Search results for: multi-vehicle routing problem

Authors: Sara Alshehri, Bayan Alenzi, Atheer Alshehri, Samia Chelloug, Zainab Almry, Hussah Albugmai

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This paper concerns body area networks sensor that collect signals around a human body. The black hole attacks are the main security challenging problem because the data traffic can be dropped at any node. The focus of our proposed solution is to efficiently route data packets while detecting black hole nodes.

Keywords: body sensor networks, security, black hole, routing, broadcasting, OMNeT++

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Authors: Si-Gwan Kim

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In Delay Tolerant Networks (DTN), there may not exist an end-to-end path between source and destination at the time of message transmission. Employing ‘Store Carry and Forward’ delivery mechanism for message transmission in such networks usually incurs long message delays. In this paper, we present the modified Binary Spray and Wait (BSW) routing protocol that enhances the performance of the original one. Our proposed algorithm adjusts the number of forward messages depending on the number of neighbor nodes. By using beacon messages periodically, the number of neighbor nodes can be managed. The simulation using ONE simulator results shows that our modified version gives higher delivery ratio and less latency as compared to BSW.

Keywords: delay tolerant networks, store carry and forward, one simulator, binary spray and wait

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Authors: S. Vasundra, D. Venkatesh

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Wireless networks have gone through an extraordinary growth in the past few years, and will keep on playing a crucial role in future data communication. The present wireless networks aim to make communication possible anywhere and anytime. With the converging of mobile and wireless communications with Internet services, the boundary between mobile personal telecommunications and wireless computer networks is disappearing. Wireless networks of the next generation need the support of all the advances on new architectures, standards, and protocols. Since an ad hoc network may consist of a large number of mobile hosts, this imposes a significant challenge on the design of an effective and efficient routing protocol that can work well in an environment with frequent topological changes. This paper proposes improved ant colony optimization (IACO) technique. It also maintains load balancing in wireless networks. The simulation results show that the proposed IACO performs better than existing routing techniques.

Keywords: wireless networks, ant colony optimization, load balancing, architecture

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Authors: M. K. Benhaoua, A. K. Singh, A. E. Benyamina, P. Boulet

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Mapping parallelized tasks of applications onto these MPSoCs can be done either at design time (static) or at run-time (dynamic). Static mapping strategies find the best placement of tasks at design-time, and hence, these are not suitable for dynamic workload and seem incapable of runtime resource management. The number of tasks or applications executing in MPSoC platform can exceed the available resources, requiring efficient run-time mapping strategies to meet these constraints. This paper describes a new Spiral Dynamic Task Mapping heuristic for mapping applications onto NoC-based Heterogeneous MPSoC. This heuristic is based on packing strategy and routing Algorithm proposed also in this paper. Heuristic try to map the tasks of an application in a clustering region to reduce the communication overhead between the communicating tasks. The heuristic proposed in this paper attempts to map the tasks of an application that are most related to each other in a spiral manner and to find the best possible path load that minimizes the communication overhead. In this context, we have realized a simulation environment for experimental evaluations to map applications with varying number of tasks onto an 8x8 NoC-based Heterogeneous MPSoCs platform, we demonstrate that the new mapping heuristics with the new modified dijkstra routing algorithm proposed are capable of reducing the total execution time and energy consumption of applications when compared to state-of-the-art run-time mapping heuristics reported in the literature.

Keywords: multiprocessor system on chip, MPSoC, network on chip, NoC, heterogeneous architectures, run-time mapping heuristics, routing algorithm

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Authors: S. Aditya, K. T. Nideesh, N. Guruprasad

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Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost.

Keywords: NW method, optimum utilization, transportation problem, Vogel’s approximation method

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Authors: AmirHossein Mohajerzadeh, Mohammad Alishahi, Saeed Aslishahi, Mohsen Zabihi

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In this paper, we consider sensor nodes with the capability of measuring the bearings (relative angle to the target). We use geometric methods to select a set of observer nodes which are responsible for collecting data from the target. Considering the characteristics of target tracking applications, it is clear that significant numbers of sensor nodes are usually inactive. Therefore, in order to minimize the total network energy consumption, a set of sensor nodes, called sentinel, is periodically selected for monitoring, controlling the environment and transmitting data through the network. The other nodes are inactive. Furthermore, the proposed algorithm provides a joint scheduling and routing algorithm to transmit data between network nodes and the fusion center (FC) in which not only provides an efficient way to estimate the target position but also provides an efficient target tracking. Performance evaluation confirms the superiority of the proposed algorithm.

Keywords: coverage, routing, scheduling, target tracking, wireless sensor networks

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Authors: Sandeep Singh Waraich

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Wireless sensor network (WSN ) consists of a large number of sensor nodes. The disparity in their energy consumption usually lead to the loss of equilibrium in wireless sensor network which may further results in an energy hole problem in wireless network. In this paper, we have considered the inclusion of orphan nodes which usually remain unutilized as intermediate nodes in multi-hop routing. The Orphan Node Inclusion (ONI) Protocol lets the cluster member to bring the orphan nodes into their clusters, thereby saving important resources and increasing network lifetime in critical applications of WSN.

Keywords: wireless sensor network, orphan node, clustering, ONI protocol

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Authors: Takumi Shindo, Koji Okamura

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The first generation of the wide area network was circuit centric network. How the optimal circuit can be signed was the most important issue to get the best performance. This architecture had succeeded for line based telephone system. The second generation was host centric network and Internet based on this architecture has very succeeded world widely. And Internet became as new social infrastructure. Currently the architecture of the network is based on the location of the information. This future network is called Information centric network (ICN). The information-centric network (ICN) has being researched by many projects and different architectures for implementation of ICN have been proposed. The goal of this study is to compare performances of those ICN architectures. In this paper, the authors propose general ICN model which can represent two typical ICN architectures and compare communication performances using request routing. Finally, simulation results are shown. Also, we assume that this network architecture should be adapt to energy on-demand routing.

Keywords: ICN, information centric network, CCN, energy

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Authors: Bander Alzahrani

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Information-centric networking (ICN) using architectures such as Publish-Subscribe Internet Routing Paradigm (PSIRP) is one of the promising candidates for a future Internet, has recently been under the spotlight by the research community to investigate the possibility of redesigning the current Internet architecture to solve many issues such as routing scalability, security, and quality of services issues.. The Bloom filter-based forwarding is a source-routing approach that is used in the PSIRP architecture. This mechanism is vulnerable to brute force attacks which may lead to denial-of-service (DoS) attacks. In this work, we present a new forwarding approach that keeps the advantages of Bloom filter-based forwarding while mitigates attacks on the forwarding mechanism. In practice, we introduce a special type of forwarding nodes called Edge-FW to be placed at the edge of the network. The role of these node is to add an extra security layer by validating and inspecting packets at the edge of the network against brute-force attacks and check whether the packet contains a legitimate forwarding identifier (FId) or not. We leverage Certificateless Aggregate Signature (CLAS) scheme with a small size of 64-bit which is used to sign the FId. Hence, this signature becomes bound to a specific FId. Therefore, malicious nodes that inject packets with random FIds will be easily detected and dropped at the Edge-FW node when the signature verification fails. Our preliminary security analysis suggests that with the proposed approach, the forwarding plane is able to resist attacks such as DoS with very high probability.

Keywords: bloom filter, certificateless aggregate signature, denial-of-service, information centric network

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Authors: Jingya Liu, Yue Wu, Jiabin Luo

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This work investigates an intermodal transportation system for delivering goods from a Regional Distribution Centre to supermarkets on the Isle of Wight (IOW) via the port of Southampton or Portsmouth in the UK. We consider this integrated logistics chain as a 3-echelon transportation system. In such a system, there are two types of transport methods used to deliver goods across the Solent Channel: one is accompanied transport, which is used by most supermarkets on the IOW, such as Spar, Lidl and Co-operative food; the other is unaccompanied transport, which is used by Aldi. Five transport scenarios are studied based on different transport modes and ferry routes. The aim is to determine an optimal delivery plan for supermarkets of different business scales on IOW, in order to minimise the total running cost, fuel consumptions and carbon emissions. The problem is modelled as a vehicle routing problem with time windows and solved by genetic algorithm. The computing results suggested that accompanied transport is more cost efficient for small and medium business-scale supermarket chains on IOW, while unaccompanied transport has the potential to improve the efficiency and effectiveness of large business scale supermarket chains.

Keywords: genetic algorithm, intermodal transport system, Isle of Wight, optimization, supermarket

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Authors: James Brown, Stella Kortekaas, Ian Finnie, George Zhang, Christine Devine, Neil Healy

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The use of GIS as an analysis tool for engineering decision making is now best practice in the offshore industry. GIS enables multidisciplinary data integration, analysis and visualisation which allows the presentation of large and intricate datasets in a simple map-interface accessible to all project stakeholders. Presenting integrated geoscience and geotechnical data in GIS enables decision makers to be well-informed. This paper is a successful case study of how GIS spatial analysis techniques were applied to help select the most favourable pipeline route. Routing a pipeline through any natural environment has numerous obstacles, whether they be topographical, geological, engineering or financial. Where the pipeline is subjected to external hydrostatic water pressure and is carrying pressurised hydrocarbons, the requirement to safely route the pipeline through hazardous terrain becomes absolutely paramount. This study illustrates how the application of modern, GIS-based pipeline routing techniques enabled the identification of a single most-favourable pipeline route crossing of a challenging seabed terrain. Conventional approaches to pipeline route determination focus on manual avoidance of primary constraints whilst endeavouring to minimise route length. Such an approach is qualitative, subjective and is liable to bias towards the discipline and expertise that is involved in the routing process. For very short routes traversing benign seabed topography in shallow water this approach may be sufficient, but for deepwater geohazardous sites, the need for an automated, multi-criteria, and quantitative approach is essential. This study combined multiple routing constraints using modern least-cost-routing algorithms deployed in GIS, hitherto unachievable with conventional approaches. The least-cost-routing procedure begins with the assignment of geocost across the study area. Geocost is defined as a numerical penalty score representing hazard posed by each routing constraint (e.g. slope angle, rugosity, vulnerability to debris flows) to the pipeline. All geocosted routing constraints are combined to generate a composite geocost map that is used to compute the least geocost route between two defined terminals. The analyses were applied to select the most favourable pipeline route for a potential gas development in deep water. The study area is geologically complex with a series of incised, potentially active, canyons carved into a steep escarpment, with evidence of extensive debris flows. A similar debris flow in the future could cause significant damage to a poorly-placed pipeline. Protruding inter-canyon spurs offer lower-gradient options for ascending an escarpment but the vulnerability of periodic failure of these spurs is not well understood. Close collaboration between geoscientists, pipeline engineers, geotechnical engineers and of course the gas export pipeline operator guided the analyses and assignment of geocosts. Shorter route length, less severe slope angles, and geohazard avoidance were the primary drivers in identifying the most favourable route.

Keywords: geocost, geohazard, pipeline route determination, pipeline route optimisation, spatial analysis

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Authors: Rohaya Abdul Wahab, Raja Mohd Fuad Tengku Aziz, Nazaliza Othman, Sharifah Saleh, Nabihah Razali, Rozaimah Baharim, Md Hanif Md Nasir

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This paper will discuss flip chip methodology, in which I/O pads, standard cells, macros and bump cells array are placed in the floorplan, then routed using Astro place and route tool. Final DRC and LVS checking is done using Calibre verification tool. The design vehicle to run this methodology is an OpenRISC design targeted to Silterra 0.18 micrometer technology with 6 metal layers for routing. Astro has extensive support for flip chip placement and routing. Astro tool commands for flip chip are straightforward approach like the conventional standard wire bond packaging. However since we do not have flip chip commands in our Astro tool, no LEF file for bump cell and no LEF file for flip chip I/O pad, we create our own methodology to prepare for future flip chip tapeout. 

Keywords: methodology, flip chip, bump cell, LEF, astro, calibre, SCHEME, TCL

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: Masood Ahmad, Ataul Aziz Ikram, Ishtiaq Wahid

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Wireless sensor network (WSN) is the interconnection of mobile wireless nodes with limited energy and memory. These networks can be deployed formany critical applications like military operations, rescue management, fire detection and so on. In flat routing structure, every node plays an equal role of sensor and router. The topology may change very frequently due to the mobile nature of nodes in WSNs. The topology maintenance may produce more overhead messages. To avoid topology maintenance overhead messages, an optimized cluster based mobile wireless sensor network using memetic algorithm is proposed in this paper. The nodes in this network are first divided into clusters. The cluster leaders then transmit data to that base station. The network is validated through extensive simulation study. The results show that the proposed technique has superior results compared to existing techniques.

Keywords: WSN, routing, cluster based, meme, memetic algorithm

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Authors: Terence Soule, Tami Al Ghamdi

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To study how the partial knowledge transfer may affect the Genetic Algorithm (GA) performance, we model the Transfer Learning (TL) process using GA as the model solver. The objective of the TL is to transfer the knowledge from one problem to another related problem. This process imitates how humans think in their daily life. In this paper, we proposed to study a case where the knowledge transferred from the S problem has less information than what the T problem needs. We sampled the transferred population using different strategies of TL. The results showed transfer part of the knowledge is helpful and speeds the GA process of finding a solution to the problem.

Keywords: transfer learning, partial transfer, evolutionary computation, genetic algorithm

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Ravneil Nand

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Cooperative coevolution uses problem decomposition methods to solve a larger problem. The problem decomposition deals with breaking down the larger problem into a number of smaller sub-problems depending on their method. Different problem decomposition methods have their own strengths and limitations depending on the neural network used and application problem. In this paper we are introducing a new problem decomposition method known as Hidden-Neuron Level Decomposition (HNL). The HNL method is competing with established problem decomposition method in time series prediction. The results show that the proposed approach has improved the results in some benchmark data sets when compared to the standalone method and has competitive results when compared to methods from literature.

Keywords: cooperative coevaluation, feed forward network, problem decomposition, neuron, synapse

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Authors: Ebrahim Alrashed

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Wireless sensor networks are vulnerable to attacks from adversaries attempting to disrupt their operations. Sink-hole attacks are a type of attack where an adversary node drops data forwarded through it and hence affecting the reliability and accuracy of the network. Since sensor nodes have limited battery power, it is essential that any solution to the sinkhole attack problem be very energy-aware. In this paper, we present a reliable and energy efficient scheme to forward data from source nodes to the base station while under sink-hole attack. The scheme also detects sink-hole attack nodes and avoid paths that includes them.

Keywords: energy-aware routing, reliability, sink-hole attack, WSN

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Authors: Diana Fajardo, Sebastián Ortiz, Oscar Herrera, Angélica Santis

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Currently, in Colombia is arising a problem related to collecting used lubricant oils which are generated by the increment of the vehicle fleet. This situation does not allow a proper disposal of this type of waste, which in turn results in a negative impact on the environment. Therefore, through the comparative analysis of various heuristics, the best solution to the VRP (Vehicle Routing Problem) was selected by comparing costs and times for the collection of used lubricant oils in the city of Pereira, Colombia; since there is no presence of management companies engaged in the direct administration of the collection of this pollutant. To achieve this aim, six proposals of through methods of solution of two phases were discussed. First, the assignment of the group of generator points of the residue was made (previously identified). Proposals one and four of through methods are based on the closeness of points. The proposals two and five are using the scanning method and the proposals three and six are considering the restriction of the capacity of collection vehicle. Subsequently, the routes were developed - in the first three proposals by the Clarke and Wright's savings algorithm and in the following proposals by the Traveling Salesman optimization mathematical model. After applying techniques, a comparative analysis of the results was performed and it was determined which of the proposals presented the most optimal values in terms of the distance, cost and travel time.

Keywords: Heuristics, optimization Model, savings algorithm, used vehicular oil, V.R.P.

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Authors: Feng Tao, Ma Jing, Guo Xian, Wang Jing

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Named Data Networking (NDN) replaces IP address of traditional network with data name, and adopts dynamic cache mechanism. In the existing mechanism, however, only one-to-one search can be achieved because every data has a unique name corresponding to it. There is a certain mapping relationship between data content and data name, so if the data name is intercepted by an adversary, the privacy of the data content and user’s interest can hardly be guaranteed. In order to solve this problem, this paper proposes a one-to-many fuzzy search scheme based on order-preserving encryption to reduce the query overhead by optimizing the caching strategy. In this scheme, we use hash value to ensure the user’s query safe from each node in the process of search, so does the privacy of the requiring data content.

Keywords: NDN, order-preserving encryption, fuzzy search, privacy

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Authors: J. Van Engeland, C. Lavigne, S. De Jaeger

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In the light of the transition towards a more circular economy, recovery of products, parts or materials will gain in importance. Additionally, the EU proximity principle related to waste management and emissions generated by transporting large amounts of end-of-life products, shift attention to local recovery networks. The Flemish inter-communal cooperation for municipal solid waste management Meetjesland (IVM) is currently investigating the set-up of such a network. More specifically, the network encompasses the recycling of polyvinyl chloride (PVC), which is collected in separate containers. When these containers are full, a truck should transport them to the processor which can recycle the PVC into new products. This paper proposes a model to optimize the container collection. The containers are located at different Civic Amenity sites (CA sites) in a certain region. Since people can drop off their waste at these CA sites, the containers will gradually fill up during a planning horizon. If a certain container is full, it has to be collected and replaced by an empty container. The collected waste is then transported to a single processor. To perform this collection and transportation of containers, the responsible firm has a set of vehicles stationed at a single depot and different personnel crews. A vehicle can load exactly one container. If a trailer is attached to the vehicle, it can load an additional container. Each day of the planning horizon, the different crews and vehicles leave the depot to collect containers at the different sites. After loading one or two containers, the crew has to drive to the processor for unloading the waste and to pick up empty containers. Afterwards, the crew can again visit sites or it can return to the depot to end its collection work for that day. All along the collection process, the crew has to respect the opening hours of the sites. In order to allow for some flexibility, a crew is allowed to wait a certain amount of time at the gate of a site until it opens. The problem described can be modelled as a variant to the PVRP-TW (Periodic Vehicle Routing Problem with Time Windows). However, a vehicle can at maximum load two containers, hence only two subsequent site visits are possible. For that reason, we will refer to the model as a model for building tactical waste collection schemes. The goal is to a find a schedule describing which crew should visit which CA site on which day to minimize the number of trucks and the routing costs. The model was coded in IBM CPLEX Optimization studio and applied to a number of test instances. Good results were obtained, and specific suggestions concerning route and truck costs could be made. For a large range of input parameters, collection schemes using two trucks are obtained.

Keywords: container collection, crew scheduling, mixed integer linear programming, waste management

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Authors: Mrinal Jana, Geetanjali Panda

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In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: M. Jamuna Rani, K. Ramanathan

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A steam power plant is housed with various types of equipments like boiler, turbine, heat exchanger etc. These equipments are mainly connected with piping systems. Such a piping layout design depends mainly on stress analysis and flexibility. It will vary with respect to pipe geometrical properties, pressure, temperature, and supports. The present paper is to analyze the presence and effect of hangers and expansion joints in the piping layout/routing using CAESAR-II software. Main aim of piping stress analysis is to provide adequate flexibility for absorbing thermal expansion, code compliance for stresses and displacement incurred in piping system. The design is said to be safe if all these are in allowable range as per code. In this study, a sample problem is considered for analysis as per power piping ASME B31.1 code and the results thus obtained are compared.

Keywords: ASTM B31.1, hanger, expansion joint, CAESAR-II

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Huang Xiaoling, Liu Lufeng

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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, regional transportation network

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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