Search results for: simulation constraint

Authors: Nebras Gharbi, Itebeddine Ghorbel

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In the latest years and with the advancements of the multicore computing world, the constraint programming community tried to benefit from the capacity of new machines and make the best use of them through several parallel schemes for constraint solving. In this paper, we propose a survey of the different proposed approaches to solve Constraint Satisfaction Problems using parallel architectures. These approaches use in a different way a parallel architecture: the problem itself could be solved differently by several solvers or could be split over solvers.

Keywords: constraint programming, parallel programming, constraint satisfaction problem, speed-up

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Authors: Sanam Haseen, Abdul Bari

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In this paper a three stage multivariate programming problem with random survey cost and variances as random variables has been formulated as a non-linear stochastic programming problem. The problem has been converted into an equivalent deterministic form using chance constraint programming and modified E-modeling. An empirical study of the problem has been done at the end of the paper using R-simulation.

Keywords: chance constraint programming, modified E-model, stochastic programming, stratified sample surveys, three stage sample surveys

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Authors: Tzu-Yang Lin, Chuan-Ching Sue

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Sleep mechanisms are commonly used to ensure the energy efficiency of each optical network unit (ONU) that concerns a single class delay constraint in the Ethernet Passive Optical Network (EPON). How long the ONUs can sleep without violating the delay constraint has become a research problem. Particularly, we can derive an analytical model to determine the optimal sleep time of ONUs in every cycle without violating the maximum class delay constraint. The bandwidth allocation considering such optimal sleep time is called Green Bandwidth Allocation (GBA). Although the GBA mechanism guarantees that the different class delay constraints do not violate the maximum class delay constraint, packets with a more relaxed delay constraint will be treated as those with the most stringent delay constraint and may be sent early. This means that the ONU will waste energy in active mode to send packets in advance which did not need to be sent at the current time. Accordingly, we proposed a QoS-aware GBA using a novel intra-ONU scheduling to control the packets to be sent according to their respective delay constraints, thereby enhancing energy efficiency without deteriorating delay performance. If packets are not explicitly classified but with different packet delay constraints, we can modify the intra-ONU scheduling to classify packets according to their packet delay constraints rather than their classes. Moreover, we propose the switchable ONU architecture in which the ONU can switch the architecture according to the sleep time length, thus improving energy efficiency in the QoS-aware GBA. The simulation results show that the QoS-aware GBA ensures that packets in different classes or with different delay constraints do not violate their respective delay constraints and consume less power than the original GBA.

Keywords: Passive Optical Networks, PONs, Optical Network Unit, ONU, energy efficiency, delay constraint

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Authors: Sangwon Han, Chengquan Jin

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Time-cost trade-off (TCTO) is one of the most significant part of construction project management. Despite the significance, current TCTO analysis, based on the Critical Path Method, does not consider resource constraint, and accordingly sometimes generates an impractical and/or infeasible schedule planning in terms of resource availability. Therefore, resource constraint needs to be considered when doing TCTO analysis. In this research, genetic algorithms (GA) based optimization model is created in order to find the optimal schedule. This model is utilized to compare four distinct scenarios (i.e., 1) initial CPM, 2) TCTO without considering resource constraint, 3) resource allocation after TCTO, and 4) TCTO with considering resource constraint) in terms of duration, cost, and resource utilization. The comparison results identify that ‘TCTO with considering resource constraint’ generates the optimal schedule with the respect of duration, cost, and resource. This verifies the need for consideration of resource constraint when doing TCTO analysis. It is expected that the proposed model will produce more feasible and optimal schedule.

Keywords: time-cost trade-off, genetic algorithms, critical path, resource availability

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Authors: Safayat Ali Shaikh

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Software has been developed for optimal cropping pattern in an irrigation project considering land constraint, water availability constraint and pick up flow constraint using modified Simplex Algorithm. Artificial Neural Network Models (ANN) have been developed to predict rainfall. AR (1) model used to generate 1000 years rainfall data to train the ANN. Simulation has been done with expected rainfall data. Eight number crops and three types of soil class have been considered for optimization model. Area under each crop and each soil class have been quantified using Modified Simplex Algorithm to get optimum net return. Efficacy of the software has been tested using data of large irrigation project in India.

Keywords: artificial neural network, large irrigation project, modified simplex algorithm, optimal cropping pattern

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Authors: Khodamorad Nabaki, Jianhu Shen, Xiaodong Huang

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This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.

Keywords: topology optimization, BESO method, p-norm, fatigue constraint

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Authors: M. Alam, P. Seshaiyer

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The rupture predictability of intracranial aneurysm is one of the most important parameters for physicians in surgical treatment. As most of the intracranial aneurysms are asymptomatic, still the rupture potential of both symptomatic and asymptomatic lesions is relatively unknown. Moreover, an intracranial aneurysm constrained by a nerve tissue might be a common scenario for a physician to deal with during the treatment process. Here, we perform a computational modeling of nerve tissue constrained intracranial saccular aneurysm to show a protective role of constrained tissue on the aneurysm. A comparative parametric study of the model also performs taking long constraint, medium constraint, short constraint, point contact, narrow neck aneurysm, wide neck aneurysm as parameters for the analysis. Results show that contact constraint aneurysm generates less stress near the fundus compared to no constraint aneurysm, hence works as a protective wall for the aneurysm not to be ruptured.

Keywords: rupture potential, intracranial saccular aneurysm, anisotropic hyper-elastic material, finite element analysis

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Authors: Uyanga Sukhbaatar, Ahmed Lbath, Mendamar Majig

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The Orienteering Problem is the most known example to start modeling tourist trip design problem. In order to meet tourist’s interest and constraint the OP is becoming more and more complicate to solve. The Multi Constraint Team Orienteering Problem with Time Windows is the last extension of the OP which differentiates from other extensions by including more extra associated constraints. The goal of the MCTOPTW is maximizing tourist’s satisfaction score in same time not to violate any of these constraints. This paper presents a genetic algorithmic approach to tackle the MCTOPTW. The benchmark data from literature is tested by our algorithm and the performance results are compared.

Keywords: multi constraint team orienteering problem with time windows, genetic algorithm, tour planning system

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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: Ahmed Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: airport terminal, integer programming, scheduling, simulation

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Authors: Yohei Saika

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On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, multiple interferograms, statistical mechanics

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Authors: Abdessalem Abbassi, Ahlem Dakhlaoui, Lota D. Tamini

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In this paper, we analyze infinite discrete-time games between hydraulic and thermal power operators in the wholesale electricity market under Cournot competition. We consider a deregulated electrical industry where certain demand is satisfied by hydraulic and thermal technologies. The hydraulic operator decides the production in each season of each period that maximizes the sum of expected profits from power generation with respect to the stochastic dynamic constraint on the water stored in the dam, the environmental constraint and the non-negative output constraint. In contrast, the thermal plant is operated with quadratic cost function, with respect to the capacity production constraint and the non-negativity output constraint. We show that under imperfect competition, the hydraulic operator has a strategic storage of water in the peak season. Then, we quantify the strategic inter-annual and intra-annual water transfer and compare the numerical results. Finally, we show that the thermal operator can restrict the hydraulic output without compensation.

Keywords: asymmetric risk aversion, electricity wholesale market, hydropower dams, imperfect competition

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Authors: Zijian Cheng, Frank Liu, Yupu Sun

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The relationship between the intensity of share pledging activities and the level of financial constraint in publicly listed firms in China is examined in this paper. Empirical results show that the high financial constraint level may motivate insiders to use share pledging as an alternative funding source and an expropriation mechanism. Share collateralization can cause a subsequently more constrained financing condition. Evidence is found that share pledging made by the controlling shareholder is likely to mitigate financial constraints in the following year. Research findings are robust to alternative measures and an instrumental variable for dealing with endogeneity problems.

Keywords: share pledge, financial constraint, controlling shareholder, dividend policy

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Authors: Mahdi Biabanaki

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Religion is present in all human societies and has been for tens of thousands of years. What is noteworthy is that although religious traditions vary in different societies, there are considerable similarities in their religious beliefs. In all human cultures, for example, there is a widespread belief in the afterlife. Cognitive science of Religion (CSR), an emerging branch of cognitive science, searches for the root of these widespread similarities and the widespread prevalence of beliefs such as beliefs in the afterlife in common mental structures among humans. Accordingly, the cognitive architecture of the human mind has evolved to produce such beliefs automatically and non-reflectively. For CSR researchers, belief in the afterlife is an intuitive belief resulting from the functioning of mental tools. Our purpose in this article is to extract and evaluate the cognitive explanations presented in the CSR field for explaining beliefs in the afterlife. Our research shows that there are two basic theories in this area of CSR, namely "intuitive dualism" and "simulation constraint" theory. We show that these two theories face four major challenges and limitations in explaining belief in the afterlife: inability to provide a causal explanation, inability to explain cultural/religious differences in afterlife belief, the lack of distinction between the natural and the rational foundations of belief in the afterlife and disregarding the supernatural foundations of the afterlife belief.

Keywords: afterlife, cognitive science of religion, intuitive dualism, simulation constraint

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Authors: Martha Ndeley, John Ikome

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In this paper, we expand the scope of constraint-directed techniques to deal with the case of transportation schedule with capacity restrictions where the scheduling problem includes alternative activities. That is, not only does the scheduling problem consist of determining when an activity is to be executed, but also determining which set of alternative activities is to be executed at all level of transportation from input to output. Such problems encompass both alternative resource problems and alternative process plan problems. We formulate a constraint-based representation of alternative activities to model problems containing such choices. We then extend existing constraint-directed scheduling heuristic commitment techniques and propagators to reason directly about the fact that an activity does not necessarily have to exist in a final transportation schedule without being completed. Tentative results show that an algorithm using a novel texture-based heuristic commitment technique propagators achieves the best overall performance of the techniques tested.

Keywords: production, transportation, scheduling, integrated

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Authors: Chee Sun Won

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This paper presents the size reduction of images for machine-to-machine communications. Here, the salient image regions to be preserved include the image patches of the key-points such as corners and blobs. Based on a saliency image map from the key-points and their image patches, an axis-aligned grid-size optimization is proposed for the reduction of image size. To increase the size-reduction efficiency the aspect ratio constraint is relaxed in the constraint optimization framework. The proposed method yields higher matching accuracy after the size reduction than the conventional content-aware image size-reduction methods.

Keywords: image compression, image matching, key-point detection and description, machine-to-machine communication

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Authors: Wolfram Jahn, Jose Manuel Munita

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While computational fluid dynamics (CFD) simulations of fire scenarios are commonly used in the design of buildings, less attention has been given to the use of CFD simulations as an operational tool for the fire services. The reason of this lack of attention lies mainly in the fact that CFD simulations typically take large periods of time to complete, and their results would thus not be available in time to be of use during an emergency. Firefighters often face uncertain conditions when entering a building to attack a fire. They would greatly benefit from a technology based on predictive fire simulations, able to assist their decision-making process. The principal constraint to faster CFD simulations is the fine grid necessary to solve accurately the physical processes that govern a fire. This paper explores the possibility of overcoming this constraint and using coarse grid CFD simulations for fire scenarios, and proposes a methodology to use the simulation results in a meaningful way that can be used by the fire fighters during an emergency. Data from real scale compartment fire tests were used to compare CFD fire models with different grid arrangements, and empirical correlations were obtained to interpolate data points into the grids. The results show that the strongly predominant effect of the heat release rate of the fire on the fluid dynamics allows for the use of coarse grids with relatively low overall impact of simulation results. Simulations with an acceptable level of accuracy could be run in real time, thus making them useful as a forecasting tool for emergency response purposes.

Keywords: CFD, fire simulations, emergency response, forecast

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Authors: Raneem Osama Salem, Ayesha Nuzhat, Fatimah Nasser Al Shehri, Nasser Al Hamdan

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Background: Recently, most medical schools around the globe are using simulation for teaching and assessing students’ clinical skills and competence. There are many obstacles that could face students and faculty when simulation sessions are introduced into undergraduate curriculum. Objective: The aim of this study is to obtain the opinion of undergraduate medical students and our faculty regarding the role of simulation in undergraduate curriculum, the simulation modalities used, and perceived barriers in implementing stimulation sessions. Methods: To address the role of simulation, modalities used, and perceived challenges to implementation of simulation sessions, a self-administered pilot tested questionnaire with 18 items using a 5 point Likert scale was distributed. Participants included undergraduate male medical students (n=125) and female students (n=70) as well as the faculty members (n=14). Result: Various learning outcomes are achieved and improved through the technology enhanced simulation sessions such as communication skills, diagnostic skills, procedural skills, self-confidence, and integration of basic and clinical sciences. The use of high fidelity simulators, simulated patients and task trainers was more desirable by our students and faculty for teaching and learning as well as an evaluation tool. According to most of the students,' institutional support in terms of resources, staff and duration of sessions was adequate. However, motivation to participate in the sessions and provision of adequate feedback by the staff was a constraint. Conclusion: The use of simulation laboratory is of great benefit to the students and a great teaching tool for the staff to ensure students learning of the various skills.

Keywords: simulators, medical students, skills, simulated patients, performance, challenges, skill laboratory

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Authors: G. R. Kavitha, T. S. Indumathi

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With the constantly rising demands of the multimedia services, the requirements of long haul transport network are constantly changing in the area of optical network. Maximum data transmission using optimization of the communication channel poses the biggest challenge. Although there has been a constant focus on this area from the past decade, there was no evidence of a significant result that has been accomplished. Hence, after reviewing some potential design of optical network from literatures, it was understood that optical signal to noise ratio was one of the elementary attributes that can define the performance of the optical network. In this paper, we propose a framework termed as ECON (Enhanced Constraint-based Optical Network) that primarily optimize the optical signal to noise ratio using ROADM. The simulation is performed in Matlab and optical signal to noise ratio is extracted considering the system matrix. The outcome of the proposed study shows that optimized OSNR as compared to the existing studies.

Keywords: component, optical network, reconfigurable optical add-drop multiplexer, optical signal-to-noise ratio

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Authors: Matloub Hussaina

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This paper investigates the impact of information sharing and capacity constraints on backlog bullwhip effect of Automatic Pipe Line Inventory and Order Based Production Control System (APIOBPCS). System dynamic simulation using iThink Software has been applied. It has been found that smooth ordering by Tier 1 can be achieved when Tier 1 has medium capacity constraints. Simulation experiments also show that information sharing helps to reduce 50% of backlog bullwhip effect in capacitated supply chains. This knowledge is of value per se, giving supply chain operations managers and designers a practical way in to controlling the backlog bullwhip effect. Future work should investigate the total cost implications of capacity constraints and safety stocks in multi-echelon supply chain.

Keywords: supply chain dynamics, information sharing, capacity constraints, simulation, APIOBPCS

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Authors: Oğuzhan Urhan

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In this paper, an improved motion estimation (ME) approach based on weighted constrained one-bit transform is proposed for block-based ME employed in video encoders. Binary ME approaches utilize low bit-depth representation of the original image frames with a Boolean exclusive-OR based hardware efficient matching criterion to decrease computational burden of the ME stage. Weighted constrained one-bit transform (WC‑1BT) based approach improves the performance of conventional C-1BT based ME employing 2-bit depth constraint mask instead of a 1-bit depth mask. In this work, the range of constraint mask is further extended to increase ME performance of WC-1BT approach. Experiments reveal that the proposed method provides better ME accuracy compared existing similar ME methods in the literature.

Keywords: fast motion estimation; low-complexity motion estimation, video coding

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Authors: M. F. F. Ab Rashid, A. N. Mohd Rose, N. M. Z. Nik Mohamed, W. S. Wan Harun, S. A. Che Ghani

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Traveling salesman problem with precedence constraint (TSPPC) is one of the most complex problems in combinatorial optimization. The existing algorithms to solve TSPPC cost large computational time to find the optimal solution. The purpose of this paper is to present an efficient genetic algorithm that guarantees optimal solution with less number of generations and iterations time. Unlike the existing algorithm that generates priority factor as chromosome, the proposed algorithm directly generates sequence of solution as chromosome. As a result, the proposed algorithm is capable of generating optimal solution with smaller number of generations and iteration time compare to existing algorithm.

Keywords: traveling salesman problem, sequencing, genetic algorithm, precedence constraint

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Authors: N. Gharbi

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Constraint Satisfaction problems are mathematical problems that are often used to model many real-world problems for which we look if there exists a solution satisfying all its constraints. Table constraints are important for modeling parts of many problems since they list all combinations of allowed or forbidden values. However, they admit practical limitations because they are sometimes too large to be represented in a direct way. In this paper, we present a survey of the different categories of the proposed approaches to compress table constraints in order to reduce both space and time complexities.

Keywords: constraint programming, compression, data mining, table constraints

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Authors: Phinyo Mueangmeesap

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This paper describes about pure sinusoidal inverter simulation and implementation from high voltage DC (156 Vdc). This simulation is to study and improve the efficiency of the inverter. By reducing the loss of power from boost converter in current inverter. The simulation is done by using the H-bridge circuit with pulse width modulate (PWM) signal and low-pass filter circuit. To convert the DC into AC. This paper used the PSCad for simulation. The result of simulation can be used to create prototype inverter by converting 156 Vdc to 110Vac. The inverter gives the output signal similar to the output from a simulation.

Keywords: inverter simulation, PWM signal, single-phase inverter, sinusoidal inverter

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

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Authors: Yueguang Gao, Qi Huang, Shunshan Feng

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In order to study the process and characteristic of the fragments in the warhead with one end cap under full constraint condition, we established a cylindrical casing with two end caps which one of which was fully constrained using the simulation analysis. The result showed that the fragmentation of cylindrical casing with one end full constrained has its own characteristic. The Mach stem was generated when the detonation wave propagated to the fully constrained end cap under the condition of one end detonation, working on unreactive explosives and causing the nearby fragment subjected to nearly 2.5 times the normal pressure to obtain a higher speed. The cylindrical casing first ruptured at the contact surface with the fully constrained end, and then at the end cover of the initiating end, and then the rupture extends to the whole cylindrical casing. The detonation products started to leak out from the rupture. Driving fragments to fly and forming two dense flying areas. The analysis of this paper can provide a reference for the optimal design of this kind of warhead.

Keywords: fragment, cylindrical casing, detonation waves, numerical simulation

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Authors: Lydia Novozhilova, Vladimir Urazhdin

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An optimization problem for reinforced thin-walled vessels under uniform external pressure is considered. The conventional approaches to optimization generally start with pre-defined geometric parameters of the vessels, and then employ analytic or numeric calculations and/or experimental testing to verify functionality, such as stability under the projected conditions. The proposed approach consists of two steps. First, the feasibility domain will be identified in the multidimensional parameter space. Every point in the feasibility domain defines a design satisfying both geometric and functional constraints. Second, an objective function defined in this domain is formulated and optimized. The broader applicability of the suggested methodology is maximized by implementing the Support Vector Machines (SVM) classification algorithm of machine learning for identification of the feasible design region. Training data for SVM classifier is obtained using the Simulation package of SOLIDWORKS®. Based on the data, the SVM algorithm produces a curvilinear boundary separating admissible and not admissible sets of design parameters with maximal margins. Then optimization of the vessel parameters in the feasibility domain is performed using the standard algorithms for the constrained optimization. As an example, optimization of a ring-stiffened closed cylindrical thin-walled vessel with semi-spherical caps under high external pressure is implemented. As a functional constraint, von Mises stress criterion is used but any other stability constraint admitting mathematical formulation can be incorporated into the proposed approach. Suggested methodology has a good potential for reducing design time for finding optimal parameters of thin-walled vessels under uniform external pressure.

Keywords: design parameters, feasibility domain, von Mises stress criterion, Support Vector Machine (SVM) classifier

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Authors: Jiri Barta

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This paper deals with a simulation programs and technologies using in the educational process for members of the crisis management. Risk analysis, simulation, preparation and planning are among the main activities of workers of crisis management. Made correctly simulation of emergency defines the extent of the danger. On this basis, it is possible to effectively prepare and plan measures to minimize damage. The paper is focused on simulation programs that are trained at the University of Defence. Implementation of the outputs from simulation programs in decision-making processes of crisis staffs is one of the main tasks of the research project.

Keywords: crisis management, continuity, critical infrastructure, dangerous substance, education, flood, simulation programs

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Authors: Jelili Kunle Adedeji, Toeb Akorede Akinbola

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The problem of vehicle mishap as a result of miscalculation, recklessness, or malfunction of some part in a vehicle is acknowledged to be a global issue. In most of the cases, it results into death or life injuries, all over the world; the issue becomes a nightmare to the stakeholders on how to curb mishaps on our roads due to these endemic factors. Hence this research typically examined the design of a device, specifically for learners that can lead to a society of intelligent vehicles (traffic) without withdrawing the driving authority from them, unlike pre-existing systems. Though ILASS shears a lot of principle with existing advance drivers assistance systems, yet there are two fundamental differences between ILASS system and existing systems. Firstly ILASS is meant to accept continuous input from the throttle at all time such that the devices will not constraint the driving process unnecessarily and ensure a change of speed at any point in time. Secondly, it made use of a variable threshold distance between the host vehicle and front vehicle which can be set by the host driver under the constraint of road maintenance agency, who communicates the minimum possible threshold for a different lane to the host vehicle. The results obtained from the simulation of the ILASS system concluded that ILASS is a good solution to road accidents, particularly road accident which occurs as a result of driving at high speed.

Keywords: front-vehicle, host-speed, threshold-distance, ILASS

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Authors: Bahare Fatemi, Seyed Mehran Kazemi, Nazanin Mehrasa

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Sudoku is a logic-based combinatorial puzzle game which people in different ages enjoy playing it. The challenging and addictive nature of this game has made it a ubiquitous game. Most magazines, newspapers, puzzle books, etc. publish lots of Sudoku puzzles every day. These puzzles often come in different levels of difficulty so that all people, from beginner to expert, can play the game and enjoy it. Generating puzzles with different levels of difficulty is a major concern of Sudoku designers. There are several works in the literature which propose ways of generating puzzles having a desirable level of difficulty. In this paper, we propose a method based on constraint satisfaction problems to evaluate the difficulty of the Sudoku puzzles. Then, we propose a hill climbing method to generate puzzles with different levels of difficulty. Whereas other methods are usually capable of generating puzzles with only few number of difficulty levels, our method can be used to generate puzzles with arbitrary number of different difficulty levels. We test our method by generating puzzles with different levels of difficulty and having a group of 15 people solve all the puzzles and recording the time they spend for each puzzle.

Keywords: constraint satisfaction problem, generating Sudoku puzzles, hill climbing

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