energy density. Compared to conventional fuels such as jet-propulsion fuel 8 , ammonia provides about one-third less endurance range, meaning that ships require more frequent refueling stops (3). This limitation directly affects operational parameters such as travel time and routing.

In this study, JP-8 was chosen as the baseline for comparison rather than commercial fuels such as heavy fuel oil (HFO), low-sulfur fuel oil (LSFO), or marine gas oil (MGO). JP-8 was selected because it represents a practical midpoint with respect to energy density, cost, and emissions, providing a meaningful benchmark for evaluating ammonia's operational performance. While HFO and LSFO are widely used in commercial shipping, their inclusion would have required expanding the scope of the analysis to multiple fuel types. The choice of JP-8 allows the study to focus on ammonia's feasibility while maintaining analytical clarity.

To explore the implications of adopting ammonia as a shipping fuel, this study addresses the following key research questions.

1. Can current shipping operations be maintained using ammonia as a fuel source and the existing refueling logistics network? 2. How significantly will ammonia's fuel characteristics affect total travel time? 3. How do the optimal routes and speeds of ammonia-fueled ships differ from those of JP-8powered ships?

These questions aim to provide insights into the operational trade-offs associated with ammonia as a fuel, particularly with respect to routing strategies, refueling station selection, ship speeds between stations, and overall travel time. While prior research has explored the advantages and limitations of ammonia as a shipping fuel, no studies to date have specifically analyzed its impact on fleet-wide optimization of ship routes and speeds. This study fills that gap by developing a model that optimizes the routes and speeds of ammonia-fueled ships, with the objective of minimizing total travel time.

Unlike previous studies, which typically focus on optimizing routes for a single ship or homogeneous fleet, this study considers multiple ships of varying types, each with distinct characteristics such as fuel tank capacity, endurance range, maximum speed, and fuel consumption rate. Furthermore, this study accounts for operational complexities, such as ships departing from and traveling to different locations, which are often overlooked in prior research. These considerations are relevant for both commercial shipping and defense logistics.

To address these challenges, a mixed-integer non-linear programming (MINLP) model is developed to optimize the routes and speeds of ships in a fleet, subject to constraints related to fuel capacity, endurance range, refueling station availability, and non-linear fuel consumption rates. The objective is to minimize total travel time. Solving this complex optimization problem requires a novel hybrid genetic algorithm-particle swarm optimization (GA-PSO) approach. Unlike conventional hybrid methods, which sequentially apply the GA and PSO, this study's approach integrates the GA to optimize routes and PSO to refine speeds, leveraging the strengths of both algorithms. The GA explores the solution space for optimal routes through selection, crossover, and mutation, while PSO converges on the optimal speeds for the selected routes. This combination enhances both exploration and convergence efficiency, ensuring robust solutions for the complex optimization problem.

The remainder of this paper is structured as follows. The second section reviews related work on alternative fuels for ships and naval logistics. The third section describes the problem context and assumptions. The fourth section presents the mathematical model formulation. The fifth section outlines the proposed solution methodology. The sixth, seventh, and eighth sections detail the design of experiments, numerical experiments, and an illustrative example, respectively. The ninth section discusses the results, followed by the final section, which concludes the study and outlines future research directions.

The fossil fuels used in conventional marine diesel engines emit high levels of harmful emissions, contributing to the greenhouse effect and global warming. As a result, various international regulations have been implemented to limit these emissions within specific boundaries. To comply with increasingly strict emissions regulations, the maritime industry has been exploring low-carbon shipping strategies. Significant research has been conducted in the area of shipping decarbonization that has warranted several systematic review papers, summarized here. Yu et al. ( 4) reviewed the latest articles on emission control-driven voyage optimization, investigating the state-of-the-art methodologies that integrate factors affecting fuel consumption, cargo operation, and emission control regulations to develop advanced and effective shipping voyage optimization systems. Similarly, in studies by Xing et al. (5), Bouman et al. (6), and Jimenez et al. (7), the authors presented a comprehensive review categorizing the pathways for improving energy efficiency and reducing carbon emissions in international shipping. These studies underscored the diversity of abatement measures, their context-sensitive nature, and the comprehensive strategies needed to achieve low-carbon or zero-carbon objectives. The reviews also highlighted the potential of eco-friendly fuels and alternative power sources, although their effectiveness can vary significantly depending on ship types and operational routes. Economic and legal challenges continue to pose significant barriers to the widespread adoption of these technologies. Furthermore, Huang and Duan (8) provided an in-depth review of various decarbonization technologies, including advances in navigation systems, hull design configuration, propulsion and power systems, and alternative fuels. Their review assessed the emission reduction potential and economic viability of these technologies, offering a holistic view of potential future advancements in green shipping. Lastly, Davarzani et al. (9) conducted an analysis of past and present research on green ports and maritime logistics, utilizing bibliometric and network analysis tools to map the existing literature and identify key investigators and research clusters. Their findings emphasized the critical role of environmental considerations in maritime logistics, especially in route optimization, noting that reducing fuel consumption not only cuts operational costs but also lessens the environmental footprint of maritime operations.

Ammonia's potential as a marine fuel has garnered significant interest because of its zero-carbon emission capabilities. Research, such as that conducted by Brohi (10), demonstrated the feasibility of using ammonia in internal combustion engines, highlighting its zero-carbon emissions potential. Similarly, Afif et al. (11) explored the use of ammonia in fuel cells and showed its efficiency and environmental benefits. Further, studies have expanded on these foundational works. For instance, Rocha et al. (12) conducted numerical investigations on the combustion and emission characteristics of ammonia in three modern stationary gas turbine concepts: leanburn dry-low emissions (DLE), rich-burn quick-quench lean-burn (RQL), and moderate or intense low oxygen dilution (MILD). Their results indicated that, with suitable modifications, ammonia could achieve efficient combustion with considerably lower NO x emissions, particularly under RQL and MILD concepts, unlike the DLE concept, which showed acceptable emissions only under unstable conditions. In addition, Juangsa et al. (13) reviewed the potential of ammonia as a hydrogen carrier, highlighting its high hydrogen density, superior storage capabilities, and high stability. The ease of storing and transporting ammonia compared to pure hydrogen makes it attractive for large-scale energy applications. Despite the significant energy requirements for its production through the Haber-Bosch process, alternative methods such as thermochemical, electrochemical, photochemical, and plasma-assisted processes present viable future production avenues. Schwarzkopf et al. (14) developed emission scenarios for 2025, 2040, and 2050, focusing on transitioning to ammonia as the primary marine fuel by 2050. Their study, which included efficiency improvements and fleet growth aligned with the IMO's Energy Efficiency Design Index, found that using ammonia could reduce CO 2 emissions by 40% and NO x emissions by 39% by 2050 compared to 2015 levels. Their study also highlighted the potential for further reductions with advanced ammonia engine technologies.

The following review focuses on studies that are related to this work, which focuses on the development of a model to determine the optimal routes for several ships in a fleet with different origins and destinations with the objective of minimizing the total travel time.

Optimization of ship routes has been a critical area of research, aiming to enhance operational efficiency and reduce fuel consumption. Classical models, such as the traveling salesman problem (TSP) and vehicle routing problem (VRP), have been extensively studied in container liner shipping to address not just the routing but also schedule design, port selection, and fleet management. For instance, Tran and Haasis (15) effectively applied these models in maritime logistics, enhancing fleet size optimization, assignment, and container movements to reduce travel distances and operational costs. Recent studies have utilized more sophisticated techniques to handle the complexities of real-world scenarios. For example, Kim et al. (16) sought to challenge the state-of-the-art methods in route decision-making by employing a real-number grid method. The authors implemented a real-number grid in the grid generation procedure, global speed optimization in the speed optimization procedure, and a Monte Carlo evaluation in the cost evaluation procedure. They claimed that their method not only improved the optimization performance of the conventional method but also upgraded constraint satisfaction in route decision-making. Lashgari et al. (17) developed a stochastic linear integer programming model that integrates routing, sailing speed, and bunkering policies under varying fuel price conditions. Their model demonstrated substantial cost reductions while ensuring schedule reliability and environmental compliance, offering optimal solutions for speed and route decisions. These developments highlight a trend toward integrating economic and environmental considerations, underlining the need for models that can dynamically adapt to fluctuating market conditions and stringent environmental regulations.

The relationship between a ship's speed and its fuel consumption exhibits a non-linear characteristic, which consequently categorizes the associated optimization problems as non-linear-these are notoriously challenging to solve because of their complex solution landscapes. Foundational research in this domain, such as the study conducted by Chaal (18), has been instrumental in developing models that correlate ship speed with fuel efficiency. Their research underscores the critical importance of optimizing ship speed to minimize fuel consumption. However, the practical implementation of these speed optimization strategies is rather challenging. Scheduling constraints and logistical limitations at ports frequently impede the application of optimal speed settings, thus complicating the operationalization of theoretical models. More recent studies have broadened the scope of variables considered in the optimization process. For instance, Tadros et al. (19) advanced the research by incorporating meteorological conditions into their optimization models. They utilized a non-linear optimization framework integrated with NavCad software to first optimize the propeller for calm water conditions. Subsequently, they adjusted the model to account for added resistance from adverse weather conditions, thereby recalibrating ship speed and propeller performance. Their empirical findings indicated that this comprehensive approach could reduce fuel consumption by up to 2.6%, demonstrating the potential benefits of including environmental factors in speed optimization models.

Meta-heuristics such as the GA and PSO have been widely applied to solve route optimization problems. Notably, in their comprehensive and comparative overview of the existing state-of-the-art methods for ship weather routing, Walther et al. (20) concluded that the GA, when integrated with meteorological and oceanographic data, can be effective as a solution algorithm in reducing a ship's travel time and consumption while enhancing economic feasibility, energy efficiency, and compliance with emission regulations. Conversely, Rahmana and Asiha (21) provided empirical evidence supporting the proficiency of PSO in curtailing navigational distances and associated transportation expenditures, thereby underscoring its utility in maritime logistics.

The integration of the GA and PSO into a hybrid GA-PSO framework has shown significant promise in addressing complex optimization problems. The hybrid approach leverages the strengths of both algorithms, balancing exploration and exploitation capabilities to enhance solution quality. Rabbani et al. (22) utilized a hybrid GA-PSO algorithm to optimize the multi-period, multi-item inventory routing problem (IRP), incorporating lateral trans-shipment and financial decisions. Their study formulated the problem as a mixed-integer linear programming (MILP) model and demonstrated that the hybrid approach outperformed traditional methods and the general algebraic modeling system (GAMS), achieving significant reductions in inventory and transportation costs. Liu et al. (23) developed a hybrid GA-PSO algorithm to optimize shipping route planning in restricted waters. Their approach aimed to automate and enhance the accuracy and robustness of route planning compared to traditional experience-based methods. The experimental results demonstrated that the hybrid GA-PSO algorithm outperformed existing schemes with respect to both accuracy and robustness, proving to be effective for optimizing maritime traffic networks and ensuring stable shipping routes.

Alternative Fuel Technologies. Alternative fuels have been extensively studied for their potential to mitigate emissions in the maritime sector. Among these, ammonia, hydrogen, and biofuels have emerged as leading candidates because of their environmental benefits and alignment with decarbonization goals. Comprehensive reviews on decarbonization strategies, including the adoption of alternative fuels, are available in the works of Feng et al. (24) and Al-Enazi et al. (25).

Ammonia has gained significant attention for its zerocarbon emission potential, compatibility with existing marine engines, and role in reducing GHG emissions. However, challenges such as NO x emissions, lower energy density, and safety concerns remain barriers to its adoption. Studies such as those by Tornatore et al. (26) and El-Kadi et al. (27) have emphasized ammonia's potential as a green fuel to decarbonize industrial processes and transportation systems. For instance, El-Kadi et al. (27) projected that green ammonia could achieve a 75%-90% reduction in CO 2 emissions compared to conventional methods of ammonia production by utilizing renewable energy sources and advanced synthesis processes. In addition, Tornatore et al. ( 26) highlighted ammonia's capability to significantly lower NO x emissions in internal combustion engines when equipped with advanced after-treatment systems, although precise reduction figures depend on specific combustion configurations and operational parameters. Hydrogen, another promising zero-carbon fuel, is highly regarded for its potential in the maritime sector because of its high energy density and zero emissions when used in fuel cells. However, as highlighted by Fu et al. (28), challenges such as the high cost of production, storage complexities because of its low boiling point, and the lack of infrastructure significantly hinder its large-scale application in shipping. The development of green hydrogen production methods and maritime hydrogen transport systems is critical to overcoming these barriers and realizing hydrogen's potential as a sustainable energy solution. Biofuels and synthetic fuels, while more mature, offer immediate compatibility with existing infrastructure but face scalability issues because of limited feedstock availability, as highlighted by Sheikh Othman (29).

Ammonia Fuel Technologies and Challenges. From a technological perspective, ammonia is compatible with existing marine engine technology, which is a significant advantage for its adoption. Internal combustion engines can be modified to burn ammonia, allowing for a gradual transition from conventional marine fuels without the need for entirely new infrastructure (26,30,31). Machaj et al. (32) reviewed its advantages, including its zero-carbon emissions and compatibility with internal combustion engines, which facilitates gradual adoption without the need for substantial infrastructure changes. In addition, advancements in ammonia-hydrogen engines have been proposed to address challenges such as low flame speed and high ignition temperature. For example, Qi et al. (33) reviewed advancements in ammonia-hydrogen engines, proposing a conceptual hybrid power system using ammoniahydrogen mixtures. The review also discussed ignition methods, fuel supply, emission control, and efficient combustion measures, providing insights into the development of effective ammonia-hydrogen engines.

Despite these advancements, several challenges remain. Ammonia's low reactivity and high NO x and N 2 O emissions require the adoption of co-combustion techniques and catalytic reduction systems to optimize combustion and control emissions, as discussed by Erdemir and Dincer (34) and Chavando et al. (35). Furthermore, its toxicity poses significant safety risks during handling and storage. Specialized equipment, robust safety protocols, and comprehensive personnel training are necessary to mitigate these risks and ensure safe operations both onboard and during fuel transfer.

Life Cycle Analysis of Alternative Fuels. Life cycle analysis (LCA) is critical for evaluating the overall environmental impact of alternative fuels, encompassing their production, storage, and usage stages. Ammonia, while having low operational emissions, is currently produced primarily via the Haber-Bosch process, which has a high carbon footprint. Renewable production methods, such as electrochemical synthesis, offer a promising pathway for green ammonia, as reviewed by Wu et al. (36). Similarly, hydrogen's life cycle emissions depend on the production method, with renewable energy electrolysis resulting in near-zero emissions, whereas steam methane reforming contributes significantly to GHG emissions, as noted by Valente et al. (37). Biofuels and synthetic fuels vary widely in their life cycle outcomes: waste-based biofuels typically exhibit favorable environmental performance, while synthetic fuels show potential for net-zero emissions if produced using captured carbon and renewable energy, as reviewed by Yan et al. (38).

The following shortcomings have been identified based on the above literature review. This study contributes to the literature as follows.

(c) Tackling shortcoming 1: This study develops a MINLP model to optimize the routes and speeds of ships in a fleet with the goal of minimizing the total travel time. The numerical experiment results provide insights on differences in routes and ship speeds when using NH 3 as fuel versus JP-8. (d) Tackling shortcoming 2: This study introduces a new scheme for combining the GA and PSO algorithm to take advantage of PSO's ability to quickly find the optimal speeds given a route from the GA. The proposed synchronous hybrid GA-PSO performs significantly faster than the GA by itself.

This study investigates the potential of ammonia (NH 3 ) as an alternative fuel in maritime operations, motivated by the broader goal of reducing reliance on conventional petroleum fuels and transitioning toward more sustainable energy sources. Ammonia, known for its zero-carbon emission benefits, fits into the paradigm of green energy initiatives. However, it presents the challenge of having a shorter endurance range. To quantify the impacts this limitation has on ships' operations, this study models a fleet with five different ship types (39), each characterized by unique speed ranges and nonlinear fuel consumption profiles, as detailed below.

Ship Type 1: f(speed) = 1, 429:04 + 2, 215:39

3 (f(speed): fuel consumption at designated speed [kJ/h]): -capacity of fuel tank: 500,000 gal; -speed range (knots): (0,32.5). Ship Type 2: f speed ð Þ= 764:433 + 1, 379:62 E 51:59 3 speed=100 ð Þ 3 : -capacity of fuel tank: 300,000 gal; -speed range (knots): (0,30). Ship Type 3: f speed ð Þ= 700:811 + 2, 039:41 E 78:21 3 speed=100 ð Þ 3 : -capacity of fuel tank: 1,500,000 gal; -speed range (knots): (0,22). Ship Type 4: f speed ð Þ= 4, 834:54 À 4, 614:81 E À44:96 3 speed=100 ð Þ 3 : -capacity of fuel tank: 7,560,000 gal; -speed range (knots): (0,20). Ship Type 5: f speed ð Þ= 92:06 + 699:55 E 112:94 3 speed=100 ð Þ 3

: -capacity of fuel tank: 1,000,000 gal; -speed range (knots): (0,23).

To facilitate a direct comparison between NH 3 and JP-8 fuel consumption, it is essential to express fuel usage with respect to energy content rather than volumetric consumption. Given that one gallon is equivalent to 3.785 L, the energy content per gallon for each fuel type is calculated based on their respective energy densities.

For NH 3 , with an energy density of 12.7 MJ/L, the energy content per gallon is computed as follows (40):

For JP-8, with an energy density of 34.5 MJ/L, the energy content per gallon is as follows (41):

These ships navigate a global network of 33 refueling stations (including origins and destinations), as depicted in Figure 1. The ships in the fleet may originate from different ports, and they can also have different destinations.

The MINLP model developed to determine the optimal routes for ships in the fleet is presented below. Notations and decision variables of the model are presented in Table 1.

The objective function is as follows:

Figure 1. Refueling network with 33 ports.

s:t: The objective in Equation 1 minimizes the total travel times for all ships. The constraints in Equations 2 and 3 ensure each ship leaves its origin exactly once and arrives at its destination exactly once. The constraint in Equation 4restricts the flow conservation for each ship and station, which ensures that each ship arrives at and departs from the station, if applicable. The constraint in Equation 5ensures that the fuel consumption does not exceed the remaining fuel. The constraint in Equation 6ensures the fuel after refueling does not exceed the ship's type-specific capacity. The constraint in Equation 7guarantees that a ship cannot be processed until it finishes the service, including the refueling time at the station (time requirement). The constraint in Equation 8 links refueling to the ship present at that station, which means that the ship can refuel when it is present at that station. The constraint in Equation 9 confirms that the start time of a ship's service at a station is properly linked to the ship's start service at that station during a specific time period. The constraint in Equation 10 ensures that no more than three ships can be refueled at any station during the same time window. The constraint in Equation 11 sums the refueled amount over each interval l, ensuring that the total fuel refueled at station i over all intervals does not exceed the station's fuel capacity. The constraint in Equation 12 ensures that ships operate within their speed limits. The constraints in Equations 13-17 define the range of the decision variables.

As mentioned, the proposed MINLP is NP-hard and non-linear. To solve this model, a hybrid GA-PSO algorithm is developed.

GAs are heuristic algorithms inspired by the process of natural evolution. These algorithms have been effectively employed to solve complex optimization problems, such as the TSP and VRP, among others. The GA involves several key operations: initial population generation, fitness evaluation, selection, crossover, and mutation (42). In this paper, the GA was utilized to generate the initial population, serving as a set of potential solutions. Subsequently, the algorithm iteratively refined these solutions through the following steps.

Step I: Generation of the initial feasible population of chromosomes using the greedy algorithm. The first chromosome encodes the ship IDs and their sequence of visits, representing the chosen route. As illustrated in Table 2, the selected route for ship 1 involves visits to stations 12, 15, 7, ., and 17, in that specific order. The second chromosome encodes the remaining fuel after the ship departs from each station. For example, ship 1 has 500,000 gal of fuel remaining after leaving station 12. The third chromosome encodes the amount of fuel refueled at each station. For instance, a value of 0 in the second column of the third row indicates that ship 1 did not refuel at station 12. The fourth chromosome encodes the service start time at each station for the different ships. For instance, the value in the cell located in the fifth row and second column indicates that the service start time for ship 1 at station 12 is 0.

Step II: During each iteration, a crossover operation employing two points on all chromosomes is performed, producing offspring that subsequently undergo mutation. Subsequently, a fitness evaluation is conducted. If it does not satisfy the constraints, the repair process will be applied based on the needed constraints to ensure viability.

PSO is a well-established evolutionary computation technique grounded in swarm intelligence, developed by Kennedy and Eberhart (43). In the context of this study, PSO is used to optimize ship speeds for a given route, complementing the route optimization performed by the GA. Here, each particle represents a potential solution for ship speeds along the route, encoded as a vector of speed values at each segment of the journey. The position vector y m of a particle corresponds to the current speed profile of a ship, while the velocity vector u m determines how the speed profile is adjusted in the next iteration.

Each particle retains a memory of its personal best position (q m ), which represents the best speed profile it has found so far, and the global best position (h p ), which represents the best speed profile found by any particle in the swarm (44). The movement of particles is guided by three key parameters. Inertia factor (v): This parameter controls the influence of the particle's current velocity on its next movement. A higher inertia factor encourages exploration of the search space, while a lower value promotes exploitation of known good solutions. In this study, we set v = 0:75 to balance exploration and exploitation.

Cognitive parameter (a 1 ): This parameter determines how much the particle is influenced by its own best-known solution (q m ). A higher a 1 value encourages the particle to move toward its personal best. In this study, we set a 1 = 1:4 to prioritize individual learning. Social parameter (a 2 ): This parameter determines how much the particle is influenced by the global best solution (h p ). A higher a 2 value encourages the particle to move toward the best solution found by the swarm. In this study, we set a 2 = 1:6 to prioritize collective learning.

The position and velocity of each particle at time step k are updated using the following equations:

where m = 1, 2, . . . , N (with N being the population size), v is the inertia factor, a 1 and a 2 are cognitive and social parameters, and r 1 and r 2 are random numbers uniformly distributed between 0 and 1. These equations guide the particles toward optimal speed profiles that minimize total travel time while satisfying fuel consumption and refueling constraints. PSO typically offers a simpler implementation and requires fewer parameters to adjust than the GA. Its adeptness at balancing local and global search strategies reduces the risk of premature convergence, a common issue in the GA, thereby enhancing its effectiveness in exploring solution spaces. These benefits make PSO an ideal complement to the GA, and integrating both into a hybrid algorithm can significantly enhance optimization performance.

The hybrid GA-PSO algorithm begins with the generation of an initial population using a greedy algorithm and a random method within the GA framework, as shown in Figure 2. This population undergoes selection, two-point crossover, and mutation to introduce diversity and evolve solutions.

At each iteration, the feasibility of the GA solutions is verified, and any solutions that do not meet the constraints are adjusted accordingly. Once feasible solutions are obtained, their fitness is evaluated to guide the selection of the best candidates.

The feasible speed solution will be passed to the PSO phase. The initial population for PSO is generated using the feasible speeds from the GA. The PSO process involves checking the feasibility of speed solutions and applying constraints as necessary. The particles' personal best (pBest) and global best (gBest) positions are updated iteratively.

The optimized speed solutions from PSO are then integrated back into the GA population for a new round of fitness evaluation. The best solutions are updated accordingly, and the GA process continues with crossover and mutation, guided by the new speed values from PSO.

This iterative cycle of the GA followed by PSO continues until the stopping criteria are met, ensuring that the algorithm does not prematurely converge to local optima. By leveraging the strengths of both the GA and PSO, the hybrid approach provides a robust mechanism for iterative refinement and enhances the overall optimization performance. The effectiveness of this combined method is demonstrated in the subsequent Results and Discussion section.

A full factorial design of experiments (DOE) was used to investigate the main and interaction effects of three factors (number of origins, number of destinations, and number of ships) on the response variable (total travel time). This experimental design incorporated three levels for each factor, conforming to a 3 3 full factorial design to optimize the number of experimental runs while capturing critical effects. Specifically, the levels chosen for the number of origins are 1, 2, and 3. For the number of destinations, the levels are also set at 1, 2, and 3. The number of ships is varied at three substantially different scales: 5, 10, and 15. The experimental parameters are summarized in Table 3. To analyze the output from the optimization model (solved using the developed GA-PSO) State-Ease 360 software was utilized, enabling the identification and quantification of both main effects and interactions among the studied factors.

The experiments in this study were designed to evaluate the efficacy and applicability of ships powered by NH 3 fuel in comparison to those utilizing traditional JP-8 fuel. The optimal solutions were obtained using the hybrid GA-PSO algorithm, implemented using Python. All experiments were run on a desktop computer equipped with an Intel Core i7 3.6-GHz processor and 16 GB of RAM.

Before presenting the results of the full factorial DOE outlined in Table 6, an illustrative example is presented to clarify the nature of the input data and the output of the model. Table 4 shows the input data for an illustrative scenario involving five ships, three origins, and three destinations. Column 1 shows the ship ID. Column 2 shows the ship type, which determines the speed range, fuel capacity, and the relationship between the fuel consumption and speed. Columns 3 and 4 show the origins and destinations, respectively.

Figure 3 presents a comparative visualization of maritime routes for 10 different ships, categorized by their fuel type-JP-8 and NH 3 -across five different types. This comparison highlights significant variations in route, speed, and overall travel time. Specifically, ships fueled by NH 3 tend to follow longer routes (notably ships 2 and 3 with NH 3 ). They also tend to travel at lower speeds. Conversely, ships utilizing JP-8 are able to take more direct routes and travel at higher speeds.

The results indicate that despite similar origins and destinations, ships using NH 3 generally have higher total travel times and exhibit variable speeds across different journey segments, suggesting that the ships had to regulate their speeds to conserve fuel so that they were able to reach the next destination. For example, ship 3 with NH 3 fuel has a travel time of 749.58 h at an average speed of 21 knots, in contrast to ship 3 with JP-8 fuel, which covers its route in 455.53 h at a consistently higher speed of 22 knots. The difference in total travel time is significant between NH 3 and JP-8 fuel, primarily because of the lower energy density of NH 3 , necessitating more frequent refueling or adjusted route planning. In this study, we use the same storage capacity for NH 3 tanks and JP-8 tanks to maintain a consistent baseline for comparison. By keeping the tank capacity constant, we are able to isolate and highlight the differences in performance, range, and operational logistics between the two fuels. This approach allows us to better understand how NH 3 , despite its lower volumetric energy density, affects ship range and fuel logistics when compared to JP-8. In addition, it provides insights into necessary adjustments, such as more frequent refueling or route optimization, to compensate for the reduced energy content of NH 3 while maintaining operational efficiency. This suggests that the ships had to regulate their speeds to conserve fuel to reach the next destination. The difference in total travel time is significant between NH 3 and JP-8 fuel, primarily because of the lower energy density of NH 3 , necessitating more frequent refueling or adjusted route planning.

Table 5 shows a detailed comparison of total travel times and average runtimes for three different algorithms-LINDO, the GA, and hybrid GA-PSO-used to optimize all ship routes using ammonia as an alternative fuel. The table is organized as follows: Column 1 lists the experiment number; columns 2-4 show the total travel times achieved by LINDO, the GA, and GA-PSO, respectively; columns 5 and 6 show the time improvements of the GA over LINDO and GA-PSO over the GA, respectively; columns 7-9 present the average runtimes for LINDO (where applicable), the GA, and GA-PSO, respectively; and column 10 measures the runtime differences between the GA and GA-PSO. The data highlight the performance differences between these algorithms across various experiments. Notably, LINDO was able to solve very small test cases (labeled i, ii, iii) but was not able to obtain an optimal solution for experiments 1-9 within 24 h.

The comparative analysis shows that the differences in total travel times between LINDO (which can achieve the exact solution) and the heuristic methods (GA and GA-PSO) are minimal, indicating the heuristic results are acceptable. Specifically, the hybrid GA-PSO solutions match those obtained by LINDO (for the small test cases), but its runtime is drastically smaller. This ability to deliver near-optimal solutions efficiently is particularly advantageous for large-scale problems.

Because of the non-normal distribution of the runtime data associated with the GA and GA-PSO, the Wilcoxon signed-rank test was utilized rather than the paired sample t-test. This test indicated a statistically significant difference at the 95% confidence level in the median runtimes between the GA and GA-PSO, with a p-value of 0.0033, affirming the superior computational efficiency of GA-PSO. The combination of minimal difference in solution quality with significant reduction in computational time strengthens the case for adopting the developed GA-PSO algorithm. For subsequent experiments 10-27, the hybrid GA-PSO algorithm is applied exclusively.

Note: Ave. = average; Diff. = difference; GA = genetic algorithm; PSO = particle swarm optimization; NA = Not Applicable (LINDO could not solve these instances within 24 hours).

Consumption between NH 3 -Fueled and JP-8-Fueled Ships

Table 6 compares the difference in total ship travel time and energy consumption between the JP-8-fueled and the NH 3 -fueled ships. Since the fuel consumption of JP-8 is approximately three times that of NH 3 , using fuel consumption as the basis for comparison would lead to misleading conclusions, as it does not account for the fundamental difference in energy density between the two fuels. Given that NH 3 has a lower energy density, ships fueled by NH 3 inherently consume a larger volume of fuel to achieve the same energy output as JP-8fueled ships. Furthermore, the energy released per unit of fuel varies significantly between the two fuels, making fuel consumption an unreliable metric for assessing operational efficiency. Therefore, a direct comparison based on fuel consumption would unfairly disadvantage NH 3 and fail to provide an accurate assessment of its efficiency.

To ensure a meaningful and unbiased evaluation, energy consumption was chosen as the benchmark instead. Unlike fuel consumption, which does not directly reflect the actual energy utilized by the ship, energy consumption provides a more accurate measure of operational efficiency. By comparing energy consumption, which is shown in Equation 24, the analysis eliminates the distortions caused by differences in fuel energy density and allows for a fair assessment of fuel performance.

The first column shows the experiment number. Columns 2 and 3 show the total ship travel time for NH 3 -fueled and the JP-8-fueled ships, respectively. Column 4 shows the percentage reduction in total travel time of the JP-8-fueled ship over the NH 3 -fueled ship. Columns 5 and 6 show the ship energy consumption for NH 3 -fueled and JP-8-fueled ships, respectively. The last column shows the percentage reduction in fuel consumption of the JP-8-fueled ship over the NH 3 -fueled ship.

The results indicate that JP-8-fueled ships reach their destinations faster than NH 3 -fueled ships. This finding aligns with expectations, as the experiments assumed that With respect to energy consumption, two factors may contribute to the differences observed. (1) Higher speed: The relationship between energy consumption and speed is non-linear, with energy usage increasing significantly as speed approaches the ship's upper limit. (2) Longer routes: Energy consumption increases as the ship covers a greater distance, even when maintaining the same speed.

The results reveal that NH 3 -fueled ships generally consume more energy than their JP-8 counterparts, although the extent varies across experiments. A paired t-test between travel time improvement and energy consumption improvement resulted in a t-statistic of 22.92 (p = 0:0072), indicating a statistically significant difference between the two metrics at the a = 0:01 level. The negative t-statistic indicates that improvements in travel time do not necessarily correspond to proportional reductions in energy consumption. In fact, in many cases, faster travel times are associated with higher energy usage. This can be attributed to the non-linear relationship between speed and energy consumption, where energy demand increases at an accelerating rate as ship speed rises, diminishing the efficiency gains from reduced travel time. Furthermore, because of the lower energy density of NH 3 fuel, ships operating at higher speeds may require more frequent refueling, leading to additional energy expenditures associated with detours and idling during refueling operations. These factors collectively contribute to the observed discrepancy between travel time improvements and energy consumption trends.

The Pearson correlation coefficient between travel time improvement and energy consumption improvement is 0.378, indicating a moderate positive correlation rather than a strong relationship. This suggests that while higher travel time improvements sometimes correspond to increased energy consumption, the relationship is not as direct as previously assumed. One possible explanation is that operational factors, such as refueling strategies and routing efficiency, introduce variability into energy consumption trends. In some cases, ships that achieve shorter travel times may not necessarily experience proportional increases in energy consumption, depending on the specific routes taken and refueling logistics.

Thus, while NH 3 -fueled ships exhibit systematic differences in travel time and energy consumption relative to JP-8 ships, the extent of these differences depends on operational conditions, ship speed, and refueling frequency. The results highlight the need for further analysis of ship routing and operational strategies to improve the efficiency of NH 3 -powered maritime transport.

The aim of the DOE full factorial design is to explain how travel time and energy consumption (response variables) are affected by various factors (the number of ships, the number of origins, and the number of destinations). To establish this relationship for NH 3 -fueled ships, a model is estimated using results obtained from the 27 experiments. The best-fit models are presented in Table 7, which do not include any interaction terms. For the travel time model, parameters A and C correspond to the number of ships and number of destinations, respectively. A positive coefficient indicates that an increase in that variable results in higher travel time. For the energy consumption model, the results show that the number of ships and the number of destinations are significant predictors of energy consumption, whereas the number of origins does not have a statistically significant effect.

The travel time model has significant explanatory power with a high coefficient of determination (R 2 = 0:9026), indicating that approximately 90.26% of the variance in travel time is explained by the model. This model identifies the number of ships (A) and the number of destinations (C) as significant predictors, with coefficients of 1.146 and 2.03, respectively. The statistical analysis shows that both predictors are highly significant with p-values of 0.0032 for A and 0.0011 for C. The model's form, given by 8:40 + 1:146 3 A + 2:03 3 C, suggests that increases in either the number of ships or destinations result in longer travel times. In addition, the adequate precision ratio of 6.833 provides confidence in the reliability of the model's predictions at the design points.

Similarly, the energy consumption model has a moderate fit with an R 2 of 0.7466. The coefficients for the number of ships (A) and the number of destinations (C) are 0.844 and 3.311, respectively, both of which are statistically significant. The model given by À3:132 + 0:844 3 A + 3:311 3 C implies that energy consumption increases when either the number of ships or destinations increases. The number of origins (B) was excluded from the model because its effect was not statistically significant (p = 0:241). These results indicate that fleet size and route complexity are the primary drivers of energy consumption, while the number of origins does not play a critical role.

This study developed a MINLP model and a novel hybrid GA-PSO meta-heuristic to optimize ship routes with the objective of minimizing total travel time. The proposed model and algorithm were validated using a network of 33 ports. Numerical results from a full factorial experiment, incorporating three factors-number of ships, number of origins, and number of destinationsrevealed that the number of destinations and ships significantly affect travel time and energy consumption. A key finding from this analysis is that NH 3 -fueled ships generally experience longer travel times than JP-8-fueled ships because of NH 3 's lower energy density and more frequent refueling requirements. On average, the increase in total travel time is less than 20%. This study serves as a foundation for decision-makers who must also consider additional factors, such as economic feasibility, infrastructure costs, environmental impact, and regulatory requirements, when assessing ammonia's viability as an alternative fuel for fleet-wide adoption.

While the findings are promising, there are several areas where this study could be extended to enhance robustness and applicability. Ammonia supply constraints: This study assumes an unlimited availability of ammonia at refueling stations. Future research could incorporate constraints on fuel availability, reflecting potential limitations in ammonia production and distribution. Restricted travel areas: This work does not account for restricted areas or regions that ships intentionally avoid, such as conflict zones or environmentally sensitive areas. Including such constraints would make the model more realistic. Weather conditions: Weather conditions, which can significantly influence ship routes and speeds, were not considered. Incorporating weatherrelated factors into the optimization framework could provide a more comprehensive analysis.

While adopting NH 3 as an alternative marine fuel shows promise for reducing CO 2 emissions, its environmental trade-offs must be addressed. NH 3 combustion generates by-products, including nitrous oxide (N 2 O), a GHG with approximately 300 times the global warming potential of CO 2 (45), and nitrogen oxides (NO and NO 2 , collectively known as NO x ), which contribute to air pollution and respiratory health risks. In addition, unburnt ammonia can escape into the atmosphere, where it reacts to form fine particulate matter (PM), further affecting air quality and human health. Mitigating these emissions will require post-combustion treatment technologies, such as catalytic converters, selective catalytic reduction systems, and ammonia slip oxidation systems (46). However, integrating such solutions could affect ship operational efficiency and fuel logistics, topics that lie beyond the scope of this study. Future research should explore these mitigation strategies in detail, evaluating their technical feasibility, cost, and operational implications to ensure NH 3 can be adopted sustainably without compromising air quality or public health.

Although this study did not validate the optimization results against real-world routes and travel times, it employed an online tool to derive realistic travel distances between pairs of ports. These distances closely approximate actual maritime routes, providing a practical foundation for evaluating the hybrid GA-PSO model's effectiveness. Future work should incorporate realworld operational data to further validate and refine the This study demonstrates that ammonia can be a viable alternative marine fuel, capable of maintaining acceptable levels of service while reducing CO 2 emissions. The hybrid GA-PSO approach presented here provides a flexible and effective tool for addressing the challenges associated with adopting alternative fuels in maritime operations. By addressing the environmental trade-offs and integrating real-world considerations, future research can further advance the potential of ammonia as a sustainable solution for the shipping industry.