Operating cost and quality of service optimization for multi-vehicle-type timetabling for urban bus systems
Introduction
In increasingly interconnected and globalized world, more than half of the population (54%) live now in urban areas, as opposed to the 30% in 1950. This abrupt growth implies deep changes in a size and distribution of space (i.e., population density). This tendency will be accentuated in the coming years. An estimated 66% of the world population will live in cities in 2050 leading to a rise in demand for all infrastructures that interact directly with the people [31]. It involves several problems, for example, congestion, increased demand for a limited supply of resources, water, goods, energy, and services, including education, healthcare, and transportation.
Harrison et al. [16] define a smart city as an “instrumented, interconnected and intelligent city”. Different areas like public administration, education, health services, energy, transportation, and logistics can be improved to make them more intelligent, interconnected and efficient by computing technologies. Smart cities can reduce living costs, make responsible use of resources, and inspire the active citizens’ participation in decision-making processes, to achieve a sustainable and inclusive city.
The main challenges of urban mobility are often related to the inability of public transport systems to satisfy needs of a growing number of users. Though each city has specific issues, local authorities and responsible mobility agencies share common objectives such as reducing congestion by improving traffic flow, sustainable and cleaner environment, increasing the use of public transport, and other greener options, like bikes and electric vehicles.
In 2010, the European Union defined the Intelligent Transport Systems (ITS) as an advanced set of applications, which provides innovative services relating to different modes of transport and traffic management. ITS integrates telecommunications, electronics and information technologies with transport engineering to plan, design, operate, maintain and manage transport systems [11]. Technological advances in computer science allow to collect a considerable amount of transport and mobility data, and design novel algorithms and mobile applications benefiting users, government organizations and operators (i.e., transport service providers) [2].
The main objectives of the ITS are as follows: improving capacity, efficiency, safety, reducing energy consumption and negative environmental impact. It enhances economic productivity for users and operators, improves personal mobility, convenience and comfort, and creating an environment, in which new ITS technologies can be applied.
The problems with more than one optimization criteria are known as Multiobjective Optimization Problems (MOPs), where a single solution that optimizes all objectives, at the same time, does not exist. The solution consists of a set of non-dominated solutions, called Pareto front or Pareto optimal set. In most cases, for NP-hard problems, its calculating is impractical. It can contain an infinite number of non-dominated solutions. Therefore, the goal is to obtain a good approximation of the real Pareto front, in a reasonable time. Heuristics and metaheuristics are a popular class of algorithms to find a high-quality solution for MOPs [25].
In this paper, we present a MultiObjective Cellular (MOCell) metaheuristic to solve the Multiple Vehicle-Types Timetabling Problem (MVTTP). We study two conflicting objectives due to the transport service providers want to minimize the operating cost, and users expect a better service. Hence, we propose solutions for a distribution of vehicles (proper frequency calculation), reducing the operating cost, and guaranteeing the quality of service.
The paper is structured as follows. The next section briefly reviews related works, models, and algorithms for transport problems. Section 3 describes the main approaches to multiobjective MVTTP. Section 4 provides descriptions of MOCell and other evolutionary algorithms. Section 5 presents simulation setup and experimental analysis. Section 6 highlights the conclusions of the paper and future work.
Section snippets
Related work
This section presents a brief overview of models and algorithms for transport problems, mainly, for urban public transport (see Fig. 1). Most of these works are based on computational intelligence techniques to improve approximate solutions, since, the problem is NP-hard [21].
The multiobjective MVTTP
Smart city issues imply the development and implementation of computational techniques for planning mobility. The ITSs include three primary participants:
Citizens or public transport users, which are looking for an efficient, economical, safe, comfortable and friendly multimodal system.
Companies of transportation services, which are seeking to reduce operating costs and maximize profits, focusing efforts on economic subjects under the regulations of government authorities.
Governments, whose
Multiobjective evolutionary algorithms
The problem tackled in this paper is composed of two conflicting objectives that must be optimized at the same time. The general formulation of a MOP is the following:
Find a vector , which satisfies the inequality constraints , equality constraints , and minimizes the vector function , where is the vector of decision variables.
A MOP consists of objectives reflected in the objective functions,
Experimental results
This section details the experimentation methodology used in our study. First, we describe indicators used to assess the quality of the computed Pareto front approximation. Second, we report the parameter settings and experimental analysis of the proposed algorithm for a given passengers’ demand case of the route 217 in Los Angeles city (see Fig. 2) used in the literature for an approach using analytical and heuristic methods [[4], [5]].
The structure of data set represents the average of
Conclusions
In this paper, we address the multiobjective multiple vehicle-type timetabling problem and propose a cellular genetic algorithm to solve it. The objective is to determine timetables using various bus types with different capacity, operating cost, gas consumption, size, weight, etc. to optimize a quality of service, represented by the unsatisfied user demand, and total operating cost.
With the operation data of Los Angeles bus route 217 northbound, we obtain a set of non-dominated solutions that
Acknowledgments
The work is partially supported by RFBR, project no. 16-07-00931, 18-07-01224-a, Federal Agency of Scientific Organizations (FASO), project no. 0348-2017-0010, and CONACYT, México , grant no. 178415.
David Peña received the Bachelor’s Degree in Electronics from the Universidad Pedagógica Nacional (UPN), Bogotá, Colombia, in 2013 and the M.Sc. degree in Computer Science from Center for Scientific Research and Higher Education of Ensenada (CICESE), Baja California, Mexico in 2017. He is currently a Research Assistant at the Parallel Computing Laboratory at CICESE. His research interests include parallel computing, cloud computing, computational intelligence, multiobjective optimization and
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David Peña received the Bachelor’s Degree in Electronics from the Universidad Pedagógica Nacional (UPN), Bogotá, Colombia, in 2013 and the M.Sc. degree in Computer Science from Center for Scientific Research and Higher Education of Ensenada (CICESE), Baja California, Mexico in 2017. He is currently a Research Assistant at the Parallel Computing Laboratory at CICESE. His research interests include parallel computing, cloud computing, computational intelligence, multiobjective optimization and evolutionary computation.
Andrei Tchernykh received his Ph.D. degree from Institute of Precise Mechanics and Computer Technology of the Russian Academy of Sciences, Russia in 1986. He gained industrial experience as supercomputer design team leader in Advance Technical Products Corp, and Supercomputer Design Department of Electro-Mechanical Enterprise, Russian leaders in HPC design and development. He is holding a full professor position in Computer Science Department at CICESE Research Center, Ensenada, Baja California, Mexico, and a head of Parallel Computing Laboratory. He is a member of the National System of Researchers of Mexico (SNI), Level II, and a founding member of the Mexican Supercomputer Society. He has published more than 200 papers in refereed journals and conferences, and served as a TPC member and general co-chair of more than 240 professional peer-reviewed conferences. He was invited as a visiting researcher at prestigious universities and research centers. He leads a number of research projects and grants in different countries. He has served as a member of the editorial boards and guest editor of several scientific journals. His main interests include resource optimization technique, adaptive resource provisioning, multiobjective optimization, computational intelligence, incomplete information processing, cloud computing and security.
Sergio Nesmachnow is a Full Time Professor at Universidad de la República, Uruguay. He is Researcher at National Research and Innovation Agency (ANII) and National Program for the Development of Basic Sciences (PEDECIBA), Uruguay. His main research interests are scientific computing, high performance computing, and parallel metaheuristics applied to solve complex real-world problems. He holds a Ph.D. (2010) and a M.Sc. (2004) in Computer Science, and a degree in Engineering (2000) from Universidad de la República, Uruguay. He has published over 90 papers in international journals and conference proceedings. Currently, he works as Director of the Multidisciplinary Center for High Performance Computing (Universidad de la República, Uruguay) and as Editor-in-Chief for International Journal of Metaheuristics, while he is also Guest Editor in Cluster Computing and The Computer Journal. He also participates as speaker and member of several technical program committees of international conferences and is a reviewer for many journals and conferences.
Renzo Massobrio is assistant professor and engineer in computer science at Universidad de la República, Uruguay. He is M.Sc. candidate in computer science at Universidad de la República and Ph.D. candidate in computer science at Universidad de Cádiz, Spain. He received best undergraduate thesis award from the Faculty of Engineering, Universidad de la República. He participated in research internships at Universidad de Cádiz in Spain, Universidad de Málaga in Spain, Cardiff University in Wales, and Centro de Investigación Científica y de Educación Superior de Ensenada in México.
He has published two journal articles, one book chapter, and more than 15 conference articles. His main interests include computational intelligence, metaheuristics, and high-performance computing applied to solving complex optimization problems.
Alexander Feoktistov received the Ph.D. degree from Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences (ISDCT SB RAS) in 2000. He is currently a senior research officer in Laboratory of Parallel and Distributed Computing Systems of ISDCT SB RAS, and an associate professor in Graduate school in ISDCT SB RAS. He leads a number of national research projects. His main interests include computational models, distributed computing, multi-agent technologies and simulation model.
Igor Bychkov received the Dr. degree from Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences (ISDCT SB RAS) in 2003. He is Academician of RAS, professor, Ph.D., director of the Matrosov Institute for System Dynamics and Control Theory of SB RAS, scientific leader of the Irkutsk Scientific Center of SB RAS. He is a member of a number scientific and expert councils, editorial boards of scientific journals. He is an expert for the Russian Foundation for Basic Research, Russian Scientific Foundation, Russian Academy of Sciences. He leads a number of national and international research projects. His main interests include artificial intelligence, geoinformation systems, WEB-technologies, systems of intelligent data analysis, mathematical modeling, and cloud computing.
Gleb Radchenko graduated from South Ural State University (SUSU, Chelyabinsk, Russia) in applied mathematics and computer science in 2006. He obtained his Ph.D. from Moscow State University, Russia in 2010. Since 2010, he worked in SUSU in the department of system programming. He currently holds a position of a director of School of Electrical Engineering and Computer Science of SUSU. His sphere of interest is focused on such topics as high-performance systems, cloud computing, distributed computing and scientific workflows.
Alexander Yu. Drozdov received the M.Sc. degree in mathematics in 1988 from the Moscow State University, Russia. He is currently a Director of Phystech School of Radio Engineering and Computer Technology, Full Professor at The Moscow Institute of Physics and Technology, Russia, and a head of the laboratory of design and modeling of special-purpose computer systems. His research interests are in the fields of research and development of new high-performance architectures and embedded computing systems, embedded control systems, together with the development of tools, embedded and system software.
Sergey Garichev received the M.Sc. and Ph.D. degrees from Moscow Institute of Physics and Technology (State University)—MIPT. Currently he is a Vice rector for research and development and a Dean of the Department (Faculty) of Radio Engineering and Cybernetics of MIPT, senior researcher with a specialization in Systems of design automation, head of the department “Radio engineering and control systems”. His major research and educational interests are in the areas of telecommunications, radar and radio communication equipment, microprocessor and computer technology, control systems design, and application software development for special-purpose technical equipment.