Search results for: hyperbolic problem

Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: Muhammad Younis

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In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: S. Nasri, H. Bouziri

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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, tabu search metaheuristic

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Authors: Divyesh Patel, Tanuja Srivastava

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

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

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Authors: Chaghoub Soraya, Zhang Xiaoyan

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This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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Authors: Jin Liang, Guanghua Shi

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In this paper, we are concerned with the further refinements of the Heinz operator inequalities in Hilbert spaces. Our purpose is to derive several new Heinz-type operator inequalities. First, with the help of the Taylor series of some hyperbolic functions, we obtain some refinements of the ordering relations among Heinz means defined by Bhatia with different parameters, which would be more suitable in obtaining the corresponding operator inequalities. Second, we present some generalizations of Heinz operator inequalities. Finally, we give a matrix version of the Heinz inequality for the Hilbert-Schmidt norm.

Keywords: Hilbert space, means inequality, norm inequality, positive linear operator

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Authors: Abubakar Sa’adatu Mohammed

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This paper reports on a study of problem solving differences between expert and novice Problem solvers for effective physics teaching. Significant differences were found both at the conceptual level and at the level of critical thinking, creative thinking and reasoning. It is suggested for a successful solution of a problem, conceptual knowledge alone may not be sufficient. There is the need of the knowledge of how the conceptual knowledge should be applied (problem solving skills). It is hoped that this research might contribute to efforts of exploring ways for students to acquire a powerful conceptual toolkit based on experts like problem solvers approach for effective teaching delivery.

Keywords: conceptual knowledge, procedural knowledge, critical thinking, creative thinking, reasoning ability

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Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: Mahnaz Hosseinzadeh, Mohammad Reza Mehregan

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In this paper, we have developed a morphological field to assist multi- methodology (combining methodologies together in whole or part) in Operations Research (OR) for the problem contexts in Iranian organizations. So, we have attempted to identify some dimensions for problem context according to Iranian organizational problems. Then, a general morphological program is designed which helps the OR practitioner to determine the suitable OR methodology as output for any configuration of conditions in a problem context as input and to reveal the fields necessary to be improved in OR. Applying such a program would have interesting results for OR practitioners.

Keywords: hard, soft and emancipatory operations research, General Morphological Analysis (GMA), multi-methodology, problem context

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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: Sarwat Sultan, Shahzad Gul

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This study was carried out to see the mediating role of problem solving styles (sensing, intuitive, feeling, and thinking) in the predictive relationship of gratitude with subjective well-being. A sample of 454 college students aged 20-26 years old participated in this study and provided data on the measures of gratitude, problem solving styles, and subjective well-being. Results indicated the significant relationships of gratitude with subjective well-being and problem solving styles of intuitive and thinking. Results further indicated the positive link of intuitive and thinking styles with subjective well-being. Findings also provided the evidence for the significant mediating role of problem solving styles in the relationship of gratitude with subjective well-being. The implication for this study is likely to enhance the medium to long term effects of gratitude on subjective well-being among students and as well as assessing its value in promoting psychological health and problem solving strategies among students.

Keywords: gratitude, subjective well-being, problem solving styles, college students

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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. Erol Genevois, D. Celik, H. Z. Ulukan

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Automated teller machines (ATMs) can be considered among one of the most important service facilities in the banking industry. The investment in ATMs and the impact on the banking industry is growing steadily in every part of the world. The banks take into consideration many factors like safety, convenience, visibility, cost in order to determine the optimum locations of ATMs. Today, ATMs are not only available in bank branches but also at retail locations. Another important factor is the cash management in ATMs. A cash demand model for every ATM is needed in order to have an efficient cash management system. This forecasting model is based on historical cash demand data which is highly related to the ATMs location. So, the location and the cash management problem should be considered together. Although the literature survey on facility location models is quite large, it is surprising that there are only few studies which handle together ATMs location and cash management problem. In order to fulfill the gap, this paper provides a general review on studies, efforts and development in ATMs location and cash management problem.

Keywords: ATM location problem, cash management problem, ATM cash replenishment problem, literature review in ATMs

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Authors: Md. Zahidul Islam

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Illegal immigrants’ problem is a big problem all over the world including America. Malaysia is also facing this problem. Nowadays, it is turned into a major problem for Malaysia. Many illegal immigrants are staying in Malaysia from different countries such as Bangladesh, Myanmar, India, Pakistan, Indonesia, Vietnam, Thailand, Philippine, Nigeria. This article is only focusing on the present situation of illegal immigrants of Bangladesh. The aim of this article is to highlight how the Bangladeshi nationals are becoming an illegal immigrant in Malaysia. In the same time, this article also tries to identify the present situation of Bangladeshi illegal immigrants in Malaysia. The research will adopt qualitative methods of research. Both countries have to find a solution to solve this problem.

Keywords: illegal immigrants, present situation, Bangladesh, Malaysia

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Authors: E. Eroglu, S. Semsit, E. Sener, U.S. Sener

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In Electromagnetics, there are three canonical boundary value problem with given initial conditions for the electromagnetic field sought, namely: Cavity Problem, Waveguide Problem, and External Problem. The Cavity Problem and Waveguide Problem were rigorously studied and new results were arised at original works in the past decades. In based on studies of an analytical time domain method Evolutionary Approach to Electromagnetics (EAE), electromagnetic field strength vectors produced by a time dependent source function are sought. The fields are took place in L2 Hilbert space. The source function that performs signal transferring, energy and surplus of energy has been demonstrated with all clarity. Depth of the method and ease of applications are emerged needs of gathering obtained results. Main discussion is about perfect electric conductor and hollow waveguide. Even if well studied time-domain modes problems are mentioned, specifically, the modes which have a hollow (i.e., medium-free) cross-section domain are considered.

Keywords: evolutionary approach to electromagnetics, time-domain waveguide mode, Neumann problem, Dirichlet boundary value problem, Klein-Gordon

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. 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, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

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

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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: Hessam Mortezaei, Saeid Joudakian

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In this paper, the wear problem on rider rings of boil off gas compressor has been studied. This kind of oil free double acting compressor has free floating piston (FFP) technology and as a result of that it should have the lowest possible wear on its rider rings. But a design problem had caused a complete wear of rider rings after one month of continuous operation. In this case study, the source of this problem was recognized and solved.

Keywords: piston rider, rings, gas distribution, pressure wear

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: Filipe Cardoso de Oliveira, Lino Marcos da Silva, Ademar Nogueira do Nascimento, Cristiano Hora de Oliveira Fontes

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This article presents a mathematical formulation for the production Break-Even Point problem in a non-homogeneous system. The optimization problem aims to obtain the composition of the best product mix in a non-homogeneous industrial plant, with the lowest cost until the breakeven point is reached. The problem constraints represent real limitations of a generic non-homogeneous industrial plant for n different products. The proposed model is able to solve the equilibrium point problem simultaneously for all products, unlike the existing approaches that propose a resolution in a sequential way, considering each product in isolation and providing a sub-optimal solution to the problem. The results indicate that the product mix found through the proposed model has economical advantages over the traditional approach used.

Keywords: branch and bound, break-even point, non-homogeneous production system, integer linear programming, management accounting

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Authors: Tarek Aboueldahab, Hanan Farag

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Cost minimization of Multiple Vehicle Routing Problem becomes a critical issue in the field of transportation because it is NP-hard optimization problem and the search space is complex. Many researches use the hybridization of artificial intelligence (AI) models to solve this problem; however, it can not guarantee to reach the best solution due to the difficulty of searching the whole search space. To overcome this problem, we introduce the hybrid model of Discrete Particle Swarm Optimization (DPSO) with a passive congregation which enable searching the whole search space to compromise between both local and global search. The practical experiment shows that our model obviously outperforms other hybrid models in cost minimization.

Keywords: cost minimization, multi-vehicle routing problem, passive congregation, discrete swarm, passive congregation

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Authors: Temitayo Ogunsanwo

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Problem-solving is an important way of learning way of learning because it propels children to use previous experiences to deal with new situations. The purpose of this study is to find out the attitude of pre-service teachers to problem-solving as a strategy for promoting early mathematics learning in children. This qualitative study employed a descriptive design to investigate the experiences of twenty second-year undergraduate early childhood education Pre-service teachers in a teaching practice and their attitude towards five-year-old children’s problem-solving strategies in mathematics. Pre-service teachers were exposed to different strategies for teaching children how to solve problems in mathematics. They were taken through a micro teaching in class using different strategies to teach problem-solving in different topics in the five-year-old mathematics curriculum. The students were then made to teach five-year-olds in neighbouring schools for three weeks, working in pairs, observing and recording children’s problem-solving activities and strategies. After the three weeks exercise, their experiences and attitude towards children’s problem-solving strategies were collected using open-ended questions and analysed in themes. Findings were discussed.

Keywords: attitude, early mathematics learning, experience, pre-service teachers, problem-solving, strategies

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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: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: H. Mousavi, M. Sharifi, H. Pourvaziri

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Redundancy Allocation Problem (RAP) is a well-known mathematical problem for modeling series-parallel systems. It is a combinatorial optimization problem which focuses on determining an optimal assignment of components in a system design. In this paper, to be more practical, we have considered the problem of redundancy allocation of series system with interval valued reliability of components. Therefore, during the search process, the reliabilities of the components are considered as a stochastic variable with a lower and upper bounds. In order to optimize the problem, we proposed a simulated annealing based on cloud theory (CBSAA). Also, the Monte Carlo simulation (MCS) is embedded to the CBSAA to handle the random variable components’ reliability. This novel approach has been investigated by numerical examples and the experimental results have shown that the CBSAA combining MCS is an efficient tool to solve the RAP of systems with interval-valued component reliabilities.

Keywords: redundancy allocation problem, simulated annealing, cloud theory, monte carlo simulation

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Authors: E. V. Krishnan

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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

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In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: memristor, chaotic circuit, dynamical behavior, chaotic system

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Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem (UETP)

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Authors: Uyanga Sukhbaatar, Ahmed Lbath, Mendamar Majig

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

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

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