Search results for: problem solving

Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

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The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

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Authors: Lindsey Carruthers, Alexandra Willis, Rory MacLean

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Introduction: It has been proposed that distractibility, a key diagnostic criterion of Attention Deficit Hyperactivity Disorder (ADHD), may be associated with higher creativity levels in some individuals. Anecdotal and empirical evidence has shown that ADHD is therefore beneficial to creative problem-solving, and the generation of new ideas and products. Previous studies have only used one or two measures of attention, which is insufficient given that it is a complex cognitive process. The current study aimed to determine in which ways performance on creative problem-solving tasks and a range of attention tests may be related, and if performance differs between adults with and without ADHD. Methods: 150 adults, 47 males and 103 females (mean age=28.81 years, S.D.=12.05 years), were tested at Edinburgh Napier University. Of this set, 50 participants had ADHD, and 100 did not, forming the control group. Each participant completed seven attention tasks, assessing focussed, sustained, selective, and divided attention. Creative problem-solving was measured using divergent thinking tasks, which require multiple original solutions for one given problem. Two types of divergent thinking task were used: verbal (requires written responses) and figural (requires drawn responses). Each task is scored for idea originality, with higher scores indicating more creative responses. Correlational analyses were used to explore relationships between attention and creative problem-solving, and t-tests were used to study the between group differences. Results: The control group scored higher on originality for figural divergent thinking (t(148)= 3.187, p< .01), whereas the ADHD group had more original ideas for the verbal divergent thinking task (t(148)= -2.490, p < .05). Within the control group, figural divergent thinking scores were significantly related to both selective (r= -.295 to -.285, p < .01) and divided attention (r= .206 to .290, p < .05). Alternatively, within the ADHD group, both selective (r= -.390 to -.356, p < .05) and divided (r= .328 to .347, p < .05) attention are related to verbal divergent thinking. Conclusions: Selective and divided attention are both related to divergent thinking, however the performance patterns are different between each group, which may point to cognitive variance in the processing of these problems and how they are managed. The creative differences previously found between those with and without ADHD may be dependent on task type, which to the author’s knowledge, has not been distinguished previously. It appears that ADHD does not specifically lead to higher creativity, but may provide explanation for creative differences when compared to those without the disorder.

Keywords: ADHD, attention, creativity, problem-solving

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Authors: Z. M. T. Lim, W. Q. Yow

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Diversity in individual problem-solving approaches, culture and nationality have been shown to have positive effects on collaborative creative processes in organizational and scholastic settings. For example, diverse graduate and organizational teams consisting of members with both structured and unstructured problem-solving styles were found to have more creative ideas on a collaborative idea generation task than teams that comprised solely of members with either structured or unstructured problem-solving styles. However, being different may not always provide benefits to the collaborative creative process. In particular, speaking different languages may hinder mutual engagement through impaired communication and thus collaboration. Instead, sharing similar languages may have facilitative effects on mutual engagement in collaborative tasks. However, no studies have explored the relations between language diversity and adults’ collaborative creative problem solving. Sixty-four Singaporean English-speaking bilingual undergraduates were paired up into similar or dissimilar language pairs based on the second language they spoke (e.g., for similar language pairs, both participants spoke English-Mandarin; for dissimilar language pairs, one participant spoke English-Mandarin and the other spoke English-Korean). Each participant completed the Ravens Progressive Matrices Task individually. Next, they worked in pairs to complete a collaborative divergent thinking task where they used mind-mapping techniques to brainstorm ideas on a given problem together (e.g., how to keep insects out of the house). Lastly, the pairs worked on a collaborative insight problem-solving task (Triangle of Coins puzzle) where they needed to flip a triangle of ten coins around by moving only three coins. Pairs who had prior knowledge of the Triangle of Coins puzzle were asked to complete an equivalent Matchstick task instead, where they needed to make seven squares by moving only two matchsticks based on a given array of matchsticks. Results showed that, after controlling for intelligence, similar language pairs completed the collaborative insight problem-solving task faster than dissimilar language pairs. Intelligence also moderated these relations. Among adults of lower intelligence, similar language pairs solved the insight problem-solving task faster than dissimilar language pairs. These differences in speed were not found in adults with higher intelligence. No differences were found in the number of ideas generated in the collaborative divergent thinking task between similar language and dissimilar language pairs. In conclusion, sharing similar languages seem to enrich collaborative creative processes. These effects were especially pertinent to pairs with lower intelligence. This provides guidelines for the formation of groups based on shared languages in collaborative creative processes. However, the positive effects of shared languages appear to be limited to the insight problem-solving task and not the divergent thinking task. This could be due to the facilitative effects of other factors of diversity as found in previous literature. Background diversity, for example, may have a larger facilitative effect on the divergent thinking task as compared to the insight problem-solving task due to the varied experiences individuals bring to the task. In conclusion, this study contributes to the understanding of the effects of language diversity in collaborative creative processes and challenges the general positive effects that diversity has on these processes.

Keywords: bilingualism, diversity, creativity, collaboration

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Authors: Sumalee Tientongdee

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In this study, it was aimed to investigate Physics achievement of the pre-service science teacher studying in general science program at Suan Sunandha Rajabhat University, Bangkok, Thailand. The program has provided the new curriculum that focuses on 21st-century skills development. Active learning approaches are used to teach in all subjects. One of the active learning approaches Peer Instruction, or PI was used in this study to teach physics of waves as a compulsory course. It was conducted in the second semester from January to May of 2017. The concept test was given to evaluate pre-service science teachers’ understanding in concept of waves. Problem-solving assessment form was used to evaluate their problem-solving skill. The results indicated that after they had learned through Peer Instruction in physics of waves course, their concepts in physics of waves was significantly higher at 0.05 confident levels. Their problem-solving skill from the whole class was at the highest level. Based on the group interview on the opinions of using Peer Instruction in Physics class, they mostly felt that it was very useful and helping them understand more about physics, especially for female students.

Keywords: peer instruction, physics of waves, pre-service science teacher, Suan Sunandha Rajabhat university

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Authors: Svenja Pieritz, Jakab Pilaszanovich

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Collaborative Problem Solving (CPS) is recognized as being one of the most important skills of the 21st century with having a potential impact on education, job selection, and collaborative systems design. Therefore, CPS has been adopted in several standardized tests, including the Programme for International Student Assessment (PISA) in 2015. A significant challenge of evaluating CPS is the underlying interplay of cognitive and social skills, which requires a more holistic assessment. However, the majority of the existing tests are using a questionnaire-based assessment, which oversimplifies this interplay and undermines ecological validity. Two major difficulties were identified: Firstly, the creation of a controllable, real-time environment allowing natural behaviors and communication between at least two people. Secondly, the development of an appropriate method to collect and synthesize both cognitive and social metrics of collaboration. This paper proposes a more holistic and automated approach to the assessment of CPS. To address these two difficulties, a multiplayer problem-solving game called Sea of Light was developed: An environment allowing students to deploy a variety of measurable collaborative strategies. This controlled environment enables researchers to monitor behavior through the analysis of game actions and chat. The according solution for the statistical model is a combined approach of Natural Language Processing (NLP) and Bayesian network analysis. Social exchanges via the in-game chat are analyzed through NLP and fed into the Bayesian network along with other game actions. This Bayesian network synthesizes evidence to track and update different subdimensions of CPS. Major findings focus on the correlations between the evidences collected through in- game actions, the participants’ chat features and the CPS self- evaluation metrics. These results give an indication of which game mechanics can best describe CPS evaluation. Overall, Sea of Light gives test administrators control over different problem-solving scenarios and difficulties while keeping the student engaged. It enables a more complete assessment based on complex, socio-cognitive information on actions and communication. This tool permits further investigations of the effects of group constellations and personality in collaborative problem-solving.

Keywords: bayesian network, collaborative problem solving, game-based assessment, natural language processing

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Authors: Tigmanshu Bhatnagar, Petra Badke-Schaub

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

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

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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

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

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Authors: Aquil Ahmed, Srikant Gupta, Irfan Ali

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In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem, multi objective linear programming, multi-objective fractional programming, fuzzy goal programming, fuzzy sets, trapezoidal fuzzy number

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Authors: Abdallah A. Hlayel

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Operations research science (OR) deals with good success in developing and applying scientific methods for problem solving and decision-making. However, by using OR techniques, we can enhance the use of computer decision support systems to achieve optimal management for institutions. OR applies comprehensive analysis including all factors that affect on it and builds mathematical modeling to solve business or organizational problems. In addition, it improves decision-making and uses available resources efficiently. The adoption of OR by universities would definitely contributes to the development and enhancement of the performance of OR techniques. This paper provides an understanding of the structures, approaches and models of OR in problem solving and decision-making.

Keywords: best candidates' method, decision making, decision support system, operations research

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Authors: I. Salas-Menotti

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Problem-solving courts were created to assist offenders with specific needs that were not addressed properly in traditional courts. Problem-solving courts' main objective is to pursue solutions that will benefit the offender, the victim, and society as well. These courts were developed as an innovative response to deal with issues such as drug abuse, mental illness, and domestic violence. In Brooklyn, men who are charged with domestic violence related offenses for the first time are offered plea bargains that include the attendance to a domestic abuse intervention program as a condition to dismiss the most serious charges and avoid incarceration. The desired outcome is that the offender will engage in a program that will modify his behavior avoiding new incidents of domestic abuse, it requires accountability towards the victim and finally, it will hopefully bring down statistic related to domestic abuse incidents. This paper will discuss the effectiveness of the Duluth model as applied to Spanish-speaking men mandated to participate in the program by the specialized domestic violence courts in Brooklyn. A longitudinal study was conducted with 243 Spanish- speaking men who were mandated to participated in the men's program offered by EAC in Brooklyn in the years 2016 through 2018 to determine the recidivism rate of domestic violence crimes. Results show that the recidivism rate was less than 5% per year after completing the program which indicates that the intervention is effective in preventing new abuse allegations and subsequent arrests. It's recommended that comparative study with English-speaking participants is conducted to determine cultural and language variables affecting the program's efficacy.

Keywords: domestic violence, domestic abuse intervention programs, Problem solving courts, Spanish-speaking offenders

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Authors: Sharon K. O'Kelley

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At the heart of mathematics education is the concept of communication which many teachers envision as the influential dialogue they conduct with their students. However, communication in the mathematics classroom operates in different forms at different levels, both externally and internally. Specifically, it can be a central component in the building of critical thinking skills that requires students not only to know how to communicate their solutions to others but that they also be able to navigate their own thought processes in search of those solutions. This paper provides a review of research on the role of communication in the building of critical thinking skills in mathematics with a focus on the problem-solving process and the implications this interplay has for the teaching and learning of mathematics.

Keywords: communication in mathematics, critical thinking skills, mathematics education, problem-solving process

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Authors: Chen-Ya Juan

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Problem-Based Learning uses vague questions to guide student thinking and enhance their self-learning and collaboration. Most teachers implement PBL in a physical classroom, where teachers can monitor and evaluate students’ learning progress and guide them to search resources for answers. However, the prevalence of the Covid-19 in the world had changed from physical teaching to distance teaching. This instruction used many cases and applied Problem-Based Learning combined on the distance teaching via the internet for college students. This study involved an experimental group with PBL and a control group without PBL. The teacher divided all students in PBL class into eight groups, and 7~8 students in each group. The teacher assigned different cases for each group of the PBL class. Three stages of instruction were developed, including background knowledge of Learning, case analysis, and solving problems for each case. This study used a quantitative research method, a two-sample t-test, to find a significant difference in groups with PBL and without PBL. Findings indicated that PBL incased the average score of special education knowledge. The average score was improved by 20.46% in the PBL group and 15.4% without PBL. Results didn’t show significant differences (0.589>0.05) in special education professional knowledge. However, the feedback of the PBL students implied learning more about the application, problem-solving skills, and critical thinking. PBL students were more likely to apply professional knowledge on the actual case, find questions, resources, and answers. Most of them understood the importance of collaboration, working as a team, and communicating with other team members. The suggestions of this study included that (a) different web-based teaching instruments influenced student’s Learning; (b) it is difficult to monitor online PBL progress; (c) online PBL should be implemented flexible and multi-oriented; (d) although PBL did not show a significant difference on the group with PBL and without PBL, it did increase student’s problem-solving skills and critical thinking.

Keywords: problem-based learning, college students, distance learning, case analysis, problem-solving

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Authors: Verónica Díaz

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A Cartesian graph, as a mathematical object, becomes a tool for configuration of change. Its best comprehension is done through everyday life problem-solving associated with its representation. Despite this, the current educational framework favors general graphs, without consideration of their argumentation. Students are required to find the mathematical function without associating it to the development of graphical language. This research describes the use made by students of configurations made prior to Cartesian graphs with regards to an everyday life problem related to a time and distance variation phenomenon. The theoretical framework describes the function conditions of study and their modeling. This is a qualitative, descriptive study involving six undergraduate case studies that were carried out during the first term in 2016 at University of Los Lagos. The research problem concerned the graphic modeling of a real person’s movement phenomenon, and two levels of analysis were identified. The first level aims to identify local and global graph interpretations; a second level describes the iconicity and referentiality degree of an image. According to the results, students were able to draw no figures before the Cartesian graph, highlighting the need for students to represent the context and the movement of which causes the phenomenon change. From this, they managed Cartesian graphs representing changes in position, therefore, achieved an overall view of the graph. However, the local view only indicates specific events in the problem situation, using graphic and verbal expressions to represent movement. This view does not enable us to identify what happens on the graph when the movement characteristics change based on possible paths in the person’s walking speed.

Keywords: cartesian graphs, higher education, movement modeling, problem solving

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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: 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: 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: 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: 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: 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: 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: 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: 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

Abstract:

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

Abstract:

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

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

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