Distribution of demand for transport using artificial intelligence methods

. Enhancing the caliber of efforts in advancing transportation infrastructure, re-evaluating antiquated standards during the integration of contemporary information and communication technologies, ameliorating benchmarks and quality to align with global standards, assuring the security, acceptance, dependability, and endurance of transportation services, refining infrastructure, implementing adaptable tariffs and initiating novel and promising routes, the digitalization of the transportation system, and satisfying the entire gamut of demands for urban passenger transportation necessitate a range of targeted activities. The article illustrates an analytical scrutiny of optimization approaches. The peculiarity of their utilization is expounded, along with their advantages and disadvantages.


Introduction
The transportation infrastructure is a crucial element in providing sustenance for cities and regions.Comparable to the circulatory system in a living organism, the transportation system spans the entirety of the economically active expanse of our planet.The creation of transportation networks is a costly endeavor and cannot singlehandedly resolve all transportation predicaments.Consequently, methodical and informed planning for the development of the transportation complex plays an important role in enhancing the quality of transportation system functionality.Such planning includes the optimal sequencing of construction for transportation infrastructure facilities, improving traffic organization for various portions of the network, optimizing public transportation routes, and devising convenient interchange points.The resolution of these issues is founded upon the development of intelligent transportation systems (ITS) and the mathematical modeling of the transportation system.
The foundation for the development of ITS is the mathematical transport model, which allows for the construction of traffic flow distributions over a network.The primary objective of such mathematical models is to determine and predict the parameters governing the functionality of the transportation network [1].These parameters include traffic flow intensity on network elements, traffic volumes within the public transportation network, individual agents is influenced by factors such as traffic congestion, road closures, and public transport schedules.
In addition to these techniques, machine learning algorithms can also be used for transport demand modeling.These algorithms can analyze large amounts of data on past travel patterns and use this information to predict future demand.They can also be used to optimize the allocation of transport resources to meet this demand.
Overall, mathematical modeling of transport demand distribution is a complex and multidisciplinary field, requiring expertise in mathematics, statistics, computer science, and transportation engineering.By using a variety of techniques and approaches, researchers and practitioners can gain insights into the behavior of transport systems and optimize their performance to meet the needs of passengers and society as a whole.
In particular, the issue of determining informative parameters in modelling is also important, and this leads to saving resources.Interesting approaches to the detection of informative signals have been implemented in [9][10][11][12][13][14][15][16][17][18][19][20] works, which can be used to determine the optimal parameters for the model.
It is important to note that predictive and simulation models should be considered as complementary models.Together, they form an integrated transport model, which serves as a decision support tool for managing the transport complex.These models aid in long-term and current planning of traffic organization measures, as well as traffic volume forecasting and monitoring.
An integrated transport model serves the purpose of resolving the aforementioned issues and also functions to evaluate the influence of external factors on the network.These factors include: the creation of new network sections, renovation (expansion) of network sections, closure of individual network sections, modifications to traffic conditions within the network, and changes in the route network and passenger transport schedules.The fundamental goal of the transport model is to provide a thorough evaluation of the transport system's development, both as a whole and in its individual components.Additionally, the model serves as an information source for establishing a strategic planning system for the development of the transport system.This is subject to the creation of a continuous monitoring system to observe the system's condition.The transport model incorporates a forecasting mechanism that enables you to determine the potential outcome of various scenarios and assess solutions to transport issues on the scale of the city, agglomeration, and region.Consequently, the model provides a foundation for evaluating development scenarios for the transport system.The transport model serves as a suitable workspace for professionals in the fields of territorial planning and transport to create proposals for developing the transport system.
The transport model is a valuable tool for addressing a range of tasks related to the development and management of the transport system.These tasks include: Evaluating the current state of the transport system: The transport model can provide a comprehensive assessment of the current state of the transport system, including its strengths, weaknesses, and areas for improvement.
Projecting future demand for population mobility: The transport model can be used to forecast future demand for transportation, taking into account demographic, economic, and social factors.
Developing options for the development of the transport system: The transport model can be used to develop and evaluate different options for the development of the transport system, including the construction of new facilities, changes to traffic routes, and modifications to the road network.
Allocating resources and assessing feasibility: The transport model can be used to prepare options for resource allocation and to assess the feasibility of different decisions related to transport infrastructure development.
Projecting traffic and passenger volumes: The transport model can provide detailed projections of traffic and passenger volumes, including information on the purpose of the trip and the transportation means used.
Appraising transport scenarios: The transport model can be used to evaluate different transport scenarios, including the launch of new means of passenger transport, alterations to traffic routes, and modifications to the road network.
Making long-term projections: The transport model can be used to make long-term projections on the development of the transport system, taking into account factors such as population growth and changes in economic conditions.
Evaluating transport network performance: The transport model can be used to evaluate the performance of the transport network based on a set of quality indicators.
Establishing a database of transport and socio-economic indicators: The transport model can be used to establish a database of transport and socio-economic indicators, providing a comprehensive view of the transport system and its relationship to broader economic and social trends.
Systematizing and visualizing information: The transport model can be used to systematize and present information related to the transport system in a clear and visually appealing way.
Overall, the transport model is a powerful tool for strategic management of the development of the transport system, enabling decision-makers to make informed choices and optimize the allocation of resources.
In the context of this work, the term "transport model" refers to predictive models.The main objective of these models is to simulate traffic flows or the load on a transport network, which can include various types of movements made by participants such as individual transport, public passenger transport, pedestrian, cargo and information flows.
The methodology used in transport modeling involves establishing a balance between transport demand and supply.This process consists of constructing detailed models of transport demand and supply for a specific area.Transport supply includes the infrastructure of all transport systems within the study area, with a particular emphasis on individual transport and public passenger transport.
Transport demand refers to the quantitative and qualitative needs of network users for movement.The factors that affect transport demand include the location of objects generating movement such as places of residence, employment, education, and cultural and community services.Additionally, behavioral factors such as population mobility and preferences for methods and routes of movement also play a role.
The process of constructing transport models involves solving the problem of ensuring a correspondence between existing transport demand and supply, which involves the distribution of traffic flows.
The effective functioning of the digital platforms for urban passenger transport planning described above cannot be achieved without the use of artificial intelligence (AI) technologies.This requirement is prompted by the current societal stage marked by dynamic changes in the internal and external environment, an increasing quantity and diversity of information on the studied processes.Furthermore, the information includes inaccuracies such as incompleteness, statistical significance, uncertainty, inconsistency, and ambiguity due to qualitative evaluation in linguistic form.This kind of data is classified as incomplete or partial data.This situation has given rise to non-structural problems, classified as intellectual problems that cannot be resolved using precise algorithms and existing conventional methods [23][24][25][26].To address these challenges, new intelligent and scienceintensive (cognitive) algorithms and information technologies based on the theory of AI need to be utilized [27][28][29][30][31][32].
The values of 1 k and 2 k are established as constants through model calibration [1][2][3][4].In order to address the issue of distributing demand across transport services, the preference function is considered.This function is utilized to reevaluate the cost metrics associated with traveling between a given origin and destination region.The probability of performing a correspondence from a particular area to a region is denoted as "likelihood," while 1  and 2  are coefficients that remain constant and are determined through model calibration.Consequently, statistical estimations for 1  and  have been determined, the next step in obtaining the transportation matrix for the demand layers involves solving the maximization problem for each layer of demand.(ln( ) max Subject to the following constraints: .
We can simplify the problem stated in equations ( 1) -( 2) and convert it into a geometric programming problem, as follows [4]: Under the following constraints: Hence, a transportation demand model has been developed.To address the challenge of mode selection, a preference function is formulated [3][4][5]: In the equation, ijM P denotes the probability of commuting from area i to area j via the subway, while ijO P represents the probability of commuting from district I to district j using public transportation.Additionally, The coefficient ijm L is determined as the probability of selecting mode m normalized accordingly.To redistribute individual vehicles, a training procedure was employed.This learning process is a representation of the adaptation process for optimal transportation as it traverses through the network.With each subsequent iteration, drivers incorporate information from their previous trip for new pathfinding.Here, the resistance for pathfinding is a function of the resistance at the current trafficintensity and the resistance computed during the previous iteration based on the following adaptive relationship [6][7][8][21][22]: Error propagation in neural networks is a powerful tool for predictive and qualitative analysis.This technique is named after the algorithm used in reverse networks, where errors propagate from the output layer to the input layer, against the direction of signal propagation during normal network operation.The primary objective of training neural networks is to determine a specific functional relationship Y = F (X), where X represents input vectors and Y represents output vectors.In general, for a limited set of available problems, this problem has an infinite set of solutions.During training, the primary aim was to minimize the neural network error function, thereby constraining the search space and facilitating the least squares method: Here, i yj -output neuron value; i dj -j ideal value of the cost; p -number of neurons in the output layer.The neural network is typically trained using the gradient descent method, where the weights are updated at each iteration according to the following formula: here  the parameter that determines the learning rate is missing.
Finding the neural network for the last layer is relatively straightforward as we have the target vector, which represents the desired output values that the neural network must generate for a given set of input values.
We can express the formula (3) in an elaborate form.

Results and discussion
A method for analyzing a neural network in its entirety is presented as follows: Step 1: Input the data into the neural network and compute the output values of the network's neurons; Step 2: Compute the weight changes for the output layer of the neural network; Step 3: Calculate the weight changes for the remaining layers of the neural network, respectively, for n = N-1.1; Step 4:Adjust the weights for all layers of the neural network.
Step 5.In case of an error, repeat the process starting from Step 1.
Optimal solution of the model ( 1) is: The paper presents a fixed charge transportation problem with fuzzy shipping costs and crisp fixed costs.To handle the fuzziness, the Bellman and Zadeh's max-min criterion is used to formulate the problem as a crisp model, which involves nonlinear and mixed integer elements.The nonlinearity is resolved by obtaining an optimal condition, and using this condition, a fractional programming is formulated and transformed into a mixed-integer linear programming problem.Although a small numerical example is provided, finding exact solutions for larger models challenging.Hence, the paper suggests applying heuristic or meta-heuristic approaches such as evolutionary algorithms or artificial neural networks to solve the problem.This presents a new research topic worth exploring.

Conclusion
In summary, the paper presents a novel approach to solving a fixed charge transportation problem with fuzzy shipping costs and crisp fixed costs.The use of the Bellman and Zadeh's max-min criterion and the transformation of the problem into a mixed-integer linear programming problem are noteworthy.Additionally, the suggestion of using heuristic or meta-heuristic approaches to solve larger models presents a new research direction for interested researchers.Therefore, from this study, the following characteristics of the optimization process can be identified: A matrix of passenger correspondence must be obtained before optimization can occur.The optimization process requires collecting a substantial amount of initial data.The optimization task is complicated by the competing interests of carriers.Complex software and computing systems are necessary for modern optimization methods, but expert designers' final assessments are also required.
Setting an objective function for a given set of constraints is necessary for the optimization process.However, exact optimization models for constructing route networks do not exist due to the complex and uncertain nature of passenger transportation in cities, which involves a variety of initial data.Therefore, the optimization problem is combinatorial in nature.

2 2 
are obtained in the following manner[5][6].the coefficients   and 2 cost of commuting from district i to district j via the subway, and ijO U indicates the cost of commuting from district I to district j by public transportation.Let ijm F represent the matrices of movements from area i to area j for mode m.The matrices will be computed based on the following proportion: .ijm ijm ij F L F  E3S Web of Conferences 458, 03010 (2023) EMMFT-2023 https://doi.org/10.1051/e3sconf/202345803010