Search results for: combinatorial problem

Authors: Aydin Sipahioglu, Gokhan Celik

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Helicopter routing problem (HRP) is finding good tours for helicopter so as to pick up and deliver personnel or material among specified nodes, mutually. It can be encountered in case of being lots of supply and demand points for different commodities and requiring delivering commodities with helicopter. For instance, to deliver personnel or material from shore to oil rig is a good example. In fact, HRP is a branch of vehicle routing problem with pickup and delivery (VRPPD). However, it has additional constraints such that fuel capacity, performance of helicopter in different altitude and temperature, and the number of maximum takeoff and landing allowed. This kind of pickup and delivery problems can be classified into 3 groups, basically. 1-1 (one to one), M-M (many to many) and 1-M-1 (one to many to one). 1-1 means each commodity has only one supply and one demand point. M-M means there can be more than one supply and demand points for each kind of commodity. 1-M-1 means commodities at depot are delivered to demand points and commodities at customers are delivered to depot. In this case helicopter takes off from its own base, complete its tour and return to its own base. In this study, we define 1-M-M-1 type HRP. That means helicopter takes off from its home base, deliver commodities among the nodes as well as between depot and customers and return to its home base. These problems have NP-hard nature. Therefore, obtaining a good solution in a reasonable time is not easy. In this study, a model is offered for 1-M-M-1 type HRP. It is shown on small scale test instances that the model can find the optimal solution.

Keywords: helicopter routing problem, vehicle routing with pickup and delivery, integer programming

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Authors: Walied Hazim Sharif

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The problem of faithful extension with the condition of keeping constant height h and constant width w, i.e. for hw-inextensibility, seems more interesting than the brute extension of finite poset (partially ordered set). We shall investigate some theorems of hw-inextensive and hw-extensive posets that can be used to formulate the faithful extension problem. A theorem in its general form of hw-inextensive posets are given to implement the presented theorems.

Keywords: faithful extension, poset, extension, inextension, height, width, hw-extensive, hw-inextensive

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: evolutionary algorithms, portfolio optimization, skewness, stock selection

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Authors: D. Srinivasacharya, Nidhi Humnekar

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The goal of this research is to numerically investigate the convection of nanofluid flow in an inclined porous channel. Brownian motion and thermophoresis effects are accounted for by nanofluid. In addition, the flow in the porous region governs Brinkman’s equation. The perturbed state of the generalized eigenvalue problem is obtained using normal mode analysis, and Chebyshev spectral collocation was used to solve this problem. For various values of the governing parameters, the critical wavenumber and critical Rayleigh number are calculated, and preferred modes are identified.

Keywords: Brinkman model, inclined channel, nanofluid, linear stability, porous media

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Authors: Yi Xiong, Tao Kong

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Traditional safety, risk and reliability analysis approaches are problem-oriented, which make it great workload when analyzing complicated and huge system, besides, too much repetitive work would to do if the analyzed system composed by many similar components. It is pressing need an object and function oriented approach to maintain high consistency with problem domain. A new approach is proposed to overcome these shortcomings of traditional approaches, the concepts: class, abstract, inheritance, polymorphism and encapsulation are introduced into FTA and establish the professional class library that the abstractions of physical objects in real word, four areas relevant information also be proposed as the establish help guide. The interaction between classes is completed by the inside or external methods that mapping the attributes to base events through fully search the knowledge base, which forms good encapsulation. The object oriented fault tree analysis system that analyze and evaluate the system safety and reliability according to the original appearance of the problem is set up, where could mapped directly from the class and object to the problem domain of the fault tree analysis. All the system failure situations can be analyzed through this bottom-up fault tree construction approach. Under this approach architecture, FTA approach is developed, which avoids the human influence of the analyst on analysis results. It reveals the inherent safety problems of analyzed system itself and provides a new way of thinking and development for safety analysis. So that object oriented technology in the field of safety applications and development, safety theory is conducive to innovation.

Keywords: FTA, knowledge base, object-oriented technology, reliability analysis

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Authors: Bachir Bentouati, Lakhdar Chaib, Saliha Chettih, Gai-Ge Wang

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The problem of economic dispatch (ED) is the basic problem of power framework, its main goal is to find the most favorable generation dispatch to generate each unit, reduce the whole power generation cost, and meet all system limitations. A heuristic algorithm, recently developed called Stud Krill Herd (SKH), has been employed in this paper to treat non-convex ED problems. The proposed KH has been modified using Stud selection and crossover (SSC) operator, to enhance the solution quality and avoid local optima. We are demonstrated SKH effects in two case study systems composed of 13-unit and 40-unit test systems to verify its performance and applicability in solving the ED problems. In the above systems, SKH can successfully obtain the best fuel generator and distribute the load requirements for the online generators. The results showed that the use of the proposed SKH method could reduce the total cost of generation and optimize the fulfillment of the load requirements.

Keywords: stud krill herd, economic dispatch, crossover, stud selection, valve-point effect

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Authors: Hyun Seop Uhm, Yong Ho Choi, Ji Eun Kim, Young Hoon Lee

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Weapon-target assignment (WTA) is a problem that assigns available launchers to appropriate targets in order to defend assets. Various algorithms for WTA have been developed over past years for both in the static and dynamic environment (denoted by SWTA and DWTA respectively). Due to the problem requirement to be solved in a relevant computational time, WTA has suffered from the solution efficiency. As a result, SWTA and DWTA problems have been solved in the limited situation of the battlefield. In this paper, the general situation under continuous time is considered by Time based Weapon Target Assignment (TWTA) problem. TWTA are studied using the mixed integer programming model, and three heuristic algorithms; decomposed opt-opt, decomposed opt-greedy, and greedy algorithms are suggested. Although the TWTA optimization model works inefficiently when it is characterized by a large size, the decomposed opt-opt algorithm based on the linearization and decomposition method extracted efficient solutions in a reasonable computation time. Because the computation time of the scheduling part is too long to solve by the optimization model, several algorithms based on greedy is proposed. The models show lower performance value than that of the decomposed opt-opt algorithm, but very short time is needed to compute. Hence, this paper proposes an improved method by applying decomposition to TWTA, and more practical and effectual methods can be developed for using TWTA on the battlefield.

Keywords: air and missile defense, weapon target assignment, mixed integer programming, piecewise linearization, decomposition algorithm, military operations research

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Authors: Imèn Khanchouch, Malika Charrad, Mohamed Limam

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The interpretation of the quality of clusters and the determination of the optimal number of clusters is still a crucial problem in clustering. We focus in this paper on multi-SOM clustering method which overcomes the problem of extracting the number of clusters from the SOM map through the use of a clustering validity index. We then tested multi-SOM using real and artificial data sets with different evaluation criteria not used previously such as Davies Bouldin index, Dunn index and silhouette index. The developed multi-SOM algorithm is compared to k-means and Birch methods. Results show that it is more efficient than classical clustering methods.

Keywords: clustering, SOM, multi-SOM, DB index, Dunn index, silhouette index

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Authors: Marian Sagat, Mariana Remesikova

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In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros.

Keywords: geodesic, geodesic curvature flow, mesh, Rhinoceros software

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Authors: N. Bolong, J. Makinda, I. Saad

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Laboratory activities have produced benefits in student learning. With current drives of new technology resources and evolving era of education methods, renewal status of learning and teaching in laboratory methods are in progress, for both learners and the educators. To enhance learning outcomes in laboratory works particularly in engineering practices and testing, learning via hands-on by instruction may not sufficient. This paper describes and compares techniques and implementation of traditional (expository) with open-ended laboratory (problem-based) for two consecutive cohorts studying environmental laboratory course in civil engineering program. The transition of traditional to problem-based findings and effect were investigated in terms of course assessment student feedback survey, course outcome learning measurement and student performance grades. It was proved that students have demonstrated better performance in their grades and 12% increase in the course outcome (CO) in problem-based open-ended laboratory style than traditional method; although in perception, students has responded less favorable in their feedback.

Keywords: engineering education, open-ended laboratory, environmental engineering lab

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Authors: Jean Berger, Nassirou Lo, Martin Noel

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Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization

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Authors: Tae Gwan Kim, Hyun Kyu Cho, Young Hoon Lee, Young Chul Park

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Foam monitors are devices that are installed on cargo tank decks to suppress cargo area fires in oil tankers or hazardous chemical ship cargo ships. In general, the main design parameter of the foam monitor is the distance of the projection through the foam monitor. In this study, the relationship between flow characteristics and projection distance, depending on the shape was examined. Numerical techniques for fluid analysis of foam monitors have been developed for prediction. The flow pattern of the fluid varies depending on the shape of the flow path of the foam monitor, as the flow losses affecting projection distance were calculated through numerical analysis. The basic shape of the foam monitor was an L shape designed by N Company. The modified model increased the length of the flow path and used the S shape model. The calculation result shows that the L shape, which is the basic shape, has a problem that the force is directed to one side and the vibration and noise are generated there. In order to solve the problem, S-shaped model, which is a change model, was used. As a result, the problem is solved, and the projection distance from the nozzle is improved.

Keywords: CFD, foam monitor, projection distance, moment

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Authors: Tigmanshu Bhatnagar, Petra Badke-Schaub

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Facilitating Design Thinking (DT) and Creative Problem Solving (CPS) in engineering education could benefit students by aiding them to think creatively and meaningfully in their education and future profession. A study in the pseudonym of a ‘popup class’ was conducted for a week at the Indian Institute of Technology, Delhi (IITD) to have an indication for the perceived relevance, benefits and challenges of DT and CPS from the perspective of engineering students in India. 30 third year Bachelor of Technology students from various technical fields participated in the study. They were introduced to the notion of DT and CPS via a mix of theoretical lectures, case discussions and practical workshops. Their reactions were identified on the basis of silent observations made during the course and responses were recorded through a questionnaire, which was filled after the course. All the respondents felt that DT and CPS are relevant to their education. It was perceived by them that there is a subtle improvement in the quality, quantity and approach of solutions to open ended problems. 90% responded positively to the induction of such an exercise in their education and reasoned it by stating that it’s important for engineers to know, how to solve open-ended real world problems in a meaningful and innovative way.

Keywords: creative problem solving, design thinking, India, undergraduate engineering education

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Authors: Allen A. Espinosa, Larkins A. Trinidad

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The present study investigated collegiate students’ problem solving strategies and misconceptions in solving stoichiometric problems and later on formulate a teaching framework from the result of the study. The study found out that the most prominent strategies among students are the mole method and the proportionality method, which are both algorithmic by nature. Misconception was also noted as some students rely on Avogadro’s number in converting between moles. It is suggested therefore that the teaching of stoichiometry should not be confined to demonstration. Students should be involved in the process of thinking of ways to solve the problem.

Keywords: stoichiometry, Svogadro’s number, mole method, proportionality method

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: Chakib Jerry, Mounir Jerry

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In this paper, a mathematical model of infested honey bees colonies is formulated in order to investigate Colony Collapse Disorder in a honeybee colony. CCD, as it is known, is a major problem on honeybee farms because of the massive decline in colony numbers. We introduce to the model a control variable which represents forager protection. We study the controlled model to derive conditions under which the bee colony can fight off epidemic. Secondly we study the problem of minimizing prevention cost under model’s dynamics constraints.

Keywords: honey bee, disease transmission model, disease control honeybees, optimal control

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Authors: Ziwei Xu

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The increasing emphasis on mobility has driven the application of innovative communication technologies across various industries. In the retail sector, Near Field Communication (NFC) has emerged as a significant and transformative technology, particularly in the payment and retail supermarket sectors. NFC enables new payment methods, such as electronic wallets, and enhances information management in supermarkets, contributing to the growth of the trade. This report presents a comprehensive analysis of NFC technology, focusing on five key aspects. Firstly, it provides an overview of NFC, including its application methods and development history. Additionally, it incorporates Arthur's work on combinatorial evolution to elucidate the emergence and impact of NFC technology, while acknowledging the limitations of the model in analyzing NFC. The report then summarizes the positive influence of NFC on the retail industry along with its associated constraints. Furthermore, it explores the adoption of NFC from both organizational and individual perspectives, employing the Best Predictors of organizational IT adoption and UTAUT2 models, respectively. Finally, the report discusses the potential future replacement of NFC with biometrics technology, highlighting its advantages over NFC and leveraging Arthur's model to investigate its future development prospects.

Keywords: innovation, NFC, industry, biometrics

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Authors: Mehdi Seifbarghy, Zahra Nasiri

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Competitive location problem deals with locating new facilities to provide a service (or goods) to the customers of a given geographical area where other facilities (competitors) offering the same service are already present. The new facilities will have to compete with the existing facilities for capturing the market share. This paper proposes a new model to maximize the market share in which customers choose the facilities based on traveling time, waiting time and attractiveness. The attractiveness of a facility is considered as a parameter in the model. A heuristic is proposed to solve the problem.

Keywords: competitive location, market share, facility attractiveness, heuristic

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Authors: K. N. S. Kasi Viswanadham

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Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

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Authors: Dimitrios Akrivos, Alexandros K. Antoniou

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This paper looks at the crucial role of the British news media in the construction of extreme pornography as a social problem, suggesting that this paved the way for the subsequent criminalization of such material through the introduction of the Criminal Justice and Immigration Act 2008. Focusing on the high-profile case of Graham Coutts, it examines the British national press’ reaction to Jane Longhurst’s murder through a qualitative content analysis of 251 relevant news articles. Specifically, the paper documents the key arguments expressed in the corresponding claims-making process. It considers the different ways in which the consequent ‘trial by media’ presented this exceptional case as the ‘tip of the iceberg’ and eventually translated into policy. The analysis sheds light on the attempts to ‘piggyback’ the issue of extreme pornography on child sexual abuse images as well as the textual and visual mechanisms used to establish an ‘us versus them’ dichotomy in the pertinent media discourse. Finally, the paper assesses the severity of the actual risk posed by extreme pornography, concluding that its criminalization should not merely be dismissed as the outcome of an institutionalized media panic.

Keywords: criminalization, extreme pornography, social problem, trial by media

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Authors: Chutikarn Sriwiboon

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The purposes of this paper were to study the production problems of basketry in the central region and to study the development of potential in skilled labourers in producing basketry in three provinces: Suphanburi, Ayuthaya, and Aungthong. A quota sampling was utilized to get 486 respondents from 243 basketry communities that were registered with OTOP project. A focus group was also used with a connoisseurship model to study knowledge and factors that related to the development of potential in skilled labourers in producing basketry. The findings revealed that the process getting service is the major problem for customers to get service. Also, there should be more of a variety of knowledge for customers. In terms of technology, the variety of information was rated as the most important problem. In terms staff's ability, the knowledge of staff was the most important problem. For the development of potential in high skilled labours for basketry, the findings revealed that having proper tools was considered the most important factor. In terms of economy, the findings revealed that the basketry job must provide sufficient income was considered the most important factor. In terms of using natural resources, efficiency is the most important factor. In terms of mentality, integrity is the most important factor. Finally, in terms of society and culture, help in the local activities is the most important factor.

Keywords: basketry, development, potential, skilled labours

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Authors: Md Habibul Ansary, Chandan Garai, Ranjan Dasgupta

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Utilization of resources is always a great challenge for any allocation problem, particularly when resource availability is dynamic in nature. In this work VM allocation mechanism has been augmented by providing resources in a combined manner. This approach has some inherent advantages in terms of reduction of wait state for the pending jobs of some users and better utilization of unused resources from the service providers’ point of view. Moreover the algorithm takes care of released resources from the finished jobs as soon as those become available. The proposed algorithm has been explained by suitable example to make the work complete.

Keywords: Bid ratio, cloud service, virtualization, VM allocation problem

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Authors: Van Thinh Bui, Anh Tuan Tran, Quoc Viet Ngo, The Bao Pham

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Video retrieval is a searching problem on videos or clips based on content in which they are relatively close to an input image or video. The application of this retrieval consists of selecting video in a folder or recognizing a human in security camera. However, some recent approaches have been in challenging problem due to the diversity of video types, frame transitions and camera positions. Besides, that an appropriate measures is selected for the problem is a question. In order to overcome all obstacles, we propose a content-based video retrieval system in some main steps resulting in a good performance. From a main video, we process extracting keyframes and principal objects using Segmentation of Aggregating Superpixels (SAS) algorithm. After that, Speeded Up Robust Features (SURF) are selected from those principal objects. Then, the model “Bag-of-words” in accompanied by SVM classification are applied to obtain the retrieval result. Our system is performed on over 300 videos in diversity from music, history, movie, sports, and natural scene to TV program show. The performance is evaluated in promising comparison to the other approaches.

Keywords: video retrieval, principal objects, keyframe, segmentation of aggregating superpixels, speeded up robust features, bag-of-words, SVM

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Authors: Salima Bella, Assia Belbachir, Ghalem Belalem

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This paper deals with the problem of monitoring and cleaning dirty zones of oceans using unmanned vehicles. We present a centralized cooperative architecture for unmanned aerial vehicles (UAVs) to monitor ocean regions and clean dirty zones with the help of unmanned surface vehicles (USVs). Due to the rapid deployment of these unmanned vehicles, it is convenient to use them in oceanic regions where the water pollution zones are generally unknown. In order to optimize this process, our solution aims to detect and reduce the pollution level of the ocean zones while taking into account the problem of fault tolerance related to these vehicles.

Keywords: centralized architecture, fault tolerance, UAV, USV

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Authors: Mohsen S. Sajadieha, Danyar Molavia

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In this paper, a truck scheduling problem is investigated at a two-touch cross-docking center with due dates for outbound trucks as a hard constraint. The objective is to minimize the total cost comprising penalty and delivery cost of delayed shipments. The sequence of unloading shipments is considered and is assumed that shipments are sent to shipping dock doors immediately after unloading and a First-In-First-Out (FIFO) policy is considered for loading the shipments. A mixed integer programming model is developed for the proposed model. Two meta-heuristic algorithms including genetic algorithm (GA) and variable neighborhood search (VNS) are developed to solve the problem in medium and large sized scales. The numerical results show that increase in due dates for outbound trucks has a crucial impact on the reduction of penalty costs of delayed shipments. In addition, by increase the due dates, the improvement in the objective function arises on average in comparison with the situation that the cross-dock is multi-touch and shipments are sent to shipping dock doors only after unloading the whole inbound truck.

Keywords: cross-docking, truck scheduling, fixed due date, door assignment

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Authors: Jiraporn Adchariyaprasit

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Thai language is difficult in all four language skills, especially reading. The first year students may have different abilities in reading, so a teacher is required to find out a student’s reading level so that the teacher can help and support them till they can develop and resolve each problem themselves. This research is aimed to study the prosody problem among Thai students and will be focused on first year Thai students in the second semester. A total of 58 students were involved in this study. Four obstacles were found: 1) Interpretation from what they read and write; 2) Incorrectness Pronunciation of Prosody; 3) Incorrectness in Rhythm of the Poem; Incorrectness of the Thai Poem Pronunciation.

Keywords: pronunciation, prosody, interpretation, Thai language

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Authors: Midhun Paul, T. Radha Ramanan

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The objective of this work is to present a state-of-the-art literature review highlighting the challenges in the research of the scheduling of assembly job shop problem and providing an insight on how the future directions of the research would be. The number of work has been substantial that it requires a review to enable one to understand the origin of the research and how it is getting evolved. This review paper presents a comprehensive review of the literature dealing with various studies carried on assembly job shop scheduling. The review details the evolution of the AJS from the perspective of other scheduling problems and also presents a classification scheme. The work also identifies the potential directions for future research, which we believe to be worthwhile considering.

Keywords: assembly job shop, future directions, manufacturing, scheduling

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Authors: Jamaludin Sallim, Rozlina Mohamed, Roslina Abdul Hamid

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In this paper, we proposed an Ant Colony Optimization (ACO) algorithm together with Traveling Salesman Problem (TSP) approach to investigate the clustering problem in Protein Interaction Networks (PIN). We named this combination as ACOPIN. The purpose of this work is two-fold. First, to test the efficacy of ACO in clustering PIN and second, to propose the simple generalization of the ACO algorithm that might allow its application in clustering proteins in PIN. We split this paper to three main sections. First, we describe the PIN and clustering proteins in PIN. Second, we discuss the steps involved in each phase of ACO algorithm. Finally, we present some results of the investigation with the clustering patterns.

Keywords: ant colony optimization algorithm, searching algorithm, protein functional module, protein interaction network

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Authors: M. Abir Hossain, M. Shahjada Tarafder

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This paper deals with the analysis of potential flow past two-dimensional body by discretizing the body into panels where the Laplace equation was applied to each panel. The Laplace equation was solved at each panel by applying the boundary conditions. The boundary condition was applied at each panel to mathematically formulate the problem and then convert the problem into a computer-solvable problem. Kutta condition was applied at both the leading and trailing edges to see whether the condition is satisfied or not. Another approach that is applied for the analysis is Vortex Lattice Method (VLM). A vortex ring is considered at each control point. Using the Biot-Savart Law the strength at each control point is calculated and hence the pressure differentials are measured. For the comparison of the analytic result with the experimental result, different NACA section hydrofoil is used. The analytic result of NACA 0012 and NACA 0015 are compared with the experimental result of Abbott and Doenhoff and found significant conformity with the achieved result.

Keywords: Kutta condition, Law of Biot-Savart, pressure differentials, potential flow, vortex lattice method

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Authors: Yena Lee, Vassilis M. Charitopoulos, Karthik Thyagarajan, Ian Morris, Jose M. Pinto, Lazaros G. Papageorgiou

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With globalisation, the need to have better coordination of production and distribution decisions has become increasingly important for industrial gas companies in order to remain competitive in the marketplace. In this work, we investigate a problem that integrates production, inventory, and routing decisions in a liquid oxygen supply chain. The oxygen supply chain consists of production facilities, external third-party suppliers, and multiple customers, including hospitals and industrial customers. The product produced by the plants or sourced from the competitors, i.e., third-party suppliers, is distributed by a fleet of heterogenous vehicles to satisfy customer demands. The objective is to minimise the total operating cost involving production, third-party, and transportation costs. The key decisions for production include production and inventory levels and product amount from third-party suppliers. In contrast, the distribution decisions involve customer allocation, delivery timing, delivery amount, and vehicle routing. The optimisation of the coordinated production, inventory, and routing decisions is a challenging problem, especially when dealing with large-size problems. Thus, we present a two-stage procedure to solve the integrated problem efficiently. First, the problem is formulated as a mixed-integer linear programming (MILP) model by simplifying the routing component. The solution from the first-stage MILP model yields the optimal customer allocation, production and inventory levels, and delivery timing and amount. Then, we fix the previous decisions and solve a detailed routing. In the second stage, we propose a column generation scheme to address the computational complexity of the resulting detailed routing problem. A case study considering a real-life oxygen supply chain in the UK is presented to illustrate the capability of the proposed models and solution method. Furthermore, a comparison of the solutions from the proposed approach with the corresponding solutions provided by existing metaheuristic techniques (e.g., guided local search and tabu search algorithms) is presented to evaluate the efficiency.

Keywords: production planning, inventory routing, column generation, mixed-integer linear programming

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