Search results for: Transportation problem
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3923

Search results for: Transportation problem

3773 Optimization of Unweighted Minimum Vertex Cover

Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.

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3772 Two Points Crossover Genetic Algorithm for Loop Layout Design Problem

Authors: Xu LiYun, Briand Florent, Fan GuoLiang

Abstract:

The loop-layout design problem (LLDP) aims at optimizing the sequence of positioning of the machines around the cyclic production line. Traffic congestion is the usual criteria to minimize in this type of problem, i.e. the number of additional cycles spent by each part in the network until the completion of its required routing sequence of machines. This paper aims at applying several improvements mechanisms such as a positioned-based crossover operator for the Genetic Algorithm (GA) called a Two Points Crossover (TPC) and an offspring selection process. The performance of the improved GA is measured using well-known examples from literature and compared to other evolutionary algorithms. Good results show that GA can still be competitive for this type of problem against more recent evolutionary algorithms.

Keywords: Crossover, genetic algorithm, layout design problem, loop-layout, manufacturing optimization.

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3771 Performance Analysis of MATLAB Solvers in the Case of a Quadratic Programming Generation Scheduling Optimization Problem

Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: Economic dispatch, optimization, quadratic programming, MATLAB.

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3770 The Knapsack Sharing Problem: A Tree Search Exact Algorithm

Authors: Mhand Hifi, Hedi Mhalla

Abstract:

In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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3769 A New Heuristic Approach for the Stock- Cutting Problems

Authors: Stephen C. H. Leung, Defu Zhang

Abstract:

This paper addresses a stock-cutting problem with rotation of items and without the guillotine cutting constraint. In order to solve the large-scale problem effectively and efficiently, we propose a simple but fast heuristic algorithm. It is shown that this heuristic outperforms the latest published algorithms for large-scale problem instances.

Keywords: Combinatorial optimization, heuristic, large-scale, stock-cutting.

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3768 Transferring Route Plan over Time

Authors: Barıs Kocer, Ahmet Arslan

Abstract:

Travelling salesman problem (TSP) is a combinational optimization problem and solution approaches have been applied many real world problems. Pure TSP assumes the cities to visit are fixed in time and thus solutions are created to find shortest path according to these point. But some of the points are canceled to visit in time. If the problem is not time crucial it is not important to determine new routing plan but if the points are changing rapidly and time is necessary do decide a new route plan a new approach should be applied in such cases. We developed a route plan transfer method based on transfer learning and we achieved high performance against determining a new model from scratch in every change.

Keywords: genetic algorithms, transfer learning, travellingsalesman problem

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3767 Symbiotic Organism Search (SOS) for Solving the Capacitated Vehicle Routing Problem

Authors: Ruskartina Eki, Vincent F. Yu, Santosa Budi, A. A. N. Perwira Redi

Abstract:

This paper introduces symbiotic organism search (SOS) for solving capacitated vehicle routing problem (CVRP). SOS is a new approach in metaheuristics fields and never been used to solve discrete problems. A sophisticated decoding method to deal with a discrete problem setting in CVRP is applied using the basic symbiotic organism search (SOS) framework. The performance of the algorithm was evaluated on a set of benchmark instances and compared results with best known solution. The computational results show that the proposed algorithm can produce good solution as a preliminary testing. These results indicated that the proposed SOS can be applied as an alternative to solve the capacitated vehicle routing problem.

Keywords: Symbiotic organism search, vehicle routing problem, metaheuristics, Solution Representation.

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3766 Mathematical Models of Flow Shop and Job Shop Scheduling Problems

Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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3765 Voltage Stability Enhancement Using Cat Swarm Optimization Algorithm

Authors: P. Suryakumari, P. Kantarao

Abstract:

Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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3764 Integer Programming Model for the Network Design Problem with Facility Dependent Shortest Path Routing

Authors: Taehan Lee

Abstract:

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: Integer programming, multicommodity network design, routing, shortest path.

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3763 Numerical Investigation of Multiphase Flow in Pipelines

Authors: Gozel Judakova, Markus Bause

Abstract:

We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: Discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, two-phase flow.

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3762 Solving Stochastic Eigenvalue Problem of Wick Type

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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3761 Problem Based Learning in B. P. Koirala Institute of Health Sciences

Authors: Gurung S., Yadav B. N., Budhathoki SS.

Abstract:

Problem based learning is one of the highly acclaimed learning methods in medical education since its first introduction at Mc-Master University in Canada in the 1960s. It has now been adopted as a teaching learning method in many medical colleges of Nepal. B.P. Koirala Institute of Health Sciences (BPKIHS), a health science deemed university is the second institute in Nepal to establish problem-based learning academic program and need-based teaching approach hence minimizing teaching through lectures since its inception. During the first two years of MBBS course, the curriculum is divided into various organ-systems incorporated with problem-based learning exercise each of one week duration.

Keywords: PBL, medical education.

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3760 The Carbon Footprint Model as a Plea for Cities towards Energy Transition: The Case of Algiers Algeria

Authors: Hachaichi Mohamed Nour El-Islem, Baouni Tahar

Abstract:

Environmental sustainability rather than a trans-disciplinary and a scientific issue, is the main problem that characterizes all modern cities nowadays. In developing countries, this concern is expressed in a plethora of critical urban ills: traffic congestion, air pollution, noise, urban decay, increase in energy consumption and CO2 emissions which blemish cities’ landscape and might threaten citizens’ health and welfare. As in the same manner as developing world cities, the rapid growth of Algiers’ human population and increasing in city scale phenomena lead eventually to increase in daily trips, energy consumption and CO2 emissions. In addition, the lack of proper and sustainable planning of the city’s infrastructure is one of the most relevant issues from which Algiers suffers. The aim of this contribution is to estimate the carbon deficit of the City of Algiers, Algeria, using the Ecological Footprint Model (carbon footprint). In order to achieve this goal, the amount of CO2 from fuel combustion has been calculated and aggregated into five sectors (agriculture, industry, residential, tertiary and transportation); as well, Algiers’ biocapacity (CO2 uptake land) has been calculated to determine the ecological overshoot. This study shows that Algiers’ transport system is not sustainable and is generating more than 50% of Algiers total carbon footprint which cannot be sequestered by the local forest land. The aim of this research is to show that the Carbon Footprint Assessment might be a relevant indicator to design sustainable strategies/policies striving to reduce CO2 by setting in motion the energy consumption in the transportation sector and reducing the use of fossil fuels as the main energy input.

Keywords: Biocapacity, carbon footprint, ecological footprint assessment, energy consumption.

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3759 Hardware Approach to Solving Password Exposure Problem through Keyboard Sniff

Authors: Kyungroul Lee, Kwangjin Bae, Kangbin Yim

Abstract:

This paper introduces a hardware solution to password exposure problem caused by direct accesses to the keyboard hardware interfaces through which a possible attacker is able to grab user-s password even where existing countermeasures are deployed. Several researches have proposed reasonable software based solutions to the problem for years. However, recently introduced hardware vulnerability problems have neutralized the software approaches and yet proposed any effective software solution to the vulnerability. Hardware approach in this paper is expected as the only solution to the vulnerability

Keywords: Keyboard sniff, password exposure, hardware vulnerability, privacy problem, insider security.

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3758 A Robust Optimization Model for the Single-Depot Capacitated Location-Routing Problem

Authors: Abdolsalam Ghaderi

Abstract:

In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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3757 Developing of Fragility Curve for Two-Span Simply Supported Concrete Bridge in Near-Fault Area

Authors: S. Shirazian, M.R. Ghayamghamian, G.R. Nouri

Abstract:

Bridges are one of the main components of transportation networks. They should be functional before and after earthquake for emergency services. Therefore we need to assess seismic performance of bridges under different seismic loadings. Fragility curve is one of the popular tools in seismic evaluations. The fragility curves are conditional probability statements, which give the probability of a bridge reaching or exceeding a particular damage level for a given intensity level. In this study, the seismic performance of a two-span simply supported concrete bridge is assessed. Due to usual lack of empirical data, the analytical fragility curve was developed by results of the dynamic analysis of bridge subjected to the different time histories in near-fault area.

Keywords: Fragility curve, Seismic behavior, Time historyanalysis, Transportation Network.

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3756 Discrete Breeding Swarm for Cost Minimization of Parallel Job Shop Scheduling Problem

Authors: Tarek Aboueldah, Hanan Farag

Abstract:

Parallel Job Shop Scheduling Problem (JSSP) is a multi-objective and multi constrains NP-optimization problem. Traditional Artificial Intelligence techniques have been widely used; however, they could be trapped into the local minimum without reaching the optimum solution. Thus, we propose a hybrid Artificial Intelligence (AI) model with Discrete Breeding Swarm (DBS) added to traditional AI to avoid this trapping. This model is applied in the cost minimization of the Car Sequencing and Operator Allocation (CSOA) problem. The practical experiment shows that our model outperforms other techniques in cost minimization.

Keywords: Parallel Job Shop Scheduling Problem, Artificial Intelligence, Discrete Breeding Swarm, Car Sequencing and Operator Allocation, cost minimization.

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3755 Multi-Objective Multi-Mode Resource-Constrained Project Scheduling Problem by Preemptive Fuzzy Goal Programming

Authors: Phruksaphanrat B.

Abstract:

This research proposes a preemptive fuzzy goal programming model for multi-objective multi-mode resource constrained project scheduling problem. The objectives of the problem are minimization of the total time and the total cost of the project. Objective in a multi-mode resource-constrained project scheduling problem is often a minimization of makespan. However, both time and cost should be considered at the same time with different level of important priorities. Moreover, all elements of cost functions in a project are not included in the conventional cost objective function. Incomplete total project cost causes an error in finding the project scheduling time. In this research, preemptive fuzzy goal programming is presented to solve the multi-objective multi-mode resource constrained project scheduling problem. It can find the compromise solution of the problem. Moreover, it is also flexible in adjusting to find a variety of alternative solutions. 

Keywords: Multi-mode resource constrained project scheduling problem, Fuzzy set, Goal programming, Preemptive fuzzy goal programming.

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3754 Finding Viable Pollution Routes in an Urban Network under a Predefined Cost

Authors: Dimitra Alexiou, Stefanos Katsavounis, Ria Kalfakakou

Abstract:

In an urban area the determination of transportation routes should be planned so as to minimize the provoked pollution taking into account the cost of such routes. In the sequel these routes are cited as pollution routes.

The transportation network is expressed by a weighted graph G=(V,E,D,P) where every vertex represents a location to be served and contains unordered pairs (edges) of elements in V that indicate a simple road. The distances / cost and a weight that depict the provoked air pollution by a vehicle transition at every road are assigned to each road as well. These are the items of set D andrespectively.

Furthermore the investigated pollution routes must not exceed predefined corresponding values concerning the route cost and the route pollution level during the vehicle transition.

In this paper we present an algorithm that generates such routes in order that the decision maker selects the most appropriate one. 

Keywords: bi-criteria, pollution, shortest paths.

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3753 Development of an Intelligent Tool for Planning the Operation

Authors: T. R. Alencar, P. T. Leite

Abstract:

Several optimization algorithms specifically applied to the problem of Operation Planning of Hydrothermal Power Systems have been developed and are used. Although providing solutions to various problems encountered, these algorithms have some weaknesses, difficulties in convergence, simplification of the original formulation of the problem, or owing to the complexity of the objective function. Thus, this paper presents the development of a computational tool for solving optimization problem identified and to provide the User an easy handling. Adopted as intelligent optimization technique, Genetic Algorithms and programming language Java. First made the modeling of the chromosomes, then implemented the function assessment of the problem and the operators involved, and finally the drafting of the graphical interfaces for access to the User. The program has managed to relate a coherent performance in problem resolution without the need for simplification of the calculations together with the ease of manipulating the parameters of simulation and visualization of output results.

Keywords: Energy, Optimization, Hydrothermal Power Systemsand Genetic Algorithms

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3752 TELUM Land Use Model: An Investigation of Data Requirements and Calibration Results for Chittenden County MPO, U.S.A.

Authors: Georgia Pozoukidou

Abstract:

TELUM software is a land use model designed specifically to help metropolitan planning organizations (MPOs) prepare their transportation improvement programs and fulfill their numerous planning responsibilities. In this context obtaining, preparing, and validating socioeconomic forecasts are becoming fundamental tasks for an MPO in order to ensure that consistent population and employment data are provided to travel demand models. Chittenden County Metropolitan Planning Organization of Vermont State was used as a case study to test the applicability of TELUM land use model. The technical insights and lessons learned from the land use model application have transferable value for all MPOs faced with land use forecasting development and transportation modeling.

Keywords: Calibration data requirements, land use models, land use planning, Metropolitan Planning Organizations.

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3751 The Emoji Method: An Approach for Identifying and Formulating Problem Ideas

Authors: Thorsten Herrmann, Alexander Laukemann, Hansgeorg Binz, Daniel Roth

Abstract:

For the analysis of already identified and existing problems, the pertinent literature provides a comprehensive collection of approaches as well as methods in order to analyze the problems in detail. But coming up with problems, which are assets worth pursuing further, is often challenging. However, the importance of well-formulated problem ideas and their influence of subsequent creative processes are incontestable and proven. In order to meet the covered challenges, the Institute for Engineering Design and Industrial Design (IKTD) developed the Emoji Method. This paper presents the Emoji Method, which support designers to generate problem ideas in a structured way. Considering research findings from knowledge management and innovation management, research into emojis and emoticons reveal insights by means of identifying and formulating problem ideas within the early design phase. The simple application and the huge supporting potential of the Emoji Method within the early design phase are only few of the many successful results of the conducted evaluation. The Emoji Method encourages designers to identify problem ideas and describe them in a structured way in order to start focused with generating solution ideas for the revealed problem ideas.

Keywords: Emojis, problem ideas, innovation management, knowledge management.

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3750 Play in College: Shifting Perspectives and Creative Problem-Based Play

Authors: Agni Stylianou-Georgiou, Eliza Pitri

Abstract:

This study is a design narrative that discusses researchers’ new learning based on changes made in pedagogies and learning opportunities in the context of a Cognitive Psychology and an Art History undergraduate course. The purpose of this study was to investigate how to encourage creative problem-based play in tertiary education engaging instructors and student-teachers in designing educational games. Course instructors modified content to encourage flexible thinking during game design problem-solving. Qualitative analyses of data sources indicated that Thinking Birds’ questions could encourage flexible thinking as instructors engaged in creative problem-based play. However, student-teachers demonstrated weakness in adopting flexible thinking during game design problem solving. Further studies of student-teachers’ shifting perspectives during different instructional design tasks would provide insights for developing the Thinking Birds’ questions as tools for creative problem solving.

Keywords: Creative problem-based play, educational games, flexible thinking, tertiary education.

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3749 Hub Port Positioning and Route Planning of Feeder Lines for Regional Transportation Network

Authors: Huang Xiaoling, Liu Lufeng

Abstract:

In this paper, we seek to determine one reasonable local hub port and optimal routes for a containership fleet, performing pick-ups and deliveries, between the hub and spoke ports in a same region. The relationship between a hub port, and traffic in feeder lines is analyzed. A new network planning method is proposed, an integrated hub port location and route design, a capacitated vehicle routing problem with pick-ups, deliveries and time deadlines are formulated and solved using an improved genetic algorithm for positioning the hub port and establishing routes for a containership fleet. Results on the performance of the algorithm and the feasibility of the approach show that a relatively small fleet of containerships could provide efficient services within deadlines.

Keywords: Route planning, Hub port location, Container feeder service.

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3748 Simulation of Ethical Behavior in Urban Transportation

Authors: Ali Reza Honarvar , Naser Ghasem Agaee

Abstract:

For controlling urban transportations, traffic lights show similar behavior for different kinds of vehicles at intersections. Emergency vehicles need special behavior at intersections, so traffic lights should behave in different manner when emergency vehicles approach them. At the present time, intelligent traffic lights control urban transportations intelligently. In this paper the ethical aspect of this topic is considered. A model is proposed for adding special component to emergency vehicles and traffic lights for controlling traffic in ethical manner. The proposed model is simulated by JADE.

Keywords: Ethical traffic control, intelligent transportation, Ethical agent, Multi-agent system.

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3747 A Study of the Assistant Application for Tourists Taking Metros

Authors: Anqi Wang, Linye Zhang

Abstract:

With the proliferation and development of mobile devices, various mobile apps have appeared to satisfy people’s needs. Metro, with the feature of convenient, punctuality and economic, is one of the most popular modes of transportation in cities. Yet, there are still some inconveniences brought by various factors, impacting tourists’ riding experience. The aim of this study is to help tourists to shorten the time of purchasing tickets, to provide them clear metro information and direct navigation, detailed schedule as well as a way to collect metro cards as souvenir. The study collects data through three phases, including observation, survey and test. Data collected from 106 tourists totally in Wuhan metro stations are discussed in the study. The result reflects tourists’ demand when they take the metro. It also indicates the feasibility of using mobile technology to improve passenger’s experience.

Keywords: Mobile App, metro, public transportation, ticket, mobile payment, indoors positioning, tourists.

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3746 A New Heuristic Algorithm for the Classical Symmetric Traveling Salesman Problem

Authors: S. B. Liu, K. M. Ng, H. L. Ong

Abstract:

This paper presents a new heuristic algorithm for the classical symmetric traveling salesman problem (TSP). The idea of the algorithm is to cut a TSP tour into overlapped blocks and then each block is improved separately. It is conjectured that the chance of improving a good solution by moving a node to a position far away from its original one is small. By doing intensive search in each block, it is possible to further improve a TSP tour that cannot be improved by other local search methods. To test the performance of the proposed algorithm, computational experiments are carried out based on benchmark problem instances. The computational results show that algorithm proposed in this paper is efficient for solving the TSPs.

Keywords: Local search, overlapped neighborhood, travelingsalesman problem.

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3745 A Genetic Algorithm to Schedule the Flow Shop Problem under Preventive Maintenance Activities

Authors: J. Kaabi, Y. Harrath

Abstract:

This paper studied the flow shop scheduling problem under machine availability constraints. The machines are subject to flexible preventive maintenance activities. The nonresumable scenario for the jobs was considered. That is, when a job is interrupted by an unavailability period of a machine it should be restarted from the beginning. The objective is to minimize the total tardiness time for the jobs and the advance/tardiness for the maintenance activities. To solve the problem, a genetic algorithm was developed and successfully tested and validated on many problem instances. The computational results showed that the new genetic algorithm outperforms another earlier proposed algorithm. 

Keywords: Flow shop scheduling, maintenance, genetic algorithm, priority rules.

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3744 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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