Energy Demand Estimation in Turkey According to Road and Rail Transportation: Walrus Optimizer and White Shark Optimizer Algorithm-Based Model Development and Application

Abstract

Transport energy demand (TED) forecasting is a crucial issue for countries like Turkey that are dependent on external resources. The accuracy and effectiveness of these forecasts are extremely important, especially for the strategies and plans to be developed. With this in mind, different forms of forecasting models were developed in the present study using the Walrus Optimizer (WO) and White Shark Optimizer (WSO) algorithms to estimate Turkey’s energy consumption related to road and railway transportation modes. Additionally, another objective of this study was to examine the impacts of different transport modes on energy demand. To investigate the effect of demand distribution among transport modes on energy consumption, model parameters such as passenger-kilometers (P-km), freight-kilometers (F-km), carbon dioxide emissions (CO₂), gross domestic product (GDP), and population (POP) were utilized in the development of the models. It was found that the WO algorithm outperformed the WSO algorithm and was the most suitable method for energy demand forecasting. All the developed models demonstrated a better performance level than those reported in previous studies, with the best performance achieved by the semi-quadratic model developed with the WO, showing a 0.95% MAPE value. Projections for energy demand up to the year 2035 were established based on two different scenarios: the current demand distribution among transport modes, and a demand shift from road to rail transportation. It is anticipated that the proposed energy demand models will serve as an important guide for effective planning and strategy development. Moreover, the findings suggest that a balanced distribution among transport modes will have a positive impact on transport energy and will result in lower energy requirements.

1. Introduction

Transportation and energy are among the most influential factors in ensuring sustainable socio-economic development. The global increase in population, industrialization, urbanization, and the rising demands for trade and production brought about by globalization continually expand the demand for transportation and energy. Efficient utilization of limited energy resources is crucial for economic development and achieving sustainable growth. In this context, every country aims to develop strategies and formulate national programs to use their resources more effectively, to meet sustainable energy and transportation demands.

Turkey’s economy is ranked ninth in Europe and twenty-first globally in the 2019 World Economic Outlook (WEO) data [1]. In its most recent study, which was released in July, the International Monetary Fund (IMF) predicted that Turkey’s growth would be 5.5% in 2022, 4.5% in 2023, and 3.6% in 2024 [2]. The demand for transportation energy is inversely correlated with economic growth, and there is a linear link between both. In Turkey, energy consumption in the transportation sector constitutes a significant portion of the total. Transportation energy consumption makes up around 27% of Turkey’s overall energy consumption, according to the most recent data from the International Energy Agency (IEA) in 2021, which marks an increase from 22.8% in 1990 [3]. This transportation energy consumption in Turkey is similar to the levels for Europe overall, China, and other countries in the world. For instance, transportation energy consumption has an average share of 28% in European countries, 29% in China, 25% in Canada, 26% in Iran, and 29% worldwide. Today, transportation energy consumption in many countries is increasing day by day; in countries such as Canada and Iran, demand increases of nearly 50% are seen annually [4,5,6,7].

A substantial portion of transport energy consumed, which corresponds to about one-quarter of Turkey’s total energy consumption, originates from petroleum products. Moreover, roughly 95% of the energy in the transportation sector is consumed for road transportation, according to the energy balance sheets of the Ministry of Energy and Natural Resources (MENR). The remaining portion is distributed among other transportation systems [8]. The significant energy consumption in the road transportation system is largely due to the country’s road-dominated transportation infrastructure.

Energy resources are few, and over 75% of Turkey’s energy demands are fulfilled by imports, despite the country’s growing energy demand. Since the primary energy source used in the transportation sector is petroleum-based, energy dependency in this sector is becoming pronounced. Therefore, the Turkish National Committee of the World Energy Council emphasized in the final report of the 10th Energy Congress of Turkey that “climate change policies worldwide should be closely monitored, alternative scenarios should be prepared with policies and targets aligned with national interests, and supply and demand forecasts in sectors should be developed using advanced models”. In line with this proposal, it is crucial that the models developed better reflect the realities of the country and that the methods used are reliable.

Given the importance of energy demand forecasting and the need to utilize these forecasting models in developing strategies and plans, various models have been developed using different methods. Given the widespread use of artificial intelligence techniques in all fields and the highly successful outcomes achieved, these methods are increasingly being employed in developing energy demand forecasting models and scenario analyses, both in Turkey and globally.

This study aimed to make more accurate predictions of transportation energy consumption in Turkey up to 2035 using passenger and freight numbers, carbon dioxide (CO₂) emissions, gross domestic product (GDP), and population parameters in the road and rail transportation modes. To achieve this, state-of-the-art algorithms such as the Walrus Optimizer and White Shark Optimizer were used, and we developed and compared transportation energy demand models in different mathematical forms. The study design was distinguished from others through the use of parameters of transportation modes and the most up-to-date algorithms, which allowed for predicting the energy demand with higher precision than in previous studies. Additionally, we considered the impact of transitions of passenger and freight transportation between transportation modes in energy prediction, with the goal of making energy forecasts more precise and realistic and also to determine the impact levels of different transportation modes.

In the subsequent sections of this article, a detailed literature review is given, the algorithms used are introduced in detail, and then we present the energy forecast model forms created with these algorithms, along with the error values of the models. Then, we outline how the model with the lowest forecast error (in the current study) was used in the developed future transportation scenarios, and energy demand forecasts for these scenarios are presented. Finally, suggestions are offered for how we can improve the country’s capacity to meet the upcoming energy demand in future forecasts.

Literature Review

Today, artificial intelligence techniques are widely used in prediction methods and solutions to optimization problems across many fields, particularly in engineering. In recent years, many researchers have produced accurate and reliable results by using artificial intelligence techniques in the development of prediction models. Murat and Ceylan [9] used an artificial neural network (ANN) model to forecast Turkey’s transportation energy demand up to 2020, utilizing parameters such as gross national product (GNP), population, and total annual average vehicle-km. Their ANN-based model predicted that transportation energy consumption would reach 36 MTOE in 2020. Canyurt et al. [10] proposed a transportation energy demand model (GATENDM) for Turkey using the genetic algorithm (GA) method, based on socio-economic and transportation data. They stated that the proposed model had an error margin of 11% and worked with 5% lower error compared to the estimates of the Ministry of Energy and Natural Resources (MENR). Haldenbilen and Ceylan [11] used linear, exponential, and quadratic models for transportation energy prediction (GATEDE) based on the GA approach. They found that linear and quadratic models performed better, with an error margin of approximately 10%. Başkan et al. [12] developed transportation energy demand prediction models (IACOTEDE) for Turkey using the improved ant colony optimization (ACO) approach in linear, exponential, and quadratic forms. The quadratic model demonstrated a prediction performance with an 8% error margin, forecasting 30 MTOE of transportation energy consumption by 2025. Karaaslan and Gezen [13] used the Fuzzy Grey Regression Model to estimate the sectoral energy consumption in Turkey. They estimated transportation energy with an 8.5% error margin using their established model, and they projected a 2023 energy consumption of about 25 MTOE. Sönmez et al. [14] used the artificial bee colony method to forecast Turkey’s transportation energy demand in three different model forms up to 2034, based on gross domestic product (GDP), population, and total annual vehicle-km as the parameters. Using a linear model with an 11% error margin, they projected that Turkey’s transportation energy demand will be 36 MTOE in 2034. Korkmaz and Akgungor [15] used the Flower Pollination Algorithm (FPA) to create transportation energy forecasting models. By 2035, 42 MTOE of energy consumption is expected in Turkey according to the produced models, which had an error margin of about 6%. Çodur and Unal [16] conducted a transportation energy forecasting study in Turkey using an ANN approach. The study utilized parameters such as gross domestic product, oil prices, population, vehicle-km, ton-km, and passenger-km, and they developed seven different models, achieving success with MAPE values ranging from 4% to 6%. Sahraei et al. [17] used a multivariate adaptive regression model to forecast Turkey’s transportation energy in five model forms using socio-economic and transportation data from 1975 to 2019. After comparing the model results with the Ministry of Energy and Natural Resources’ data, they indicated that the third model, which provided the most accurate prediction, could be used for transportation energy forecasting, with the prediction that consumption will reach 29 MTOE by 2030. Turgut et al. have implemented transportation energy forecasting models using a hybrid approach (OPTSGULL) that combines the Seagull (Sgull) and Very Optimistic Method of Minimization (VOMMI) algorithms, utilizing parameters such as GDP, crude oil price (COP), and inflation for Turkey in percentages (INF). They have demonstrated that this method performs statistically better compared to many different artificial intelligence approaches and achieves the best objective function value. Additionally, a future forecast has been made up to the year 2028, predicting an energy consumption of approximately 44 MTOE. Ağbulut [18] used deep learning (DL), support vector machine (SVM), and artificial neural network (ANN) approaches to estimate energy demand and CO₂ emissions related to transportation in Turkey. The proposed models estimated energy demand with error rates of 8.38%, 8.39%, and 12.79% for ANN, SVM, and DL, respectively. The ANN approach showed the best performance with an R² of 0.92. Additionally, the annual growth rates for energy demand and CO₂ emissions related to transportation in Turkey were projected to increase by 3.7% and 3.65%, respectively. ANN-GA, ANN-Simulated Annealing (ANN-SA), and ANN-PSO are some of the novel hybrid metaheuristic ANN techniques that Sahraei and Çodur [19] presented for transportation energy forecasting models. With an R² of 0.99, they observed that the ANN-PSO method, which is based on GDP, population, and ton-km, performed better than the other two models. Özdemir ve Dörterler [20] have estimated transportation energy demand based on the gross domestic product (GDP), population, and total vehicle kilometers (TVKs) using an adaptive artificial bee colony (A-ABC) algorithm. In their study, three different model forms—linear, exponential, and quadratic—were developed, and forecasts were made up to the year 2034. According to these models, energy demand estimates (TEDs) are projected to be 40.0, 31.5, and 66.5 MTOE, respectively. Hoxha et al. [21] predicted transportation energy in Turkey using the machine learning stacking ensemble method with hyperparameter tuning and multicollinearity removal. They were able to make predictions with an error margin of 3.03% based on GDP, population, ton-km, vehicle-km, passenger-km, and oil price data. Kayacı and Çodur [22] used ensemble machine learning approaches to predict the energy demand in Turkey. The study, which used population, per capita GDP, import, and export data, examined the performance of 19 different machine learning (ML) approaches and demonstrated that the Extra Trees Regression approach yielded the highest R² value of 0.9882, indicating accurate and effective energy predictions.

Economic developments and the increase in national and international freight transportation activities have intensified the passenger and freight transport sector. In this context, ensuring sustainable transportation energy is of great importance. Energy planning studies play a critical role in enabling governments to meet future energy needs, develop appropriate strategic plans, and utilize resources in the correct amounts. Therefore, energy forecasting studies attract the attention of many researchers, not only in our country but also on a global scale.

Al-Ghandoor et al. [23] used the Adaptive Neuro-Fuzzy Inference System (ANFIS) method to forecast Jordan’s transportation energy consumption. With a 97% accuracy rate, their constructed model projected that Jordan’s energy consumption will reach 4.3 MTOE by 2030. Forouzanfar et al. [24] used a multi-level genetic programming approach to forecast Iran’s transportation energy demand based on energy data from 1968 to 2005, along with data on the per capita gross national product, population, and vehicle numbers. The results obtained showed that the multi-level genetic programming approach was more successful compared to results from artificial neural networks and multi-level fuzzy linear regression approaches. Limanond et al. [25] attempted to forecast Thailand’s transportation energy demand using log-linear regression and ANN models based on national gross domestic product, population, and registered vehicles as their parameters. They were able to predict energy consumption with 95% accuracy using the log-linear regression model and estimated that Thailand’s transportation energy consumption will range between 54.4 and 59.1 MTOE in 2030. Liu et al. [26] used the Long-range Energy Alternatives Planning system (LEAP) to predict China’s transportation energy use. Based on Comprehensive Policy (CP), Energy Efficiency Improvement (EEI), Transport Mode Optimization (TMO), and Business as Usual (BAU) scenarios, the anticipated energy consumption in 2050 is 509, 755, 816, or 1284 MTOE, respectively. A regression model based on GDP and P data was used by Bayomi et al. [27] to forecast transportation energy consumption for Middle Eastern nations, such as Iran, Saudi Arabia, Kuwait, and the United Arab Emirates. The model had an error of about 2%. According to their estimates, Iran will consume 75 MTOE of energy for transportation, Saudi Arabia 80 MTOE, Kuwait 16 MTOE, and the United Arab Emirates 30 MTOE by 2030. Nieves et al. [28] used the LEAP model, which is based on a model from 2015 and two future scenarios (positive and negative), to study energy demand and greenhouse gas emissions in Colombia. According to their predictions, Colombia’s overall energy consumption by 2030 will be 1,748,469 TJ in a negative scenario and 1,597,675 TJ in a positive scenario. By 2050, the total energy demand will be 2,125,453 TJ in the positive scenario and 2,498,765 TJ in the negative scenario. In both scenarios, the transportation sector emerged as the largest energy-consuming sector. They predicted that CO₂ emissions will be 108.3 Mton in the positive scenario and 118.5 Mton in the negative scenario by 2030. By 2050, CO₂ emissions reach 140.1 Mton in the positive scenario and 150.5 Mton in the negative scenario. Luis et al. [29] used the LEAP model to forecast energy demand in Ecuador’s road transport sector up to 2035. According to the BAU (Business As Usual), EOM (Energy Optimization and Mitigation), AF (Alternative Fuels), and SM (Sustainable Mobility) scenarios, energy demand will range between 85 and 112 kBOE. Taiwan’s transportation energy demand was estimated by Yao et al. [30] using an antelope swarm optimizer (WHO) and convolutional neural network (CNN). They demonstrated, by comparing the model results with those of a basic CNN and a multiple regression model, that Taiwan’s transportation energy consumption will not increase substantially. This prediction for 2020 was about 37.2 MTOE. Vergel et al. [31] proposed a bottom-up approach to forecast the transportation energy demand of the Philippines in 2016. In this approach, detailed sub-level data such as vehicle types, fuel consumption, road networks, and user behaviors are collected and analyzed. They emphasized that this model provides policymakers, planners, and energy managers the opportunity to develop more effective and targeted strategies by considering various factors affecting energy demand. Rahman et al. [32] have made a transportation energy forecast in Saudi Arabia using ANN and support vector regression (SVR). In the study, which utilized parameters such as GDP, number of vehicles, population, and fuel prices, the SVR approach demonstrated a better performance than the ANN approach, achieving predictions very close to reality, with an R² value of 0.99. Additionally, in their future projections, they estimate that energy consumption will reach approximately 70 MTOE by the year 2030. Maaouane et al. [6] used an ANN approach to forecast the transportation energy demand based on 30 years of data obtained from 28 European countries. Morocco was utilized as a case study, and a prediction for transportation energy consumption in Morocco was made up to the year 2050. They projected that by 2050, consumption will exceed 10.5 MTOE, representing a 75% increase compared to 2018, and as a result of the widespread use of electric vehicles, the demand for fuel will be around 7.2 MTOE. Liu et al. [33] proposed a new approach to predicting transportation energy demand using an artificial neural network with an improved red fox optimizer. The research findings demonstrated that the proposed method could accurately predict transportation energy demand, helping decision-makers make informed decisions and develop policies regarding energy management and sustainability. Javanmard and Ghaderi [5] have predicted energy demand in Iran for the transportation sector and other sectors using six different machine learning approaches optimized with PSO and the Grey-Wolf Optimizer (GWO). With models that achieved a 6% MAPE in the transportation sector, future forecasts have been made up to the year 2040, indicating a 75% increase compared to 2019, with an expected energy demand of 900 MKWh. Javanmard et al. [4] have predicted energy demand and CO₂ emissions in the transportation sector by optimizing eight ML approaches using the whale optimization algorithm, and they have made projections until the year 2048. They anticipate that energy demand will increase by approximately 37% and CO₂ emissions by 50% compared to the year 2019. Gharaibeh and Alkhatatbeh [34] estimated transportation energy consumption in Jordan based on the number of registered vehicles, income level, ownership level, and fuel prices using an ANN approach. With the proposed method, they achieved a prediction with a MAPE error of 2.19% and made projections up to the year 2030. It is anticipated that transportation energy consumption in Jordan will be approximately 4.1 MTOE by 2030. Qiao et al. [35] have predicted energy consumption and CO₂ emissions in transportation in the UK using an interpretable multi-stage forecasting framework approach. This framework produced energy consumption forecasting with a MAPE of 0.915 and CO₂ forecasting with a MAPE of 0.907, and they showed that the approach improved data quality by eliminating irrelevant and unnecessary features.

In the literature, it can be observed that energy demand is predicted using general models, but the parameters of transportation modes are not considered, meaning that the effects of the modes are not examined. In Turkey, road transport is the preferred mode of transportation, with a share exceeding 90%. However, in recent years, significant attention has been paid to railway investments in Turkey, with applications such as the expansion of the railway network and the popularization of high-speed train lines increasing the accessibility of and preference for the railway mode. Therefore, the impact of the shift in demand from road to rail transportation on energy consumption should be taken into account. Considering the effect of demand distribution in the model will enable more realistic predictions compared to previous studies.

2. Materials and Methods

2.1. Walrus Optimizer Algorithm

The Walrus Optimizer (WO) algorithm, a metaheuristic algorithm inspired by the social life and natural behaviors of walruses, was introduced by Han et al. in 2024 [36]. Walruses are herd-living animals that spend most of their time on sea ice and lead an amphibious life. The most distinctive features of walruses are their long tusks and whiskers. The tusks play vital roles in the lives of walruses, being used for defense, hunting for food such as clams, shrimp, and crabs, digging in mud and sand, or supporting the body while climbing on ice. Male walruses have slightly thicker and longer tusks, which are significant for dominance, fighting, or display. The social life and strong sense of community of walruses contribute to their long survival and intelligent actions with four purposes: feeding, reproduction, defense, and migration.

In regard to feeding, information about food is shared through communication among peers under the guidance of the member with the longest tusks, who is considered the strongest; individuals are directed to feed based on this information. When it comes to reproduction, risk factors are considered, and a tendency to reproduce is shown when the risk is low; furthermore, nesting and underwater feeding behaviors are crucial in reproduction. For the purpose of defense, walruses adopt a collective defensive strategy to protect themselves against predators and help injured companions, where two walruses act as guards; moreover, when members of the species are injured, they go to help. Alternatively, when risk factors are very high, they migrate to more suitable areas to survive. The WO algorithm was developed by modeling these intelligent life behaviors of walruses.

Two important assumptions were made in developing this algorithm. The first is that the population behavior of walruses is determined based on danger and safety signals. The second is that male, female, and young walruses in the population have different behavioral and role divisions, which are modeled in the algorithm. In the WO, behaviors are determined based on reactions to perceived danger and safety cues, and the search process is conducted by effectively balancing exploration and exploitation. There are four fundamental concepts in the WO: Initialization, Danger signals and safety signals, Migration (exploration), and Reproduction (exploitation).

Initialization: The optimization process starts with randomly generated candidate solutions based on the predefined lower and upper bounds of the problem variables. The initial candidate solutions are created depending on the population size and the number of variables, and they must have a sufficient search space for potential optima. The mathematical representation of the randomly generated initial candidate solutions is shown by Equations (1) and (2).

$$X=LB+rand(UB-LB)$$

(1)

where LB and UB are the lower and upper boundary of the problem variables, and rand is a uniform random vector in the range from 0 to 1.

$$X={\left[\begin{array}{c}{X}_{\mathrm{1,1}}\dots X_{1,d}\\ X_{\mathrm{2,1}}\dots X_{2,d}\\ \dots \\ X_{n,1}\dots X_{n,d}\end{array}\right]}_{n\times d}$$

(2)

where n is the population size, and d is the dimension of design variables.

Danger signals and safety signals: In the WO algorithm, the behavior of the population is determined by “safety” and “danger” signals. The safety signal reflects the attractiveness of the current position of the walrus. The danger signal, on the other hand, reflects the risk associated with the current position. Throughout the optimization process, the danger signal weakens, while the safety signal increases. This balances exploration and exploitation, allowing the walrus to efficiently navigate the search space and encouraging convergence towards the optimal solution. The danger and safety signals are defined by Equations (3) and (7).

$$Danger Signal=A \ast R$$

(3)

$$A=2 \ast \alpha$$

(4)

$$\mathsf{\alpha }=1-t/T$$

(5)

$$R=2 \ast r_1-1$$

(6)

where A and R are danger factors, α decreases from 1 to 0 with the number of iterations t, and T is the maximum iteration.

$$Safety Signal=r_2$$

(7)

where r₁ and r₂ are random numbers in the range of (0, 1).

Migration (exploration): In the natural behavior of walruses, they migrate to more suitable areas when risk factors are very high or when the weather warms up. In the algorithm, this behavior represents the exploration aspect that allows the walruses to enter new regions of the search space. Thus, the walrus updates its position based on the migration step and a random number, according to the mathematical model defined by Equations (8)–(10).

$$X_{ij}^{t+1}=X_{ij}^t+Migration step$$

(8)

$$Migration step=\left(X_m^t-X_n^t\right)\times \beta \times r_3^2$$

(9)

$$\beta =1-{\displaystyle \frac{1}{1+e^{\frac{-10(t-0.5T)}{T}}}}$$

(10)

where $X_{ij}^{t+1}$ is the updated location of the walrus, $X_{ij}^t$ is the current position of the walrus, Migration step is the step size of walrus movement, β is the migration step control factor, $X_m^t$ and $X_n^t$ denote two positions chosen at random, and r₃ is a random number in the range of (0, 1).

Reproduction (exploitation): When risk factors are low, walrus herds exhibit reproductive behavior. During the reproduction phase, there are two actions: nesting on the shore and feeding underwater. In the nesting behavior, male, female, and young walruses update their positions in different ways. Male walruses act as explorers and discover new regions of the search space. During this phase, male walruses update their positions according to the Halton sequence distribution, allowing the population to be more widely distributed in the search space. Female walruses, on the other hand, are influenced by both the male walruses and the leading walrus, representing exploitation that helps improve optimal solutions. Young walruses are typically prey targets. Therefore, young walruses need to update their positions to avoid being hunted. Female and young walruses update their positions according to the mathematical model defined by Equations (11)–(15).

$${Female}_{ij}^{t+1}={Female}_{ij}^t+\alpha \times \left({Male}_{ij}^t-{Female}_{ij}^t\right)+\left(1-\alpha \right)\times (X_{best}^t-{Female}_{ij}^t)$$

(11)

$${Juvenile}_{ij}^{t+1}=\left(O-{Juvenile}_{ij}^t\right)\times P$$

(12)

$$O=X_{best}^t-{Juvenile}_{ij}^t\times LF$$

(13)

where O denotes the location for safety, P corresponds to the risk factor associated with juvenile walruses and is a random number in the range of (0, 1), and LF is a vector of random numbers based on the Lévy distribution.

$$LF=0.05\times {\displaystyle \frac{x}{{\left|y\right|}^{\frac{1}{a}}}}$$

(14)

$${\sigma }_x={\left[{\displaystyle \frac{\mathsf{\Gamma }\left(1+a\right)\times \mathrm{s}\mathrm{i}\mathrm{n}\left(\frac{\pi a}{2}\right)}{\mathsf{\Gamma }\left(\frac{1 + a}{2}\right)\times a\times 2^{(\frac{a - 1}{2})}}}\right]}^{{\displaystyle \frac{1}{a}}},{\sigma }_y=1, a=1.5$$

(15)

where x and y are two normally distributed variables, and ${\sigma }_x$ and ${\sigma }_y$ are the standard deviations.

During underwater feeding, there are two behaviors: escaping and gathering. The escaping behavior occurs when walruses are attacked during feeding or receive danger signals from other walruses, prompting them to change their current activity area. This behavior aids the walruses in making global explorations. On the other hand, the gathering behavior helps walruses to congregate in a marine area with more abundant food as a result of collaboration with other walruses. The escaping and gathering behaviors are executed according to the mathematical model defined by Equations (16)–(20).

$$X_{ij}^{t+1}=X_{ij}^t\times R-\left|X_{best}^t-X_{ij}^t\right|\times r_4^2$$

(16)

$$X_{ij}^{t+1}=(X_1-X_2)/2$$

(17)

$$\left\{\begin{array}{c}{X}_1=X_{best}^t-a_1\times b_1\times \left|X_{best}^t-X_{ij}^t\right|\\ X_2=X_{second}^t-a_2\times b_2\times \left|X_{second}^t-X_{ij}^t\right|\end{array}\right.$$

(18)

$$a=\beta \times r_5-\beta$$

(19)

$$b=\mathrm{t}\mathrm{a}\mathrm{n}\left(\theta \right)$$

(20)

where X₁ and X₂ are two weights affecting the gathering behavior of walruses, $X_{second}^t$ is the position of the second walrus in the current iteration, a and b are the gathering coefficients, r₄ and r₅ are random numbers in the range of (0, 1), and θ takes values ranging from 0 to π.

The WO’s flowchart is shown in Figure 1. Han et al. [36] provide a more thorough description of the WO.

2.2. White Shark Optimizer Algorithm

The White Shark Optimizer (WSO) algorithm was introduced by Braik et al. in 2022 and is a metaheuristic algorithm inspired by the food-seeking behaviors of white sharks [37]. White sharks, residing in the oceans, are among the most powerful and dangerous predatory sharks in the world. They are significant predators in the ocean due to their strong muscles, acute vision, and keen sense of smell. With their massive jaws and sharp, serrated, triangular teeth, they can easily hunt various marine creatures, including other sharks, crustaceans, dolphins, and walruses. The great white shark can locate a food source in the depths of the ocean, although the exact location of the food source within a given search area is unknown. Consequently, they conduct prolonged searches to find food resources in the ocean’s depths. The algorithm is inspired by three key behaviors exhibited by great white sharks when locating prey: movement towards prey, movement towards optimal prey, and movement towards the best white shark. The WSO algorithm fundamentally comprises five concepts: Initialization, Update the parameters of the WSO algorithm, Movement towards prey, Movement towards optimal prey, and Movement towards the best white shark.

Initialization: In population-based algorithms, the optimization process begins with a pool of randomly generated initial solutions within defined boundary values. In the initial matrix created according to the problem size and population size, each position of a white shark represents a candidate solution to the problem. The initial matrix is generated according to the mathematical expressions given in Equations (21) and (22).

$$\omega =\left[\begin{array}{c}{\omega }_1^1\dots {\omega }_d^1\\ {\omega }_1^2\dots {\omega }_d^2\\ \dots \\ {\omega }_d^n\dots {\omega }_d^n\end{array}\right]$$

(21)

$${\omega }_j^i=lj+rand(uj-lj)$$

(22)

where lj and uj are the lower and upper boundaries of the problem variables, rand is a uniform random vector in the range 0 to 1, n is the population size, and d is the dimension of the problem.

Update the parameters of the WSO algorithm: The WSO algorithm utilizes several parameters, each of which needs to be updated during every iteration. The parameters used in the WSO algorithm are updated according to Equations (23a)–(23j).

$$v=\left[n\times rand(1,n)\right]+1$$

(23a)

$$p_1=p_{max}+\left(p_{max}-p_{min}\right)\times e^{{-(4\times {\displaystyle \frac{k}{K}})}^2}$$

(23b)

$$p_2=p_{min}+\left(p_{max}-p_{min}\right)\times e^{{-(4\times {\displaystyle \frac{k}{K}})}^2}$$

(23c)

$$\mu ={\displaystyle \frac{2}{\left|2-\tau -\sqrt{{\tau }^2-4\tau }\right|}}$$

(23d)

$$a=sgn\left(w_k^j-u\right)>0$$

(23e)

$$b=sgn\left(w_k^j-u\right)<0$$

(23f)

$${\omega }_0=\oplus (a,b)$$

(23g)

$$f=f_{min}+{\displaystyle \frac{{f_{max}-f}_{min}}{{f_{max}+f}_{min}}}$$

(23h)

$$mv={\displaystyle \frac{1}{a_0+e^{(\frac{k}{2}-K)/a_1}}}$$

(23i)

$$S_s=1-e^{(-a_2\times {\displaystyle \frac{k}{K}})}$$

(23j)

Movement towards prey: Great white sharks spend most of their time hunting and chasing prey. Their abilities in hearing, sight, and smell facilitate their search for prey and enable the use of various tactics. When the waves generated by the movement of prey are detected and the location of the prey is perceived, the shark moves towards it using a wave motion as defined by Equation (24).

$$v_{k+1}^i=\mu \left[v_k^i+p_1\left({\omega }_{{gbest}_k}-{\omega }_k^i\right)\times c_1+p_2\left({\omega }_{best}^{v_k^i}-{\omega }_k^i\right)\times c_2\right]$$

(24)

where $v_{k+1}^i$ denotes the new velocity vector of the white shark, $v_k^i$ defines the current speed vector of the white shark, ${\omega }_{{gbest}_k}$ represents the global best position vector obtained so far by any white shark, ${\omega }_k^i$ is the current position vector of the white shark, ${\omega }_{best}^{v_k^i}$ is best known position vector, and c₁ and c₂ are two uniformly created random numbers in the range of (0, 1).

Movement towards optimal prey: Great white sharks move towards their prey when they detect waves generated by the prey’s movement or sense its scent. Since the prey is constantly moving, it leaves behind a trail of scent at its previous locations. In such cases, the great white shark roams randomly in search of the prey, similar to the behavior of a school of fish searching for food. The mathematical expression given in Equation (25) describes the behavior of great white sharks as they move towards their prey.

$${\omega }_{k+1}^i=\left\{\begin{array}{c}{\omega }_k^i·\neg \oplus {\omega }_0+u.a+l.b;rand<mv\\ {\omega }_k^i+v_k^i/f;rand\ge mv\end{array}\right.$$

(25)

where ${\omega }_{k+1}^i$ refers to the new position vector of the white shark, $\neg$ is a negation operator, $\oplus$ is a bit-wise xor operation, l and u denote the lower and upper limits, and a, b, ${\omega }_0$, f, and $mv$ are defined in Equation (23a)–(23j).

Movement towards the best white shark: Great white sharks move towards the shark that is closer to the prey and maintain their positions. This behavior is described by Equation (26).

$${\acute{\omega }}_{k+1}^i={\omega }_{{gbest}_k}+r_1\left|rand\times \left({\omega }_{{gbest}_k}-{\omega }_k^i\right)\right|sgn\left(r_2-0.5\right) r_3<S_s$$

(26)

where ${\acute{\omega }}_{k+1}^i$ is the updated position of the white shark with respect to the position of the prey, $sgn\left(r_2-0.5\right)$ gives either 1 or −1 to change the direction of the search, and the variables r₁, r₂, and r₃ are random numbers that lie in the range of (0, 1).

In Figure 2, the WSO flowchart is shown. See Braik et al. [37] for a more thorough description of the WSO.

2.3. Energy Demand Estimation Models for Transportation

In Turkey, 90% of transportation demand is met by road transport. However, recent increases in investments in rail transportation have enhanced its flexibility and desirability. To assess the impact of demand shifts between transportation modes, this study developed transportation energy demand models for both road and rail transport. The model development parameters were chosen based on their direct relationship to energy consumption and transportation demand, as well as their availability. This study used the following five parameters: population statistics, carbon dioxide emissions, passenger and freight kilometers, and GNP. As indicated in

Table 1. Observed historical data (EC: energy consumption of the transportation sector in million-tons of oil equivalent or MTOE); P-km: passenger-km (10⁹); F-km: freight-km (10⁹); CO₂: carbon dioxide emission from transport kT; GDP: gross domestic product (10⁹), US$; POP: population (10⁶), persons.

			Road Transportation				Rail Transportation
Years	GDP	POP	EC	P-km	F-km	CO2	EC	P-km	F-km	CO2
1990	150.656	54.32	8.02	134.99	65.71	24.78	0.161	6.410	8.031	721
1991	151.035	55.32	7.54	131.03	61.97	23.29	0.168	6.048	8.093	740
1992	159.105	56.30	7.73	142.17	67.70	23.87	0.192	6.259	8.383	685
1993	180.416	57.30	9.45	146.03	97.84	29.18	0.200	7.147	8.517	751
1994	130.650	58.31	8.47	140.74	95.02	27.42	0.190	6.335	8.339	768
1995	169.320	59.31	9.19	155.20	112.52	29.76	0.211	5.797	8.632	768
1996	181.464	60.29	9.77	167.87	135.78	31.63	0.213	5.229	9.018	799
1997	189.878	61.28	9.24	180.97	139.79	29.86	0.216	5.840	9.717	799
1998	275.942	62.24	8.64	186.16	152.21	27.88	0.221	6.161	8.446	740
1999	256.396	63.19	9.37	175.24	150.97	30.22	0.223	6.146	8.446	722
2000	274.295	64.11	10.51	185.68	161.55	31.85	0.205	5.833	9.895	713
2001	201.753	65.07	9.80	168.21	151.42	31.51	0.200	5.568	7.562	587
2002	240.249	65.99	9.97	163.33	150.91	32.08	0.207	5.204	7.224	612
2003	314.596	66.87	10.95	164.31	152.16	33.35	0.165	5.878	8.669	629
2004	408.865	67.79	11.51	174.31	156.85	35.09	0.172	5.237	9.417	629
2005	506.315	68.70	11.78	182.15	166.83	35.53	0.183	5.036	9.152	757
2006	557.076	69.60	12.60	187.59	177.40	38.37	0.183	5.277	9.676	761
2007	681.321	70.16	13.59	209.12	181.33	43.67	0.220	5.553	9.921	470
2008	770.449	71.05	12.62	206.10	181.94	40.56	0.221	5.097	10.739	499
2009	649.289	72.04	12.52	212.46	176.46	40.20	0.132	5.374	10.326	484
2010	776.967	73.14	13.54	226.91	190.37	39.94	0.140	5.491	11.462	517
2011	838.785	74.22	15.45	242.27	203.07	40.90	0.136	7.300	11.677	532
2012	880.556	75.18	16.30	258.87	216.12	56.31	0.145	6.612	11.670	492
2013	957.799	76.15	17.68	268.18	224.05	62.89	0.150	6.225	11.177	505
2014	938.935	77.18	18.50	276.07	234.49	66.97	0.138	7.401	11.992	562
2015	864.314	78.22	21.53	290.73	244.33	69.31	0.142	8.326	10.474	480
2016	869.683	79.28	23.48	300.85	253.14	75.60	0.157	7.829	11.661	374
2017	858.988	80.31	24.73	314.73	262.74	77.09	0.135	8.465	12.763	369
2018	778.972	81.41	24.80	329.36	266.50	78.91	0.105	8.938	14.481	435
2019	761.006	82.58	24.11	339.60	267.58	76.72	0.118	14.259	14.707	400
2020	720.338	83.38	24.07	288.99	272.91	76.60	0.124	8.297	15.428	323
2021	819.865	84.15	27.17	336.19	311.82	86.50	0.114	10.665	14.433	356

, data for these factors were gathered over a 31-year span from 1990 to 2021. The World Bank [39] provided GNP and population data, the Ministry of Environment and Urbanization [40] provided carbon dioxide emission data, and the Turkish Statistical Institute (TSI) [41] provided annual passenger and freight data. Data on energy use were obtained from the balance tables of the MENR [8].

To forecast energy demand for road and rail transportation modes in Turkey, four different mathematical models were developed: linear, exponential, power, and semi-quadratic. The model forms are provided in Equations (27)–(30).

• Linear form:

$$\begin{array}{ll}T{EC}_{Est}=& w_1\times {GDP+w_2\times POP+w_3\times P-km}_{road}+w_4\times {F-km}_{road}+\\ & w_5\times {P-km}_{rail}+w_6\times {F-km}_{rail}+w_7\times {{Co}_2}_{road}+w_8\times {{Co}_2}_{rail}+w_9\end{array}$$

(27)

• Exponential form:

$$\begin{array}{ll}T{EC}_{Est}=& w_1\times {GDP}^{w_2}+w_3\times {POP}^{w_4}+w_5\times {{P-km}_{road}}^{w_6}+w_7{ \times {F-km}_{road}}^{w_8}+\\ & w_9\times {{P-km}_{rail}}^{w_{10}}+w_{11}\times {{F-km}_{rail}}^{w_{12}}+w_{13}\times {{{Co}_2}_{road}}^{w_{14}}+\\ & w_{15}\times {{{Co}_2}_{rail}}^{w_{16}}+w_{17}\end{array}$$

(28)

• Power form:

$$\begin{array}{ll}T{EC}_{Est}=& w_1\times {GDP}^{w_2}\times {POP}^{w_3}\times {{P-km}_{road}}^{w_4}\times {{F-km}_{road}}^{w_5}\times {{P-km}_{rail}}^{w_6}\times \\ & {{F-km}_{rail}}^{w_7}{\times {{{Co}_2}_{road}}^{w_8}\times {{{Co}_2}_{rail}}^{w_9}+w}_{10}\end{array}$$

(29)

• Semi-quadratic form:

$$\begin{array}{ll}T{EC}_{Est}=& w_1\times {GDP+w_2\times POP+w_3\times P-km}_{road}+w_4\times {F-km}_{road}+\\ & w_5\times {P-km}_{rail}+w_6\times {F-km}_{rail}+w_7\times {{Co}_2}_{road}+w_8\times {{Co}_2}_{rail}+\\ & w_9\times \sqrt{{P-km}_{road}\times {F-km}_{road}}+w_{10}\times \sqrt{{P-km}_{road}\times {{Co}_2}_{road}}+\\ & w_{11}\times \sqrt{{F-km}_{road}\times {{Co}_2}_{road}}+w_{12}\times \sqrt{{P-km}_{rail}\times {F-km}_{rail}}+\\ & w_{13}\times \sqrt{{P-km}_{rail}\times {{Co}_2}_{rail}}+w_{14}\times \sqrt{{F-km}_{rail}\times {{Co}_2}_{rail}}+w_{15}\end{array}$$

(30)

In heuristic-based optimization methods, various performance metrics such as Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) are commonly utilized. The objective function plays a crucial role in determining the optimal solution point, and the choice of an appropriate metric is essential for performance. Naser and Alavi [42] have highlighted MAPE, RMSE, and R² as the preferred metrics in optimization problems. Accordingly, the goal of this study was to minimize the difference in the Mean Absolute Percentage Error between the actual and estimated transportation energy consumption. Equation (31) gives the goal function’s mathematical expression.

$$Minf\left(x\right)={\displaystyle \frac{1}{n}}\sum _{i=1}^m\left|{\displaystyle \frac{{TEC}_{{Observed}_i}-{TEC}_{{Est}_i}}{{TEC}_{{Observed}_i}}}\right|\times 100$$

(31)

Figure 3 shows the flow chart for the suggested models based on the WO and WSO algorithms.

The WO and WSO algorithms were used to determine the coefficients of the proposed models. These algorithms’ control parameters directly affect how effective they are. The control parameters used in this study’s algorithms were chosen based on the best values suggested by Han et al. [36] and Braik et al. [37]. The number of iterations used in the model development was set to 2000 for the best results. The control parameters used in the algorithms are listed in

Table 2. Control parameters of algorithms.

Walrus Optimizer Algorithm
Population size (Npop)	100
Maximum number of iterations (Imax)	2000
White Shark Optimizer Algorithm
Population size (Npop)	30
Maximum frequency of the wave motion (Fmax)	0.75
Minimum frequency of the wave motion (Fmin)	0.07
Acceleration coefficient (tau)	4.125
Initial and subordinate velocities (Pmin–Pmax)	0.5–1.5
Maximum Number of Iterations (Imax)	2000

.

3. Results and Discussion

The model coefficients obtained using the WO and WSO algorithms are presented in

Table 3. The results of the WO and WSO for the proposed TED estimation models.

	WO		WSO
Coeff.	Linear	Power	Linear	Power
w1	3.7 × 10−7	2.5 × 10−3	1.9 × 10−6	6.0 × 10−2
w2	1.6 × 10−1	1.0 × 10−1	1.9 × 10−2	1.8 × 10−2
w3	−1.0 × 10−5	−1.1 × 10−1	−2.0 × 10−5	3.0 × 10−1
w4	−9.7 × 10−6	−2.6 × 10−1	4.3 × 10−6	−2.2 × 10−1
w5	3.0 × 10−4	8.4 × 10−2	1.0 × 10−4	4.7 × 10−2
w6	1.0 × 10−4	1.2 × 10−1	2.0 × 10−4	2.0 × 10−1
w7	3.0 × 10−4	−3.0	3.0 × 10−4	−8.3 × 105
w8	1.5 × 10−3	1.4 × 10−1	−3.0 × 10−4	−2.2 × 10−1
w9	−9.8	−8.5 × 10−2	−3.8 × 10−1	−3.0 × 10−1
w10	-	7.6 × 10−1	-	7.8 × 10−1
	Exponential	Semi-Quadratic	Exponential	Semi-Quadratic
w1	−1.01 × 10−2	1.60	−5.16 × 10−1	1.23
w2	3.50 × 10−1	2.38 × 101	6.27 × 10−2	−3.53 × 103
w3	3.68 × 10−2	−1.22 × 101	−3.09 × 10−1	6.70 × 101
w4	1.42	1.14 × 102	−8.44 × 10−1	1.30 × 102
w5	−2.80 × 10−1	−2.79 × 102	5.62 × 10−1	−1.21 × 102
w6	−2.71 × 10−1	−3.31 × 101	−5.83 × 10−1	−2.78 × 101
w7	−4.08 × 101	3.22 × 102	−4.94 × 10−2	4.91 × 102
w8	4.44 × 10−2	−2.13 × 103	2.95 × 10−1	−4.12 × 102
w9	2.78 × 10−1	−9.61 × 101	5.82 × 10−1	−1.61 × 102
w10	4.02 × 10−1	1.39 × 102	2.31 × 10−1	−1.13 × 102
w11	−3.98 × 10−1	−1.91 × 102	8.14	−8.24 × 101
w12	−4.56 × 10−2	6.31 × 102	−3.91 × 10−1	6.25 × 102
w13	1.03 × 101	3.24 × 102	1.83 × 10−2	−8.29 × 101
w14	1.69 × 10−1	5.10 × 102	6.56 × 10−1	2.75 × 102
w15	3.80 × 10−3	3.03 × 103	−2.61	−1.61 × 105
w16	9.91 × 10−1	-	1.65 × 10−1	-
w17	−3.66	-	−2.27 × 10−1	-

where Coeff. denotes the coefficients of models.

. Additionally, the performance graphs of the algorithms, categorized by model forms for the WO and WSO, are shown in Figure 4.

The primary objective of optimization algorithms is to find the point where the objective function is minimized, representing the optimal solution. As illustrated in Figure 4, the WO and WSO algorithms performed better with the linear and semi-quadratic models. The semi-quadratic model achieved the lowest fitness function value, indicating the best results. When comparing the performance of the two algorithms, it is evident that the WO algorithm outperformed the WSO algorithm across all four model forms.

It is usual practice to utilize both scale-dependent and scale-independent indicators to assess the models’ prediction accuracy. Scale-dependent metrics such as Absolute Error (AE), Mean Absolute Error (MAE), Standard Deviation of Absolute Errors (Std_AE), and Root Mean Squared Error (RMSE) are recognized techniques for assessing the precision of forecasts. On the other hand, scale-independent metrics like Standard Deviation of Absolute Percentage Errors (Std_APE), Mean Absolute Percentage Error (MAPE), Absolute Percentage Error (APE), and Determination Coefficient (R²) are used for validation in a variety of prediction problems that are based on distinct datasets. Hyndman and Koehler [43] identified these methods for assessing prediction quality. The metrics used to evaluate the quality of the models’ predictions are provided in Equations (32)–(41).

$$AE=\left|{TEC}_{Observed}-{TEC}_{Est}\right|$$

(32)

$$APE=\left|{\displaystyle \frac{T{EC}_{Observed}-T{EC}_{Est}}{T{EC}_{Observed}}}\right|$$

(33)

$$R^2=1-\left[{\displaystyle \frac{\sum _{i=1}^n{\left({TEC}_{{Observed}_i}-{TEC}_{{Est}_i}\right)}^2}{\sum _{i=1}^n({TEC}_{{Observed}_i}-{TEC}_{{MEan}_i})}}\right]$$

(34)

$$R_{adj}^2=1-\left[{\displaystyle \frac{n-1}{n-p}}\right]\times R^2$$

(35)

$$RMSE=\sqrt{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.}\sum _{i=1}^m{\left({TEC}_{{Observed}_i}-{TEC}_{{Est}_i}\right)}^2}$$

(36)

$$MAE={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.} \sum _{i=1}^m\left|{TEC}_{{Observed}_i}-{TEC}_{{Est}_i}\right|$$

(37)

$$MAPE={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.} \sum _{i=1}^m\left|{\displaystyle \frac{{TEC}_{{Observed}_i}-{TEC}_{{Est}_i}}{{TEC}_{{Observed}_i}}}\right|\times 100$$

(38)

$$Std\_AE=\sqrt{{\displaystyle \frac{\sum _{i=1}^m{\left({AE}_i-MAE\right)}^2}{m}}}$$

(39)

$$Std\_APE=\sqrt{{\displaystyle \frac{\sum _{i=1}^m{\left({APE}_i-MAPE\right)}^2}{m}}}$$

(40)

$$RAE=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{\left({TEC}_{{Observed}_i}-{TEC}_{{Est}_i}\right)}^2}{\sum _{i=1}^n\left({ {TEC}_{{Observed}_i}}^2\right)}}}$$

(41)

where m is the sample size in the dataset.

Table 4. Statistics based on model forms for the WO and WSO algorithms.

Performance Measure	WO				WSO
	Linear	Power	Exp.	Semi-Quad.	Linear	Power	Exp.	Semi-Quad.
R2	0.984	0.984	0.981	0.985	0.983	0.981	0.982	0.985
Adj. R2	0.983	0.983	0.980	0.985	0.982	0.981	0.982	0.984
RMSE	0.776	0.778	0.831	0.735	0.837	0.892	0.794	0.762
MAE	0.447	0.514	0.533	0.438	0.459	0.600	0.532	0.448
MAPE	2.795	2.999	3.137	2.662	2.894	4.295	3.497	2.671
RAE	0.050	0.050	0.053	0.047	0.054	0.057	0.051	0.049
Std_AE	0.618	0.637	0.640	0.582	0.700	0.660	0.589	0.585
Std_APE	2.767	3.068	3.106	2.632	2.864	4.297	3.473	2.645

where Exp. denotes the Exponential model and Semi-Quad. Denotes the Semi-Quadratic model. The values in bold denotes the models’ lowest error values.

displays the statistical values of the models based on the algorithms. The statistical findings indicate that, for every model form, the WO algorithm outperformed the WSO method in terms of performance. The semi-quadratic model showed the best performance among the model forms created using the WO algorithm, whereas the exponential model performed the worst across all performance metrics. The semi-quadratic model performed the best out of all the models created using the WSO technique, with the power model having the lowest performance. In terms of performance, the linear model from both methods came in second. The best model for TED prediction out of all the model forms was the semi-quadratic model created using the WO method since it had the highest R² value and the lowest error values based on other factors. In Table 4, the models’ lowest error values are bolded and highlighted.

Various methods have been employed in TED prediction studies in Turkey, resulting in prediction performances with MAPE values ranging from 5% to 13%. Although different parameters were used in studies utilizing ABC, ACO, FPA, MARS, and ANN approaches for transportation energy demand forecasting, similar performance levels were achieved. In this case, the different model parameters used and investigation of the effect of the transportation type highlight the innovative aspects of this study and provide a basis for demonstrating its superiority over previous studies. A comparison of the pro-posed approach with recent studies is provided in

Table 5. Comparison of the current approach with the recent studies in Turkey.

References	Method	Independent Variables	R2	MAPE
Murat and Ceylan [9]	ANN	GNP, population, vehicle-km	-	13%
Başkan et al. [12]	ACO	GDP, population, vehicle-km	0.950	5.49%
Sonmez et al. [14]	ABC	GDP, population, vehicle-km	0.953	11%
Korkmaz and Akgüngör [15]	FPA	GDP, vehicle-km, CO2	0.986	5.45%
Sahraei et al. [17]	MARS	Ton-km, oil price	0.989	5%
Ağbulut [18]	ANN	GDP, population, vehicle-km	0.924	8.39%
Present Study	WO	Passenger-km, freight-km, population, GDP, CO2	0.985	2.66%

. In the TED prediction model proposed with the ANN approach, predictions were made with a 13% MAPE error [9], while another ANN study achieved a prediction with an 8.39% MAPE error [13]. Elsewhere, ACO-developed linear, exponential, and quadratic models showed MAPE values of 5.49%, 5.76%, and 8.15%, respectively [12]. Moreover, models that were suggested using the ABC algorithm had respective MAPE values of 11%, 12.07%, and 16.06% [14], and FPA-developed linear, power, and quadratic models had corresponding MAPE values of 5.61%, 5.45%, and 5.75% [15]. In another study, with a TED prediction error of about 5% MAPE, the MARS method outperformed the other experiments conducted [17]. The study’s findings indicate that all model forms created using both algorithms applied performed better than those of recent research published in the literature. The WO semi-quadratic model, with a 2.66% MAPE, produced the outcome that was most similar to the observed values in the present study.

Non-parametric tests were used to compare the performance of the algorithms. To highlight the differences among the algorithms, the Friedman test, a post hoc test, was employed. The Friedman statistics are provided in

Table 6. Friedman test statistics.

Algorithm	Linear		Semi-Quadratic		Exponential		Power
	Mean Rank	p-Values	Mean Rank	p-Values	Mean Rank	p-Values	Mean Rank	p-Values
WO	2.827	0.000	1.189	0.000	6.120	0.000	4.970	0.000
WSO	3.343		3.001		7.228		7.324

. The null hypothesis of equal medians was rejected for p-values less than 0.05, indicating that one algorithm performed significantly better than the others and suggesting meaningful differences between them. According to the Friedman test statistics in Table 6, the WO method had the lowest Mean Rank value across all models. The best result among all models was achieved with the WO semi-quadratic model. Thus, it was once again demonstrated that the WO approach outperformed the WSO approach for all model forms.

In conclusion, the WO semi-quadratic model was found to provide the highest accuracy for future projections of transportation energy demand (TED). Additionally, since the model is developed based on transportation modes, we propose that it offers an understanding of how the distribution of demand across different transportation modes impacts TED.

Turkey’s Predicted Future Energy Consumption for Transportation

In determining future energy strategies, projecting emerging demands plays a crucial role in enabling decision-makers to make more effective decisions. This study developed two scenarios to project future demand forecasts. The Least Squares approach was used to derive the model parameters’ projection values. In the first scenario, TED predictions were based on the current trend and extended to 2035, maintaining a consistent demand distribution across transportation modes. In the second scenario, a distribution was created based on a shift in demand from road transportation to the rail system, which has seen increased demand and flexibility in recent years. This scenario illustrates the impact on TED of increasing the share of rail transportation in Turkey, where road transport currently accounts for 90%.

Scenario I: The distribution of transportation modes in freight and passenger transport, as well as the distribution of CO₂ emissions, is shown in

Table 7. Current demand distribution over transportation modes.

	Rail Transportation	Road Transportation
Passenger-km	1.5%	91.2%
Freight-km	4.6%	89.3%
CO2 emissions	0.4%	95.2%

. The projection values of the parameters up to 2035 were obtained based on the current trend and are presented in

Table 8. Projections values of different parameters for transportation modes in scenario I.

			Road Transportation			Rail Transportation
Years	GDP	POP	P-km	F-km	CO2	P-km	F-km	CO2
2022	1004.138	84.95	323.69	289.46	77.73	8.71	13.75	358
2023	1040.091	85.86	331.76	295.77	80.39	8.94	14.02	338
2024	1075.403	86.85	339.41	301.26	82.96	9.15	14.30	318
2025	1110.304	87.80	347.58	306.42	85.54	9.39	14.59	294
2026	1145.487	88.75	355.84	312.87	88.46	9.71	14.89	275
2027	1176.032	89.71	363.55	318.68	91.27	9.99	15.19	256
2028	1206.908	90.67	371.91	325.09	94.23	10.25	15.50	239
2029	1236.386	91.64	380.92	332.65	97.31	10.48	15.84	225
2030	1263.924	92.61	390.73	340.29	100.28	10.75	16.22	212
2031	1294.474	93.58	400.91	348.56	103.08	11.05	16.53	197
2032	1321.527	94.56	410.37	356.65	105.95	11.35	16.84	182
2033	1346.911	95.53	420.37	365.28	108.85	11.64	17.23	167
2034	1364.160	96.52	429.06	373.12	111.64	11.92	17.47	146
2035	1379.279	97.50	436.98	380.60	114.35	12.17	17.66	126

. TED forecasts using the WO semi-quadratic model, which demonstrated the best performance, are shown, and the TED changes up to 2035 are illustrated in Figure 5.

The Ministry of Energy and Natural Resources (MENR) provided the energy balance tables, which show that Turkey’s TED value for 2022 is 27.17 MTOE. [8]. According to Scenario I, the forecasted value for 2022 is 27.232 MTOE, which is very close to the MENR value. Additionally, with the current distribution of transportation modes, TED is projected to reach 39 MTOE by 2035, representing an approximate increase of 45% compared to 2022.

Scenario II: Road transportation holds a significant share of 91% in Turkey. However, with the increase in railway investments and their growing prevalence, there has been a rise in demand for the railway transportation mode. Therefore, this scenario explores the impact on TED when there is a 5% demand shift from road transportation to the rail system. As a result of this demand shift, calculations indicate a 50% increase in demand for rail transportation, leading to a revised demand distribution. The new distribution for freight and passenger transportation, as well as CO₂ emissions, is shown in

Table 9. New demand distribution over transportation modes.

	Rail Transportation	Road Transportation
Passenger-km	2.25%	86.2%
Freight-km	6.9%	84.3%
CO2 emissions	0.6%	90.2%

. According to the projected demand distribution, the parameter values for P-km, F-km, and CO₂ up to 2035 are presented in

Table 10. Projections values of different parameters for transportation modes in scenario II.

	Road Transportation			Rail Transportation
Years	P-km	F-km	CO2	P-km	F-km	CO2
2022	321.22	280.27	77.57	11.18	22.94	516
2023	329.23	286.36	80.19	11.46	23.44	533
2024	336.84	291.69	82.73	11.72	23.88	550
2025	344.97	296.72	85.27	12.01	24.29	567
2026	353.25	302.97	88.14	12.29	24.80	586
2027	360.97	308.61	90.92	12.56	25.26	605
2028	369.30	314.82	93.84	12.85	25.77	624
2029	378.24	322.12	96.89	13.16	26.37	645
2030	387.97	329.54	99.83	13.50	26.97	664
2031	398.10	337.48	102.59	13.86	27.62	682
2032	407.54	345.23	105.43	14.18	28.26	701
2033	417.48	353.57	108.30	14.53	28.94	720
2034	426.15	361.03	111.05	14.83	29.55	739
2035	434.05	368.12	113.72	15.11	30.13	756

. GDP and POP parameter values remain the same as in Scenario I. TED projections for Scenario II up to 2035 are shown in Figure 6.

When demand shifts from road to rail transportation, the model predicts an approximate 10% decrease in TED values. According to Scenario II, the TED value for 2035 is projected to be around 35 MTOE. In Turkey, where road transportation predominantly handles freight and passenger movement, an increase in the share of rail systems has a significant impact on energy consumption. Therefore, a balanced demand across transportation modes and an increase in the shares of both rail and other modes are anticipated to result in the lowest levels of energy consumption.

4. Conclusions

The demand for energy has grown dramatically in recent years due to population growth and travel demand. In countries like Turkey, where a large proportion of energy sources, particularly oil, are imported, the efficient use of energy resources has become essential. Therefore, estimating energy consumption in the transportation sector is crucial for national energy planning. Optimization techniques have long been applied to these forecasts, yielding successful results. This study developed TED forecasting models for Turkey, considering the effects of transportation modes, using advanced optimization techniques such as the WO and WSO algorithms. The following results were obtained.

• The two new artificial intelligence algorithms showed a successful performance in TED estimation and could make estimations with an error rate of approximately 2.70%. In addition, it was found that the WO algorithm is a more effective optimization method and provides better solutions. It is thought that the algorithms, which have been shown to be successful in TED estimation, can also provide positive results in various other areas such as developing estimation models and finding the optimum solution to the problem;
• The proposed estimation models produced quite effective results compared to those from the existing studies in the literature. While the estimated values in the existing studies approach the real values with a maximum error of 5%, this error rate can be reduced to 2.70% with the proposed models. This situation will allow for more realistic estimations and will help increase the effectiveness of the new strategic plans to be implemented. In countries dependent on foreign countries, such as Turkey, ensuring energy efficiency is an issue that is especially important in economic terms. In the transportation sector, strategic plans are being made to ensure a balanced demand distribution and energy efficiency by making new investments in different transportation modes. In this regard, knowing the extent to which each mode of transportation affects energy consumption and using models that can make more realistic estimates offers a promising step toward achieving the goals set out;
• The impact on energy consumption was examined when there was a shift in demand between transportation modes. In Turkey, where road transportation is predominant, energy consumption is positively affected when demand is shifted from road transportation to railway transportation, and it was predicted that approximately 10% energy efficiency will be achieved. Increasing the share of other transportation modes such as air and railway in transportation will both create alternative transportation opportunities to highways and provide advantages such as energy efficiency, a reduction in environmental impacts, and a reduction in the accident risk.

In a country like Turkey, where road transportation constitutes over 90% of the transportation system, significant investments are being made in rail transportation, rapidly developing an alternative mode of transport. This shift reduces the dependency on road transportation and provides a more sustainable transportation option. A decrease in road demand and a shift towards rail will have a positive impact on energy consumption and contribute to reducing environmental effects. In parallel with railway investments in Turkey, airway and seaway investments are also increasing. In particular, new airports and ports are being put into operation. Therefore, the share of airway and seaway transportation modes is increasing day by day. A key limitation of this study is that the level of impact of airway and seaway transportation was not examined; in future studies, other transportation modes will be examined, and the effect of a balanced demand distribution among all modes on energy consumption will be revealed.