Search results for: Localization problem

Authors: Hai Quang Hong Dam, Hai Ho, Minh Hoang Le Ngo

Abstract:

This paper investigates the problem of blind speech separation from the speech mixture of two speakers. A voice activity detector employing the Steered Response Power - Phase Transform (SRP-PHAT) is presented for detecting the activity information of speech sources and then the desired speech signals are extracted from the speech mixture by using an optimal beamformer. For evaluation, the algorithm effectiveness, a simulation using real speech recordings had been performed in a double-talk situation where two speakers are active all the time. Evaluations show that the proposed blind speech separation algorithm offers a good interference suppression level whilst maintaining a low distortion level of the desired signal.

Keywords: Blind speech separation, voice activity detector, SRP-PHAT, optimal beamformer.

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Authors: Zohreh O. Akbari

Abstract:

In this paper a deterministic polynomial-time algorithm is presented for the Clique problem. The case is considered as the problem of omitting the minimum number of vertices from the input graph so that none of the zeroes on the graph-s adjacency matrix (except the main diagonal entries) would remain on the adjacency matrix of the resulting subgraph. The existence of a deterministic polynomial-time algorithm for the Clique problem, as an NP-complete problem will prove the equality of P and NP complexity classes.

Keywords: Clique problem, Deterministic Polynomial-time Algorithm, Equality of P and NP Complexity Classes.

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Authors: Ben Mohamed Ahemed Mohamed, Yassine Adnan

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The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins. This article treats the case of objects with a free orientation of 90Ôùª. We propose an approach of resolution combining optimization by colony of ants (ACO) and the heuristic method IMA to resolve this NP-Hard problem.

Keywords: Ant colony algorithm, bin-packing problem, heuristics methods.

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Authors: Lalita Gupta, R. P. Singh

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Array signal processing involves signal enumeration and source localization. Array signal processing is centered on the ability to fuse temporal and spatial information captured via sampling signals emitted from a number of sources at the sensors of an array in order to carry out a specific estimation task: source characteristics (mainly localization of the sources) and/or array characteristics (mainly array geometry) estimation. Array signal processing is a part of signal processing that uses sensors organized in patterns or arrays, to detect signals and to determine information about them. Beamforming is a general signal processing technique used to control the directionality of the reception or transmission of a signal. Using Beamforming we can direct the majority of signal energy we receive from a group of array. Multiple signal classification (MUSIC) is a highly popular eigenstructure-based estimation method of direction of arrival (DOA) with high resolution. This Paper enumerates the effect of missing sensors in DOA estimation. The accuracy of the MUSIC-based DOA estimation is degraded significantly both by the effects of the missing sensors among the receiving array elements and the unequal channel gain and phase errors of the receiver.

Keywords: Array Signal Processing, Beamforming, ULA, Direction of Arrival, MUSIC

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Authors: Xiang Zhang, Daohong Yang, Ziyuan Wu, Lei Li, Wanting Zhou

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Visual Simultaneous Localization and Mapping (VSLAM) uses cameras to gather information in unknown environments to achieve simultaneous localization and mapping of the environment. This technology has a wide range of applications in autonomous driving, virtual reality, and other related fields. Currently, the research advancements related to VSLAM can maintain high accuracy in static environments. But in dynamic environments, the presence of moving objects in the scene can reduce the stability of the VSLAM system, leading to inaccurate localization and mapping, or even system failure. In this paper, a robust VSLAM method was proposed to effectively address the challenges in dynamic environments. We proposed a dynamic region removal scheme based on a semantic segmentation neural network and geometric constraints. Firstly, a semantic segmentation neural network is used to extract the prior active motion region, prior static region, and prior passive motion region in the environment. Then, the lightweight frame tracking module initializes the transform pose between the previous frame and the current frame on the prior static region. A motion consistency detection module based on multi-view geometry and scene flow is used to divide the environment into static regions and dynamic regions. Thus, the dynamic object region was successfully eliminated. Finally, only the static region is used for tracking thread. Our research is based on the ORBSLAM3 system, which is one of the most effective VSLAM systems available. We evaluated our method on the TUM RGB-D benchmark and the results demonstrate that the proposed VSLAM method improves the accuracy of the original ORBSLAM3 by 70%˜98.5% under a high dynamic environment.

Keywords: Dynamic scene, dynamic visual SLAM, semantic segmentation, scene flow, VSLAM.

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Authors: Laila Salah Seada, Ashraf Ibrahim, Fawaz Al Rashid, Ihab Abdo, Hassan Kasim, Waleed Al Mansi, Saud Al Shabli

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Background and Objectives: Colorectal carcinoma is increasing among both men and women worldwide. It has a multifactorial etiology including genetic factors, environmental factors and inflammatory conditions of the digestive tract. A clinicopathologic assessment of colorectal carcinoma in Hail region is done, considering any changing patterns in two 5-year periods from 2005-2009 (A) and from 2012 to 2017 (B). All data had been retrieved from histopathology files of King Khalid Hospital, Hail. Results: During period (A), 75 cases were diagnosed as colorectal carcinoma. Male patients comprised 56/75 (74.7%) of the study, with a mean age of 58.4 (36-97), while females were 19/75 (25.3%) with a mean age of 50.3(30-85) and the difference was significant (p = 0.05). M:F ratio was 2.9:1. Most common histological type was adenocarcioma in 68/75 (90.7%) patients mostly well differentiated in 44/68 (64.7%). Mucinous neoplasms comprised only 7/75 (9.3%) of cases and tended to have a higher stage (p = 0.04). During period (B), 115 cases were diagnosed with an increase of 53.3% in number of cases than period (A). Male to female ratio also decreased to 1.35:1, females being 44.83% more affected. Adenocarcinoma remained the prevalent type (93.9%), while mucinous type was still rare (5.2%). No distal metastases found at time of presentation. Localization of tumors was rectosigmoid in group (A) in 41.4%, which increased to 56.6% in group (B), with an increase of 15.2%. Iliocecal location also decreased from 8% to 3.5%, being 56.25% less. Other proximal areas of the colon were decreased by 25.75%, from 53.9% in group (A) to 40% in group (B). Conclusion: Colorectal carcinoma in Hail region has increased by 53.3% in the past 5 years, with more females being diagnosed. Localization has also shifted distally by 15.2%. These findings are different from Western world patterns which experienced a decrease in incidence and proximal shift of the colon cancer localization. This might be due to better diagnostic tools, population awareness of the disease, as well as changing of life style and/or food habits in the region.

Keywords: Colorectal cancer, Hail Region, changing pattern, distal shift.

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Authors: Maricar G. Misola, Bryan B. Navarro

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Facility Layout Problem (FLP) is one of the essential problems of several types of manufacturing and service sector. It is an optimization problem on which the main objective is to obtain the efficient locations, arrangement and order of the facilities. In the literature, there are numerous facility layout problem research presented and have used meta-heuristic approaches to achieve optimal facility layout design. This paper presented genetic algorithm to solve facility layout problem; to minimize total cost function. The performance of the proposed approach was verified and compared using problems in the literature.

Keywords: Facility Layout Problem, Genetic Algorithm, Material Handling Cost, Meta-heuristic Approach.

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

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This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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Authors: Buthainah Fahran Al-Dulaimi, Hamza A. Ali

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The well known NP-complete problem of the Traveling Salesman Problem (TSP) is coded in genetic form. A software system is proposed to determine the optimum route for a Traveling Salesman Problem using Genetic Algorithm technique. The system starts from a matrix of the calculated Euclidean distances between the cities to be visited by the traveling salesman and a randomly chosen city order as the initial population. Then new generations are then created repeatedly until the proper path is reached upon reaching a stopping criterion. This search is guided by a solution evaluation function.

Keywords: Genetic algorithms, traveling salesman problem solving, optimization.

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: I. Mahdavi, A. Jazayeri, M. Jahromi, R. Jafari, H. Iranmanesh

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One of the most important problems in production planning of flexible manufacturing system (FMS) is machine tool selection and operation allocation problem that directly influences the production costs and times .In this paper minimizing machining cost, set-up cost and material handling cost as a multi-objective problem in flexible manufacturing systems environment are considered. We present a 0-1 integer linear programming model for the multiobjective machine tool selection and operation allocation problem and due to the large scale nature of the problem, solving the problem to obtain optimal solution in a reasonable time is infeasible, Paretoant colony optimization (P-ACO) approach for solving the multiobjective problem in reasonable time is developed. Experimental results indicate effectiveness of the proposed algorithm for solving the problem.

Keywords: Flexible manufacturing system, Production planning, Machine tool selection, Operation allocation, Multiobjective optimization, Metaheuristic.

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Authors: Somnath Dey, Debasis Samanta

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Iris-based biometric system is gaining its importance in several applications. However, processing of iris biometric is a challenging and time consuming task. Detection of iris part in an eye image poses a number of challenges such as, inferior image quality, occlusion of eyelids and eyelashes etc. Due to these problems it is not possible to achieve 100% accuracy rate in any iris-based biometric authentication systems. Further, iris detection is a computationally intensive task in the overall iris biometric processing. In this paper, we address these two problems and propose a technique to localize iris part efficiently and accurately. We propose scaling and color level transform followed by thresholding, finding pupil boundary points for pupil boundary detection and dilation, thresholding, vertical edge detection and removal of unnecessary edges present in the eye images for iris boundary detection. Scaling reduces the search space significantly and intensity level transform is helpful for image thresholding. Experimental results show that our approach is comparable with the existing approaches. Following our approach it is possible to detect iris part with 95-99% accuracy as substantiated by our experiments on CASIA Ver-3.0, ICE 2005, UBIRIS, Bath and MMU iris image databases.

Keywords: Iris recognition, iris localization, biometrics, image processing.

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Authors: Jindřiška Šedová, Miloš Šeda

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This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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Authors: Tami Alghamdi, Terence Soule

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed that combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: Transfer Learning, Multiple Sources, Knowledge Transfer, Domain Adaptation, Source, Target.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

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A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: S. Nasri, H. Bouziri

Abstract:

Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: Dynamic network flow, Load dependent transit time, Evacuation strategy, Earliest arrival flow problem.

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Authors: Bremananth R., Veerabadran C. S., Andy W. H. Khong

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Automatic reading of handwritten cheque is a computationally complex process and it plays an important role in financial risk management. Machine vision and learning provide a viable solution to this problem. Research effort has mostly been focused on recognizing diverse pitches of cheques and demand drafts with an identical outline. However most of these methods employ templatematching to localize the pitches and such schemes could potentially fail when applied to different types of outline maintained by the bank. In this paper, the so-called outline problem is resolved by a cheque information tree (CIT), which generalizes the localizing method to extract active-region-of-entities. In addition, the weight based density plot (WBDP) is performed to isolate text entities and read complete pitches. Recognition is based on texture features using neural classifiers. Legal amount is subsequently recognized by both texture and perceptual features. A post-processing phase is invoked to detect the incorrect readings by Type-2 grammar using the Turing machine. The performance of the proposed system was evaluated using cheque and demand drafts of 22 different banks. The test data consists of a collection of 1540 leafs obtained from 10 different account holders from each bank. Results show that this approach can easily be deployed without significant design amendments.

Keywords: Cheque reading, Connectivity checking, Text localization, Texture analysis, Turing machine, Signature verification.

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Authors: M. Dinakaran, P. Balasubramanie

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With the demand of mobility by users, wireless technologies have become the hotspot developing arena. Internet Engineering Task Force (IETF) working group has developed Mobile IP to support node mobility. The concept of node mobility indicates that in spite of the movement of the node, it is still connected to the internet and all the data transactions are preserved. It provides location-independent access to Internet. After the incorporation of host mobility, network mobility has undergone intense research. There are several intricacies faced in the real world implementation of network mobility significantly the problem of nested networks and their consequences. This article is concerned regarding a problem of nested network called pinball route problem and proposes a solution to eliminate the above problem. The proposed mechanism is implemented using NS2 simulation tool and it is found that the proposed mechanism efficiently reduces the overload caused by the pinball route problem.

Keywords: Mobile IP, Pinball routing problem, NEMO

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

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Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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Authors: S. H. Mohades Kasaei, S. M. Mohades Kasaei, S. A. Mohades Kasaei, M. Taheri, M. Rahimi, H. Vahiddastgerdi, M. Saeidinezhad

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Omni directional mobile robots have been popularly employed in several applications especially in soccer player robots considered in Robocup competitions. However, Omni directional navigation system, Omni-vision system and solenoid kicking mechanism in such mobile robots have not ever been combined. This situation brings the idea of a robot with no head direction into existence, a comprehensive Omni directional mobile robot. Such a robot can respond more quickly and it would be capable for more sophisticated behaviors with multi-sensor data fusion algorithm for global localization base on the data fusion. This paper has tried to focus on the research improvements in the mechanical, electrical and software design of the robots of team ADRO Iran. The main improvements are the world model, the new strategy framework, mechanical structure, Omni-vision sensor for object detection, robot path planning, active ball handling mechanism and the new kicker design, , and other subjects related to mobile robot

Keywords: Mobile robot, Machine vision, Omni directional movement, Autonomous Systems, Robot path planning, Object Localization.

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Authors: Divyesh Patel, Tanuja Srivastava

Abstract:

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.

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Authors: A. Badoud, M. Khemliche, S. Latreche

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The main objective developed in this paper is to find a graphic technique for modeling, simulation and diagnosis of the industrial systems. This importance is much apparent when it is about a complex system such as the nuclear reactor with pressurized water of several form with various several non-linearity and time scales. In this case the analytical approach is heavy and does not give a fast idea on the evolution of the system. The tool Bond Graph enabled us to transform the analytical model into graphic model and the software of simulation SYMBOLS 2000 specific to the Bond Graphs made it possible to validate and have the results given by the technical specifications. We introduce the analysis of the problem involved in the faults localization and identification in the complex industrial processes. We propose a method of fault detection applied to the diagnosis and to determine the gravity of a detected fault. We show the possibilities of application of the new diagnosis approaches to the complex system control. The industrial systems became increasingly complex with the faults diagnosis procedures in the physical systems prove to become very complex as soon as the systems considered are not elementary any more. Indeed, in front of this complexity, we chose to make recourse to Fault Detection and Isolation method (FDI) by the analysis of the problem of its control and to conceive a reliable system of diagnosis making it possible to apprehend the complex dynamic systems spatially distributed applied to the standard pressurized water nuclear reactor.

Keywords: Bond Graph, Modeling, Simulation, Monitoring, Analytical Redundancy Relations, Pressurized Water Reactor, Directed Graph.

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Authors: R. Hashemi, M.H.Kargarnovin

Abstract:

This paper presents the identification of the impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and the genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness vs. the measurement noise and sensor location.

Keywords: Genetic Algorithm, Inverse problem, Optimization, Vibration.

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: Binary cat swarm optimization, set covering problem, metaheuristic, binarization methods.

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

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The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

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

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Authors: Halizah Awang, Ishak Ramly

Abstract:

Problem-based learning (PBL) is one of the student centered approaches and has been considered by a number of higher educational institutions in many parts of the world as a method of delivery. This paper presents a creative thinking approach for implementing Problem-based Learning in Mechanics of Structure within a Malaysian Polytechnics environment. In the learning process, students learn how to analyze the problem given among the students and sharing classroom knowledge into practice. Further, through this course-s emphasis on problem-based learning, students acquire creative thinking skills and professional skills as they tackle complex, interdisciplinary and real-situation problems. Once the creative ideas are generated, there are useful additional techniques for tender ideas that will grow into a productive concept or solution. The combination of creative skills and technical abilities will enable the students to be ready to “hit-the-ground-running" and produce in industry when they graduate.

Keywords: Creative Thinking Skills, Problem-based Learning, Problem Solving.

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s problem solves the problem of fitting three circles into a right triangle such that these three 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; it is called the 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 the 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 the 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 as in Tri(Tn) problems. We call these problems the Carc(Tn) problems. The algorithm is a mO(Tn) algorithm, where m is the number of iterations in the loop. It takes less than 1000 iterations and less than 1 second for the Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties. This algorithm gives a solution for circle packing problem inside convex circular triangle with arbitrarily-sized circles. Many applications concerning circle packing may come from the result of the algorithm, such as logo design, architecture design, etc.

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

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Authors: Fatma A. Karkory, Ali A. Abudalmola

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The travelling salesman problem (TSP) is a combinatorial optimization problem in which the goal is to find the shortest path between different cities that the salesman takes. In other words, the problem deals with finding a route covering all cities so that total distance and execution time is minimized. This paper adopts the nearest neighbor and minimum spanning tree algorithm to solve the well-known travelling salesman problem. The algorithms were implemented using java programming language. The approach is tested on three graphs that making a TSP tour instance of 5-city, 10 –city, and 229–city. The computation results validate the performance of the proposed algorithm.

Keywords: Heuristics, minimum spanning tree algorithm, Nearest Neighbor, Travelling Salesman Problem (TSP).

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