Search results for: spatial problem solving

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Wang Xingjuan, Qian Dongming

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As a common thinking ability, spatial thinking ability plays an increasingly important role in the information age. The key to cultivating students' spatial thinking ability is to cultivate students' ability to process and transform graphics. The 3D printing course enables students to constantly touch the rotation and movement of objects during the modeling process and to understand spatial graphics from different views. To this end, this article combines the classic PSVT: R test to explore the impact of 3D printing courses on the spatial thinking ability of middle school students. The results of the study found that: (1) Through the study of the 3D printing course, the students' spatial ability test scores have been significantly improved, which indirectly reflects the improvement of the spatial thinking ability level. (2) The student's spatial thinking ability test results are influenced by the parent's occupation.

Keywords: 3D printing, middle school students, spatial thinking ability, influence

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: Alireza Mirrashid, Mohammad Khoshbin, Ali Atghaei, Hassan Shahbazi

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In various industries, smoke and fire are two of the most important threats in the workplace. One of the common methods for detecting smoke and fire is the use of infrared thermal and smoke sensors, which cannot be used in outdoor applications. Therefore, the use of vision-based methods seems necessary. The problem of smoke and fire detection is spatiotemporal and requires spatiotemporal solutions. This paper presents a method that uses spatial features along with temporal-based features to detect smoke and fire in the scene. It consists of three main parts; the task of each part is to reduce the error of the previous part so that the final model has a robust performance. This method also uses transformer modules to increase the accuracy of the model. The results of our model show the proper performance of the proposed approach in solving the problem of smoke and fire detection and can be used to increase workplace safety.

Keywords: attention, fire detection, smoke detection, spatio-temporal

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Authors: Rachid Ziteuni, Selt Omar

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In this paper, we propose a new polynomial metaheuristic elaboration (tabu search) for solving scheduling problems. This method allows us to solve the scheduling problem of n tasks on m identical parallel machines with unavailability periods. This problem is NP-complete in the strong sens and finding an optimal solution appears unlikely. Note that all data in this problem are integer and deterministic. The performance criterion to optimize in this problem which we denote Pm/N-c/summs of (wjCj) is the weighted sum of the end dates of tasks.

Keywords: scheduling, parallel identical machines, unavailability periods, metaheuristic, tabu search

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Authors: Aydin Teymourifar, Gurkan Ozturk, Ozan Bahadir

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NSGA-II is one of the most well-known and most widely used evolutionary algorithms. In addition to its new versions, such as NSGA-III, there are several modified types of this algorithm in the literature. In this paper, a hybrid NSGA-II algorithm has been suggested for solving the multi-objective flexible job shop scheduling problem. For a better search, new neighborhood-based crossover and mutation operators are defined. To create new generations, the neighbors of the selected individuals by the tournament selection are constructed. Also, at the end of each iteration, before sorting, neighbors of a certain number of good solutions are derived, except for solutions protected by elitism. The neighbors are generated using a constraint-based neural network that uses various constructs. The non-dominated sorting and crowding distance operators are same as the classic NSGA-II. A comparison based on some multi-objective benchmarks from the literature shows the efficiency of the algorithm.

Keywords: flexible job shop scheduling problem, multi-objective optimization, NSGA-II algorithm, neighborhood structures

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Authors: Alireza Alizadeh, Hossein Ghadimi, Oveis Abedinia, Noradin Ghadimi

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A Particle Swarm Optimization with Time Varying Acceleration Coefficients (PSO-TVAC) is proposed to determine optimal economic load dispatch (ELD) problem in this paper. The proposed methodology easily takes care of solving non-convex economic load dispatch problems along with different constraints like transmission losses, dynamic operation constraints and prohibited operating zones. The proposed approach has been implemented on the 3-machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems and 13 thermal units power system. The proposed technique is compared to solve the ELD problem with hybrid approach by using the valve-point effect. The comparison results prove the capability of the proposed method giving significant improvements in the generation cost for the economic load dispatch problem.

Keywords: PSO-TVAC, economic load dispatch, non-convex cost function, prohibited operating zone, transmission losses

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Authors: Zohra Mekranfar, Ahmed Saidi, Abdellah Mebrek

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This work aims to develop multi-criteria decision making (MCDM) and spatial data warehouse (SDW) methods, which will be integrated into a GIS according to a ‘GIS dominant’ approach. The GIS operating tools will be operational to operate the SDW. The MCDM methods can provide many solutions to a set of problems with various and multiple criteria. When the problem is so complex, integrating spatial dimension, it makes sense to combine the MCDM process with other approaches like data mining, ascending analyses, we present in this paper an experiment showing a geo-decisional methodology of SWD construction, On-line analytical processing (OLAP) technology which combines both basic multidimensional analysis and the concepts of data mining provides powerful tools to highlight inductions and information not obvious by traditional tools. However, these OLAP tools become more complex in the presence of the spatial dimension. The integration of OLAP with a GIS is the future geographic and spatial information solution. GIS offers advanced functions for the acquisition, storage, analysis, and display of geographic information. However, their effectiveness for complex spatial analysis is questionable due to their determinism and their decisional rigor. A prerequisite for the implementation of any analysis or exploration of spatial data requires the construction and structuring of a spatial data warehouse (SDW). This SDW must be easily usable by the GIS and by the tools offered by an OLAP system.

Keywords: data warehouse, GIS, MCDM, SOLAP

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Authors: Hong-Ming Chen

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This work considers the resolution of the Hull and White interest rate model with the jump process. A deterministic process is adopted to model the random behavior of interest rate variation as deterministic perturbations, which is depending on the time t. The Brownian motion and jumps uncertainty are denoted as the integral functions piecewise constant function w(t) and point function θ(t). It shows that the interest rate function and the yield function of the Hull and White interest rate model with jump process can be obtained by solving a nonlinear semi-infinite programming problem. A relaxed cutting plane algorithm is then proposed for solving the resulting optimization problem. The method is calibrated for the U.S. treasury securities at 3-month data and is used to analyze several effects on interest rate prices, including interest rate variability, and the negative correlation between stock returns and interest rates. The numerical results illustrate that our approach essentially generates the yield functions with minimal fitting errors and small oscillation.

Keywords: optimization, interest rate model, jump process, deterministic

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Authors: Yang Zhou, Heli Sun, Jianbin Huang, Jizhong Zhao, Shaojie Qiao

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Traffic prediction is a fundamental problem in urban environment, facilitating the smart management of various businesses, such as taxi dispatching, bike relocation, and stampede alert. Most earlier methods rely on identifying the intrinsic spatial-temporal correlation to forecast. However, the complex nature of this problem entails a more sophisticated solution that can simultaneously capture the mutual influence of both adjacent and far-flung areas, with the information of time-dimension also incorporated seamlessly. To tackle this difficulty, we propose a new multi-phase architecture, DSTDS (Dual Spatial-Temporal Data Scheme for traffic prediction), that aims to reveal the underlying relationship that determines future traffic trend. First, a graph-based neural network with an attention mechanism is devised to obtain the static features of the road network. Then, a multi-granularity recurrent neural network is built in conjunction with the knowledge from a grid-based model. Subsequently, the preceding output is fed into a spatial-temporal super-resolution module. With this 3-phase structure, we carry out extensive experiments on several real-world datasets to demonstrate the effectiveness of our approach, which surpasses several state-of-the-art methods.

Keywords: traffic prediction, spatial-temporal, recurrent neural network, dual data scheme

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Authors: Guangtong Xu, Yi He

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Like most historic and cultural cities in China, the historic urban area of Jingmen city is facing a typical spatial problem of fragmentation and fuzzification. This study focuses on exploring a method for evaluating the existing values of historic urban area based on spatial prototype, a concept introduced into urban morphology from 'Archetype' in architectural typology. As the spatial elements and built-up relationship of historic city, spatial prototype has habitual structural characteristics and formal modulus. It is the inherent logic and order rules behind the scattered historic environment, providing a clue to understand the spatial characteristics and a basis for guiding the construction and conservation in historic urban areas. Three criteria, the resolution of historical elements, the completeness of historical structure and the renewal potential of associated land, were selected to construct the integrated assessment system. These three dimensions are linked to the spatial prototype and its constituent elements, as well as the transformation relationship in ancient and present day. The results showed that historic urban areas have changed from a holistic city to different existing types dominated by their historic structure elements. It is necessary to improve the pertinence of planning strategies and develop diversified management measures in the conservation scope of historic urban area. Moreover, a constructive-conservation strategy should be put forward to enhance the integrity of historic urban area based on the trace of spatial prototype and evaluation results.

Keywords: constructive conservation, existing value, historic urban area, spatial prototype

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Authors: Yun Hang Stanley Cheung

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In recent years, many educators and entrepreneurs have often suggested that students’ and workers’ ability of the adversity response is very important, it would affect problem-solving strategies and ultimate success in their career or life. The meaning of resilience is discussed as the process of bouncing back and the ability to adapt well in adversity’s response, being resilient does not mean to live without any stress and difficulty, but to grow and thrive under pressure. The purpose of this study is to describe the process of resilience and adversity’s response. The use of the narrative inquiry aims for understanding the experiential process of adversity response, and the problem-solving strategies (such as emotion control, motivation, decisions making process), as well as making the experience become life story, which may be evaluated by its teller and its listeners. The narrative study describes the researcher’s self-experience of adversity’s response to the recovery of the seriously burnt injury from a hill fire at his 12 years old, as well as the adversities and obstacles related to the tragedy after the physical recovery. Sense-Making Theory and McCormack’s Lenses were used for constructive perspective and data analyzing. To conclude, this study has described the life story of fighting the adversities, also, those narratives come out some suggestions, which point out positive thinking is necessary to build up resilience and the ability of immediate adversity response. Also, some problem-solving strategies toward adversities are discussed, which are helpful for resilience education for youth and young adult.

Keywords: adversity response, life story, narrative inquiry, resilience

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

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This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: bus scheduling problem, decision support system, genetic algorithm, shortest path

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Authors: Mediha B. Sılaydın Aydın, Emine D. Kahraman

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One of the important impacts of climate change is the sea level rise. Turkey is a peninsula, so the coastal areas of the country are threatened by the problem of sea level rise. Therefore, the urbanized coastal areas are highly vulnerable to climate change. At the aim of enhancing spatial resilience of urbanized areas, this question arises: What should be the priority intervention subject in the urban planning process for a given city. To answer this question, by focusing on the problem of sea level rise, this study aims to determine spatial vulnerability typologies and levels of Turkey coastal cities based on morphological, physical and social characteristics. As a method, spatial vulnerability of coastal cities is determined by two steps as level and type. Firstly, physical structure, morphological structure and social structure were examined in determining spatial vulnerability levels. By determining these levels, most vulnerable areas were revealed as a priority in adaptation studies. Secondly, all parameters are also used to determine spatial typologies. Typologies are determined for coastal cities in order to use as a base for urban planning studies. Adaptation to climate change is crucial for developing countries like Turkey so, this methodology and created typologies could be a guide for urban planners as spatial directors and an example for other developing countries in the context of adaptation to climate change. The results demonstrate that the urban settlements located on the coasts of the Marmara Sea, the Aegean Sea and the Mediterranean respectively, are more vulnerable than the cities located on the Black Sea’s coasts to sea level rise.

Keywords: climate change, coastal cities, vulnerability, urban land use planning

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Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

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Authors: Mohammed A. Alazawi, Shiguo Jiang, Steven F. Messner

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Research has long focused on two main spatial aspects of crime: spatial patterns and spatial processes. When analyzing these patterns and processes, a key issue has been to determine the proper spatial scale. In addition, it is important to consider the possibility that these patterns and processes might differ appreciably for different temporal scales and might vary across geographic units of analysis. We examine the spatial-temporal dependence of residential burglary. This dependence is tested at varying geographical scales and temporal aggregations. The analyses are based on recorded incidents of crime in Columbus, Ohio during the 1994-2002 period. We implement point pattern analysis on the crime points using Ripley’s K function. The results indicate that spatial point patterns of residential burglary reveal spatial scales of clustering relatively larger than the average size of census tracts of the study area. Also, spatial scale is independent of temporal scale. The results of our analyses concerning the geographic scale of spatial patterns and processes can inform the development of effective policies for crime control.

Keywords: inhomogeneous K function, residential burglary, spatial point pattern, spatial scale, temporal scale

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Authors: Maja Ruzic-Baf, Mirjana Radetic-Paic

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The use of computers by children has many positive aspects, including the development of memory, learning methods, problem-solving skills and the feeling of one’s own competence and self-confidence. Playing on line video games can encourage hanging out with peers having similar interests as well as communication; it develops coordination, spatial relations and presentation. On the other hand, the Internet enables quick access to different information and the exchange of experiences. How kids use computers and what the negative effects of this can be depends on various factors. ICT has improved and become easy to get for everyone. In the past 12 years so many video games has been made even to that level that some of them are free to play. Young people, even some adults, had simply start to forget about the real outside world because in that other, digital world, they have found something that makes them feal more worthy as a man. This article present the use of ICT, forms of behavior and addictions to on line video games. The use of computers by children has many positive aspects, including the development of memory, learning methods, problem-solving skills and the feeling of one’s own competence and self-confidence. Playing on line video games can encourage hanging out with peers having similar interests as well as communication; it develops coordination, spatial relations and presentation. On the other hand, the Internet enables quick access to different information and the exchange of experiences. How kids use computers and what the negative effects of this can be depends on various factors. ICT has improved and become easy to get for everyone. In the past 12 years so many video games has been made even to that level that some of them are free to play. Young people, even some adults, had simply start to forget about the real outside world because in that other, digital world, they have found something that makes them feal more worthy as a man. This article present the use of ICT, forms of behavior and addictions to on line video games.

Keywords: addiction to video games, behaviour, ICT, young people

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Authors: Karla Hrbackova, Irena Balaban Cakirpaloglu

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This paper is a report on self-regulation in socially rejected pupils. A certain form of social rejection can be found in almost every class within the school environment. Research shows that due to social rejection mechanisms supporting the individual´s effort of reintegration into the group are not triggered. Paradoxically the opposite tendency arises, i.e., an increase in selfish and defeating behaviour. The link between peer exposure and self-regulation is likely to vary as a function of a type and quality of peer interaction (e.g., rejection or acceptance). The paper aims to clarify the level of self-regulation related to interpersonal cognitive problem-solving within the process of social rejection in a school class. The research was done on a sample of 1,133 upper-primary school pupils using the Means-Ends Problem Solving technique (MEPS) and peer sociometric nomination. The results showed that the level of self-regulated skills is related to the status of social rejection. Socially rejected pupils achieve lower levels of self-regulation than other classmates. We found deficiency in the regulation of behaviour, emotions and the regulation of will in the peer rejected pupils with the exception of cognitive regulation in which no differences were detected between socially rejected pupils and other classmates. The results have implications for early prevention and intervention efforts to foster adaptive self-regulation and reduce the risk of later social rejection.

Keywords: interpersonal cognitive problem-solving, self-regulation, socially rejected pupils, upper-primary school pupils

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Authors: Burak Köken, Hatice D. Arslan, Bilgehan Y. Çakmak

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Analyzing the relation networks between the hospital buildings which have complex structure and distinctive spatial relationships is quite difficult. The hospital buildings which require specialty in spatial relationship solutions during design and self-innovation through the developing technology should survive and keep giving service even after the disasters such as earthquakes. In this study, a hospital building where the load-bearing system was strengthened because of the insufficient earthquake performance and the construction of an additional building was required to meet the increasing need for space was discussed and a comparative spatial evaluation of the hospital building was made with regard to its status before the change and after the change. For this reason, spatial organizations of the building before change and after the change were analyzed by means of Space Syntax method and the effects of the change on space organization parameters were searched by applying an analytical procedure. Using Depthmap UCL software, connectivity, visual mean depth, beta and visual integration analyses were conducted. Based on the data obtained after the analyses, it was seen that the relationships between spaces of the building increased after the change and the building has become more explicit and understandable for the occupants. Furthermore, it was determined according to findings of the analysis that the increase in depth causes difficulty in perceiving the spaces and the changes considering this problem generally ease spatial use.

Keywords: architecture, hospital building, space syntax, strengthening

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Authors: S. H. Borghei, E. Teymourian, M. Mobin, G. M. Komaki, S. Sheikh

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Imperialist competitive algorithm (ICA) is a recent meta-heuristic method that is inspired by the social evolutions for solving NP-Hard problems. The ICA is a population based algorithm which has achieved a great performance in comparison to other meta-heuristics. This study is about developing enhanced ICA approach to solve the cell formation problem (CFP) using sequence data. In addition to the conventional ICA, an enhanced version of ICA, namely EICA, applies local search techniques to add more intensification aptitude and embed the features of exploration and intensification more successfully. Suitable performance measures are used to compare the proposed algorithms with some other powerful solution approaches in the literature. In the same way, for checking the proficiency of algorithms, forty test problems are presented. Five benchmark problems have sequence data, and other ones are based on 0-1 matrices modified to sequence based problems. Computational results elucidate the efficiency of the EICA in solving CFP problems.

Keywords: cell formation problem, group technology, imperialist competitive algorithm, sequence data

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Authors: Sihem Oujdi, Hafida Belbachir

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Existing methods of data mining cannot be applied on spatial data because they require spatial specificity consideration, as spatial relationships. This paper focuses on the classification with decision trees, which are one of the data mining techniques. We propose an extension of the C4.5 algorithm for spatial data, based on two different approaches Join materialization and Querying on the fly the different tables. Similar works have been done on these two main approaches, the first - Join materialization - favors the processing time in spite of memory space, whereas the second - Querying on the fly different tables- promotes memory space despite of the processing time. The modified C4.5 algorithm requires three entries tables: a target table, a neighbor table, and a spatial index join that contains the possible spatial relationship among the objects in the target table and those in the neighbor table. Thus, the proposed algorithms are applied to a spatial data pattern in the accidentology domain. A comparative study of our approach with other works of classification by spatial decision trees will be detailed.

Keywords: C4.5 algorithm, decision trees, S-CART, spatial data mining

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Authors: Daijun Chen

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Affordable housing is subsidized by the government to meet the housing demand of low and middle-income urban residents in the process of urbanization and to alleviate the housing inequality caused by market-based housing reforms. It is a recognized fact that the living conditions of the insured have been improved while constructing the subsidized housing. However, the choice of affordable housing is mostly in the suburbs, where the surrounding urban functions and infrastructure are incomplete, resulting in the spatial mismatch of "jobs-housing" in affordable housing. The main reason for this problem is that the residents of affordable housing are more sensitive to the spatial location of their residence, but their selectivity and controllability to the housing location are relatively weak, which leads to higher commuting costs. Their real cost of living has not been effectively reduced. In this regard, 92 subsidized housing communities in Nanjing, China, are selected as the research sample in this paper. The residents of the affordable housing and their commuting Spatio-temporal behavior characteristics are identified based on the LBS (location-based service) data. Based on the spatial mismatch theory, spatial mismatch indicators such as commuting distance and commuting time are established to measure the spatial mismatch degree of subsidized housing in different districts of Nanjing. Furthermore, the geographically weighted regression model is used to analyze the influencing factors of the spatial mismatch of affordable housing in terms of the provision of employment opportunities, traffic accessibility and supporting service facilities by using spatial, functional and other multi-source Spatio-temporal big data. The results show that the spatial mismatch of affordable housing in Nanjing generally presents a "concentric circle" pattern of decreasing from the central urban area to the periphery. The factors affecting the spatial mismatch of affordable housing in different spatial zones are different. The main reasons are the number of enterprises within 1 km of the affordable housing district and the shortest distance to the subway station. And the low spatial mismatch is due to the diversity of services and facilities. Based on this, a spatial optimization strategy for different levels of spatial mismatch in subsidized housing is proposed. And feasible suggestions for the later site selection of subsidized housing are also provided. It hopes to avoid or mitigate the impact of "spatial mismatch," promote the "spatial adaptation" of "jobs-housing," and truly improve the overall welfare level of affordable housing residents.

Keywords: affordable housing, spatial mismatch, commuting characteristics, spatial adaptation, welfare benefits

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Authors: Thierno Diop, Michel Fortin, Jean Deteix

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Since the precise formulation of the elastic part is irrelevant for the description of the algorithm, we shall consider a generic case. In practice, however, we will have to deal with a non linear material (for instance a Mooney-Rivlin model). We are interested in solving a finite element approximation of the problem, leading to large-scale non linear discrete problems and, after linearization, to large linear systems and ultimately to calculations needing iterative methods. This also implies that penalty method, and therefore augmented Lagrangian method, are to be banned because of their negative effect on the condition number of the underlying discrete systems and thus on the convergence of iterative methods. This is in rupture to the mainstream of methods for contact in which augmented Lagrangian is the principal tool. We shall first present the problem and its discretization; this will lead us to describe a general solution algorithm relying on a preconditioner for saddle-point problems which we shall describe in some detail as it is not entirely standard. We will propose an iterative approach for solving three-dimensional frictional contact problems between elastic bodies, including contact with a rigid body, contact between two or more bodies and also self-contact.

Keywords: frictional contact, three-dimensional, large-scale, iterative method

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: Ching-Shoei Chiang

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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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Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Dhea Kothari

Abstract:

There is an extensive amount of research that has examined the positive relationship between creativity and hypomania in terms of creative accomplishments, eminence, behaviors, occupations. Previous research had recruited participants based on creative occupations or stages of hypomania or bipolar disorder. This thesis focused on the relationship between hypomania and creative cognitive potential, such as divergent thinking and insight problem-solving. This was examined at an undergraduate educational level by recruiting students majoring in art, majoring in natural sciences (NSCI) and those double majoring in arts and NSCI. Participants were given a modified Alternate Uses Task (AUT) to measure divergent thinking and a set of rebus puzzles to measure insight problem-solving. Both tasks involved a level of overcoming functional fixedness. A negative association was observed between hypomania and originality of responses on the AUT when an object with low functional fixedness was given to all participants. On the other hand, a positive association was found between hypomania and originality of responses on the AUT when an object with high functional fixedness was given to the participants majoring in NSCI. Therefore, the research suggests that an increased ability to overcome functional fixedness might be central to individuals with hypomania and individuals with higher creative cognitive potential.

Keywords: creative cognition, convergent thinking, creativity, divergent thinking, insight, major type, problem-solving

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