Search results for: bouncing ball problem

Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Litim Tarek, Taamallah Ouahiba

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This work relates to the physico-geometrical aspect of the surface layers of 16NC6 steel having undergone the burnishing treatment by hard steel ball. The results show that the optimal effects of burnishing are closely linked to the shape and the material of the active part of the device as well as to the surface plastic deformation ability of the material to be treated. Thus the roughness is improved by more than 70%, and the consolidation rate is increased by 30%. In addition, modeling of the rational traction curves provides a work hardening coefficient of up to 0.3 in the presence of burnishing.

Keywords: 16NC6 steel, burnishing, hardening, roughness

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Authors: Nusrat T. Chowdhury, M. F. Baki, A. Azab

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The production planning problem is concerned with specifying the optimal quantities to produce in order to meet the demand for a prespecified planning horizon with the least possible expenditure. Making the right decisions in production planning will affect directly the performance and productivity of a manufacturing firm, which is important for its ability to compete in the market. Therefore, developing and improving solution procedures for production planning problems is very significant. In this paper, we develop a Dantzig-Wolfe decomposition of a multi-item hierarchical production planning problem with capacity constraint and present a column generation approach to solve the problem. The original Mixed Integer Linear Programming model of the problem is decomposed item by item into a master problem and a number of subproblems. The capacity constraint is considered as the linking constraint between the master problem and the subproblems. The subproblems are solved using the dynamic programming approach. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any kind of infeasibility that arises while solving the problem. We compare the computational performance of the developed solution approach against the state-of-the-art heuristic procedure available in the literature. The results show that the proposed heuristic-based decomposition approach improves the solution quality by 20% as compared to the literature.

Keywords: inventory, multi-level capacitated lot-sizing, emission control, setup carryover

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Authors: D. Kabeya Nahum, L. Y. Kabeya Mukeba

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In this work, the design of surface defects some support of the anchor rod ball joint. The future adhesion contact was rocking in manufacture machining, for giving by the numerical analysis of a short simple solution of thermo-mechanical coupled problem in process engineering. The analysis of geometrical evaluation and the quasi-static and dynamic states are discussed in kinematic dimensional tolerances onto surfaces of part. Geometric modeling using the finite element method (FEM) in rough part of such phase provides an opportunity to solve the nonlinearity behavior observed by empirical data to improve the discrete functional surfaces. The open question here is to obtain spherical geometry of drain wear with the operation of rolling. The formulation with (1 ± 0.01) mm thickness near the drain wear semi-finishing tool for studying different angles, do not help the professional factor in design cutting metal related vibration, friction and interface solid-solid of part and tool during this physical complex process, with multi-parameters no-defined in Sobolev Spaces. The stochastic approach of cracking, wear and fretting due to the cutting forces face boundary layers small dimensions thickness of the workpiece and the tool in the machining position is predicted neighbor to ‘Yakam Matrix’.

Keywords: FEM, geometry, part, simulation, spherical surface engineering, tool, workpiece

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Authors: Jonathan Doku

Abstract:

The study's goal was to evaluate construction site safety management in Ghana. The construction sector has long been seen as a high-risk business. It entails a variety of hazardous and challenging labor duties, such as lifting and working at a height, among others. The accident rate is a standard indicator for comparing the safety performance of construction projects. Because of its high-risk and fast-changing work environment, the construction business is regarded as one of the industries with the highest accident rates in the world. Many mishaps and work-related diseases have occurred there, and construction workers are particularly vulnerable to catastrophic calamities such as falls, collapses, and burial. The study's main goals were to discover characteristics that have a substantial impact on construction site safety, to evaluate the safety management methods utilized on construction sites, and to assess the obstacles associated with construction site safety management. The study was conducted using a quantitative research method and a purposive sampling strategy. Google forms were used to distribute self-administered surveys to 85 responders. 72 of the 85 questionnaires were completed and submitted for analysis, accounting for 84.7 percent of the total. The variables were analyzed using descriptive statistics, mean score ranking, and Cronbach's Alpha Coefficient to ensure the scale's reliability. The formal safety organization structure and the Safety checklist were identified as the key practices of safety management on site as part of the study goals. In addition, it was discovered that the most serious problem with safety management is ineffective supervision. To guarantee efficient monitoring and proper implementation of health and safety rules on building sites, management must be on the ball.

Keywords: construction, safety, risk, management

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: job-shop scheduling, classification, constraints, objective functions

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Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

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Gate Assignment Problem (GAP) is one of the most substantial issues in airport operation. In principle, GAP intends to maintain the maximum capacity of the airport through the best possible allocation of the resources (gates) in order to reach the optimum outcome. The problem involves a wide range of dependent and independent resources and their limitations, which add to the complexity of GAP from both theoretical and practical perspective. In this study, GAP was mathematically formulated as a three-objective problem. The preliminary goal of multi-objective formulation was to address a higher number of objectives that can be simultaneously optimized and therefore increase the practical efficiency of the final solution. The problem is solved by applying the second version of Non-dominated Sorting Genetic Algorithm (NSGA-II). Results showed that the proposed mathematical model could address most of major criteria in the decision-making process in airport management in terms of minimizing both airport/airline cost and passenger walking distance time. Moreover, the proposed approach could properly find acceptable possible answers.

Keywords: airport management, gate assignment problem, mathematical modeling, genetic algorithm, NSGA-II

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: flow-shop scheduling problem, makespan, Petri nets, state equation

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Authors: Yang-Kuei Lin, Yun-Xi Zhang

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This research focuses on the bicriteria correlated parallel machine scheduling problem. The two objective functions considered in this problem are to minimize maximum lateness and total weighted completion time. We first present a mixed integer programming (MIP) model that can find the entire efficient frontier for the studied problem. Next, we have proposed a bicriteria heuristic that can find non-dominated solutions for the studied problem. The performance of the proposed bicriteria heuristic is compared with the efficient frontier generated by solving the MIP model. Computational results indicate that the proposed bicriteria heuristic can solve the problem efficiently and find a set of diverse solutions that are uniformly distributed along the efficient frontier.

Keywords: bicriteria, correlated parallel machines, heuristic, scheduling

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Authors: Rajeev, N. K. Raigar

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In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: operational matrix of differentiation, similarity transformation, shifted second kind chebyshev wavelets, stefan problem

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Authors: Brian E. Usibe

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This paper addresses the problem of a linear crack located in the middle of a homogeneous elastic media under normal tension-compression harmonic loading. The problem of deformation of the fractured media is solved using the direct finite element numerical procedure, including the analysis of the dynamic field variables of the problem. A finite element algorithm that satisfies the unilateral Signorini contact constraint is also presented for the solution of the contact interaction of the crack faces and how this accounts for the qualitative and quantitative changes in the solution when determining the dynamic fracture parameter.

Keywords: harmonic loading, linear crack, fracture parameter, wave number, FEA, contact interaction

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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Authors: K. -H. Yang

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Supplier selection problem is one of the important issues of supply chain problems. Two categories of methodologies include qualitative and quantitative approaches which can be applied to supplier selection problems. However, due to the complexities of the problem and lacking of reliable and quantitative data, qualitative approaches are more than quantitative approaches. This study considers operational cost and supplier’s reliability factor and solves the problem by using a quantitative approach. A mixed integer programming model is the primary analytic tool. Analyses of different scenarios with variable cost and reliability structures show that the effectiveness of this approach to the supplier selection problem.

Keywords: mixed integer programming, quantitative approach, supplier’s reliability, supplier selection

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Authors: Jaeyoung Lee, Minji Je

Abstract:

Objectives: The adolescents not attending school are named out-of-school adolescents. They are more vulnerable to health management and are likely to be exposed to a number of risk factors. This study was conducted to investigate the problem behavior of out-of-school adolescents and analyze the difference caused by gender. Methods: In this study, the problem behaviors of out-of-school adolescents, the vulnerable class, were defined in 8 types and based on this definition, the survey on run away from home, drop out, prostitution, violence, internet game addiction, theft, drug addiction, and smoking was conducted. The study was conducted in a total of 507 out-of-school adolescents, including 342 males, and 165 females. The type, frequency and start time of the 8 problem behaviors were identified. The collected data were analyzed with chi-square test and t-test using SPSS statistics 22. Results: Among the problem behaviors of the subjects, violence ( =17.41, p < .001), internet game addiction ( =16.14, p < .001), theft ( =22.48, p < .001), drug addiction ( =4.17, p=.041), and smoking ( =3.90, p=.048) were more significantly high in male out-of-school adolescents than female out-of-school adolescents. In addition, the frequency of the problem behavior was higher in male out-of-school adolescents with statistical significance than in female out-of-school adolescents (t=5.08, p= < .001). In terms of the start time of the problem behavior, only internet game addiction was higher in male out-of-school adolescents with the statistical significance than in female out-of-school adolescents ( =6.22, p=.032). No statistically significant difference was found in other problem behaviors (p > .05). Conclusions: In this study, it was found that gender difference in problem behaviors of out-of-school adolescents exists, and its frequency and difference of types were identified. When the social countermeasures were provided for those adolescents, a distinguished approach is required depending on the patterns of problem behavior and gender. When preparing policy alternatives and interventions for out-of-school adolescents, it is required to reflect the results of this study.

Keywords: addictive behavior, adolescent, gender, problem behavior

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Authors: Olteanu Constanta, Olteanu Lucian

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Researchers note that algebraic reasoning and sense making is essential for building conceptual knowledge in school mathematics. Consequently, pre-service teachers’ own reasoning and sense making are useful in fostering and developing students’ algebraic reasoning and sense making. This article explores the forms of reasoning and sense making that pre-service mathematics teachers exhibit and use in the process of analysing problem-posing tasks with a focus on first-degree equations. Our research question concerns the characteristics of the problem-posing tasks used for reasoning and sense making of first-degree equations as well as the characteristics of pre-service teachers’ reasoning and sense making in problem-posing tasks. The analyses are grounded in a post-structuralist philosophical perspective and variation theory. Sixty-six pre-service primary teachers participated in the study. The results show that the characteristics of reasoning in problem-posing tasks and of pre-service teachers are selecting, exploring, reconfiguring, encoding, abstracting and connecting. The characteristics of sense making in problem-posing tasks and of pre-service teachers are recognition, relationships, profiling, comparing, laddering and verifying. Beside this, the connection between reasoning and sense making is rich in line of flight in problem-posing tasks, while the connection is rich in line of rupture for pre-service teachers.

Keywords: first-degree equations, problem posing, reasoning, rhizomatic assemblage, sense-making, variation theory

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Authors: Cameron Brown, Jessica Vanburen, Scott Hunt

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This study analyzed 411 international newspaper stories pertaining to gambling-related crimes from January 2013 to December 2014. These stories included accounts of crimes committed to fund gambling or pay gambling debts or that occurred at gambling establishments. Our analysis pays particular attention to those crimes that were imputed to be committed by “problem” or “addictive” gamblers, who commit crimes to fund gambling or pay gambling debts. Previous research on problem/addictive gambling has focused on its etiology or prevalence rates and has not attended to the media portrayals of this behavior and its association with crime. Using frame analysis concepts, the data demonstrate that the newspaper stories typically frame the events as “crimes” and not the result of illness or addiction. The “evidence” of motive that could have indicated psychological problems or additions were rather framed as “criminal motive.” This framing practice advances an identity of a “problem/addictive gambler” as a deviant criminal perpetrator and not a victim of addiction. The paper concludes with a discussion of how these findings can be used to advance research on social portrayals of problem/addictive gamblers. Specifically, we consider how these media frames impede an understanding of problem/addictive gambling as a public health problem.

Keywords: problem gambling, addictive gambling, identity resonace, frame analysis

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Authors: Shaharuddin Salleh, Sara Marouf, Hosein Mohammadi

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Directional sensor networks (DSNs) have recently attracted a great deal of attention due to their extensive applications in a wide range of situations. One of the most important problems associated with DSNs is covering a set of targets in a given area and, at the same time, maximizing the network lifetime. This is due to limitation in sensing angle and battery power of the directional sensors. This problem gets more complicated by the possibility that targets may have different coverage requirements. In the present study, this problem is referred to as priority-based target coverage (PTC). As sensors are often densely deployed, organizing the sensors into several cover sets and then activating these cover sets successively is a promising solution to this problem. In this paper, we propose a learning automata-based algorithm to organize the directional sensors into several cover sets in such a way that each cover set could satisfy coverage requirements of all the targets. Several experiments are conducted to evaluate the performance of the proposed algorithm. The results demonstrated that the algorithms were able to contribute to solving the problem.

Keywords: directional sensor networks, target coverage problem, cover set formation, learning automata

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Authors: Gia Sirbiladze

Abstract:

Route planning problems are among the activities that have the highest impact on logistical planning, transportation, and distribution because of their effects on efficiency in resource management, service levels, and client satisfaction. In extreme conditions, the difficulty of vehicle movement between different customers causes the imprecision of time of movement and the uncertainty of the feasibility of movement. A feasibility level of vehicle movement on the closed route of the disaster-streaking zone is defined for the construction of an objective function. Experts’ evaluations of the uncertain parameters in q-rung ortho-pair fuzzy numbers (q-ROFNs) are presented. A fuzzy bi-objective combinatorial optimization problem of fuzzy vehicle routine problem (FVRP) is constructed based on the technique of possibility theory. The FVRP is reduced to the bi-criteria partitioning problem for the so-called “promising” routes which were selected from the all-admissible closed routes. The convenient selection of the “promising” routes allows us to solve the reduced problem in real-time computing. For the numerical solution of the bi-criteria partitioning problem, the -constraint approach is used. The main results' support software is designed. The constructed model is illustrated with a numerical example.

Keywords: q-rung ortho-pair fuzzy sets, facility location selection problem, multi-objective combinatorial optimization problem, partitioning problem

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Authors: Ehsan Kadkhodaie, Shahin Parvar, Soroush Senemar, Mostafa Shriat, Abdolrasoul Malekpour

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The role of oil in supra distribution transformers is so critical and, several standards in determining the quality of oil have been offered. So far, moisture, viscosity and insulation protection of the oil have been measured based on mechanical and chemical methods and systems such as kart fisher, falling ball and TDM 4000 that most of these techniques are destructive and have many problems such as pollution. In this study, due to the properties of oil and also physical behavior of ultrasound wave new method was designed to in the determination of oil indicators including viscosity and moisture. The results show the oil viscosity can be found from the relationship μ = 42.086/√EE and moisture from (PLUS+) = −15.65 (PPM) + 26040 relationship.

Keywords: oil, viscosity, moisture, ultrasonic waves

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: Thomas Doutre, Emmanuel De Meric De Bellefon

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This paper describes the application of local-search metaheuristic quantum annealing to portfolio opti- mization. Heuristic technics are particularly handy when Markowitz’ classical Mean-Variance problem is enriched with additional realistic constraints. Once tailored to the problem, computational experiments on real collected data have shown the superiority of quantum annealing over simulated annealing for this constrained optimization problem, taking advantages of quantum effects such as tunnelling.

Keywords: optimization, portfolio risk management, quantum annealing, metaheuristic

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Authors: Ratna Sen

Abstract:

As due to very high temperature of Plasma it is very difficult to confine it for sufficient time so that nuclear fusion reactions to take place, As we know Plasma escapes faster than the binary collision rates. We studied the ball analogy and the ‘energy principle’ and calculated the total potential energy for the whole Plasma. If δ ⃗w is negative, that is decrease in potential energy then the plasma will be unstable. We also discussed different approaches of stability analysis such as Nyquist Method, MHD approximation and Vlasov approach of plasma stability. So that by using magnetic field configurations we can able to create a stable Plasma in Tokamak for generating energy for future generations.

Keywords: jello, magnetic field configuration, MHD approximation, energy principle

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Authors: Yassir AbdelRazig

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Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: ant colony, construction site layout, optimization, genetic algorithms

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Authors: Malika Yaici, Assia Arab, Betitra Yakouben, Samia Zermani

Abstract:

Ubiquitous computing is nowadays a reality through the networking of a growing number of computing devices. It allows providing users with context aware information and services in a heterogeneous environment, anywhere and anytime. Selection of the best context-aware service, between many available services and providers, is a tedious problem. In this paper, a service selection method based on Constraint Satisfaction Problem (CSP) formalism is proposed. The services are considered as variables and domains; and the user context, preferences and providers characteristics are considered as constraints. The Backtrack algorithm is used to solve the problem to find the best service and provider which matches the user requirements. Even though this algorithm has an exponential complexity, but its use guarantees that the service, that best matches the user requirements, will be found. A comparison of the proposed method with the existing solutions finishes the paper.

Keywords: ubiquitous computing, services selection, constraint satisfaction problem, backtrack algorithm

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Authors: D. K. Rao, M. G. M. Khan, K. G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries (OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy is skewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB is formulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: stratified sampling, optimum strata boundaries, optimum sample size, pareto distribution, mathematical programming problem, dynamic programming technique

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Authors: I. A. Farhat

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The dynamic economic dispatch (DED) problem is one of the complex, constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: artificial immune system, dynamic economic dispatch, optimal economic operation, large-scale problem

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Authors: Asma Ben Yaghlane, Mohamed Naceur Azaiez

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We consider the problem of attacks on networks. We define the concept of system survivability in networks in the presence of intelligent threats. Our setting of the problem assumes a flow to be sent from one source node to a destination node. The attacker attempts to disable the network by preventing the flow to reach its destination while the defender attempts to identify the best path-set to use to maximize the chance of arrival of the flow to the destination node. Our concept is shown to be different from the classical concept of network reliability. We distinguish two types of network survivability related to the defender and to the attacker of the network, respectively. We prove that the defender-based-network survivability plays the role of a lower bound while the attacker-based-network survivability plays the role of an upper bound of network reliability. We also prove that both concepts almost never agree nor coincide with network reliability. Moreover, we use the shortest-path problem to determine the defender-based-network survivability and the min-cut problem to determine the attacker-based-network survivability. We extend the problem to a variety of models including the minimum-spanning-tree problem and the multiple source-/destination-network problems.

Keywords: defense/attack strategies, information, networks, reliability, survivability

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Authors: Abbas Mirakhorli

Abstract:

A hub covering problem is a type of hub location problem that tries to maximize the coverage area with the least amount of installed hubs. There have not been many studies in the literature about multi-objective hubs covering location problems. Thus, in this paper, a bi-objective model for the hub covering problem is presented. The two objectives that are considered in this paper are the minimization of total transportation costs and the maximization of coverage of origin-destination nodes. A genetic algorithm is presented to solve the model when the number of nodes is increased. The genetic algorithm is capable of solving the model when the number of nodes increases by more than 20. Moreover, the genetic algorithm solves the model in less amount of time.

Keywords: facility location, hub covering, multi-objective optimization, genetic algorithm

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Authors: A. Giannakopoulos, S. B. Buckley

Abstract:

Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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