Search results for: swing problem

Authors: Farzad Razavi, Behrooz Taheri, Mohammad Parpaei, Mehdi Mohammadi Ghalesefidi, Siamak Zarei

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As one of the major problems in protecting large-dimension power systems, power swing and its effect on distance have caused a lot of damages to energy transfer systems in many parts of the world. Therefore, power swing has gained attentions of many researchers, which has led to invention of different methods for power swing detection. Power swing detection algorithm is highly important in distance relay, but protection relays should have general requirements such as correct fault detection, response rate, and minimization of disturbances in a power system. To ensure meeting the requirements, protection relays need different tests during development, setup, maintenance, configuration, and troubleshooting steps. This paper covers power swing scheme of the modern numerical relay protection, 7sa522 to address the effect of the different fault types on the function of the power swing blocking. In this study, it was shown that the different fault types during power swing cause different time for unblocking distance relay.

Keywords: power swing, distance relay, power system protection, relay test, transient in power system

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Authors: Agata Matuszewska, Małgorzata Syczewska

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The movement of the upper limbs contributes significantly to balance control while walking in humans. However, the impact of different arm swing modes on gait stability is yet to be determined. This work intends to establish numerical parameters for assessing the arm swing. Nineteen people, comprising fifteen young, healthy individuals, two middle-aged individuals, and two individuals with dysfunctions, were analyzed using the movement analysis system. Proposed parameters such as ASᵢₐ (reflecting the arm swing amplitude) and Pearson’s correlation coefficient between the right and left upper limbs can be used to classify the type of movement task each participant performs. The results indicate that the ASᵢₐ parameter could potentially detect any abnormalities in upper limb functions, which may be due to musculoskeletal disorders or other malfunctions.

Keywords: arm swing, human balance, interlimb coordination, motion analysis system

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Authors: Eleni Tsalaporta, Sebastien Vaesen, James M. D. MacElroy, Wolfgang Schmitt

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Carbon dioxide capture has attracted the attention of many governments, industries and scientists over the last few decades, due to the rapid increase in atmospheric CO2 composition, with several studies being conducted in this area over the last few years. In many of these studies, CO2 capture in complex Pressure Swing Adsorption (PSA) cycles has been associated with high energy consumption despite the promising capture performance of such processes. The purpose of this study is the economic capture of atmospheric carbon dioxide for its transformation into a clean type of energy. A single column Temperature /Vacuum Swing Adsorption (TSA/VSA) process is proposed as an alternative option to multi column Pressure Swing Adsorption (PSA) processes. The proposed adsorbent is SIFSIX-3-Ni, a newly developed MOF (Metal Organic Framework), with extended CO2 selectivity and capacity. There are three stages involved in this paper: (i) SIFSIX-3-Ni is synthesized and pelletized and its physical and chemical properties are examined before and after the pelletization process, (ii) experiments are designed and undertaken for the estimation of the diffusion and adsorption parameters and limitations for CO2 undergoing capture from the air; and (iii) the CO2 adsorption capacity and dynamical characteristics of SIFSIX-3-Ni are investigated both experimentally and mathematically by employing a single column TSA/VSA, for the capture of atmospheric CO2. This work is further supported by a technical-economical study for the estimation of the investment cost and the energy consumption of the single column TSA/VSA process. The simulations are performed using gProms.

Keywords: carbon dioxide capture, temperature/vacuum swing adsorption, metal organic frameworks, SIFSIX-3-Ni

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Authors: Amin Masoumiganjgah, Luke Salmon, Julianne Burnton, Fahimeh Bagheri, Gavin Lenton, S. L. Ezekial Tan

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Introduction: The incidence of proximal biceps tenodesis and acute distal biceps repair is increasing, and rehabilitation protocols following both are variable. Golf is a popular sport within Australia, and the Gold Coast has become a Mecca for golfers, with more courses per capita than anywhere else in the world. Currently, there are no clear guidelines regarding return to golf play following biceps procedures. The aim of this study was to determine biceps brachii activation during the golf swing through electromyographic analysis, and subsequently, aid in rehabilitation guidelines and return to golf following tenodesis and repair. Methods: Subjects were amateur golfers with no previous upper limb surgery. Surface electromyography (EMG) and high-speed video recording were used to analyse activation of the left and right biceps brachii and the anterior deltoid during the golf swing. Each participant’s maximum voluntary contraction (MVC) was recorded, and they were then required to hit a golf ball aiming for specific distances of 2, 50, 100 and 150 metres at a driving range. Noraxon myoResearch and Matlab were used for data analysis. Mean % MVC was calculated for leading and trailing arms during the full swing and its’ 4 phases: back-swing, acceleration, early follow-through and late follow-through. Results: 12 golfers (2 female and 10 male), participated in the study. Median age was 27 (25 – 38), with all being right handed. Over all distances, the mean activation of the short and long head of biceps brachii was < 10% through the full swing. When breaking down the 50, 100 and 150m swing into phases, mean MVC activation was lowest in backswing (5.1%), followed by acceleration (9.7%), early follow-through (9.2%), and late follow-through (21.4%). There was more variation and slightly higher activation in the right biceps (trailing arm) in backswing, acceleration, and early follow-through; with higher activation in the leading arm in late follow-through (25.4% leading, 17.3% trailing). 2m putts resulted in low MVC values (3.1% ) with little variation across swing phases. There was considerable individual variation in results – one tense subject averaged 11.0% biceps MVC through the 2m putting stroke and others recorded peak mean MVC biceps activations of 68.9% at 50m, 101.3% at 100m, and 111.3% at 150m. Discussion: Previous studies have investigated the role of rotator cuff, spine, and hip muscles during the golf swing however, to our knowledge, this is the first study that investigates the activation of biceps brachii. Many rehabilitation programs following a biceps tenodesis or repair allow active range against gravity and restrict strengthening exercises until 6 weeks, and this does not appear to be associated with any adverse outcome. Previous studies demonstrate a range of < 10% MVC is similar to the unloaded biceps brachii during walking(1), active elbow flexion with the hand positioned either in pronation or supination will produce MVC < 20% throughout range(2) and elbow flexion with a 4kg dumbbell can produce mean MVC’s of around 40%(3). Our study demonstrates that increasing activation is associated with the leading arm, increasing shot distance and the late follow-through phase. Although the cohort mean MVC of the biceps brachii is <10% through the full swing, variability is high and biceps activation reach peak mean MVC’s of over 100% in different swing phases for some individuals. Given these EMG values, caution is advised when advising patients post biceps procedures to return to long distance golf shots, particularly when the leading arm is involved. Even though it would appear that putting would be as safe as having an unloaded hand out of a sling following biceps procedures, the variability of activation patterns across different golfers would lead us to caution against accelerated golf rehabilitation in those who may be particularly tense golfers. The 50m short iron shot was too long to consider as a chip shot and more work can be done in this area to determine the safety of chipping.

Keywords: electromyographic analysis, biceps brachii rupture, golf swing, tendon surgery

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Authors: Abdelsalam Omar

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This paper presents simulation-based case study that indicate the need for accurate dynamic modeling of distance protection relay. In many cases, a static analysis based on current and voltage phasors may be sufficient to assess the performance of distance protection. There are several circumstances under which such a simplified study does not provide the depth of analysis necessary to obtain accurate results, however. This letter present study of the influences of magnetizing inrush and power swing on the performance of distance protection relay. One type of numerical distance protection relay has been investigated: 7SA511. The study has been performed in order to demonstrate the relay response when dynamic model of distance relay is utilized.

Keywords: distance protection, magnitizing inrush, power swing, dynamic model of protection relays, simulatio

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: C. S Lee, W. C. Hsu, H. Y. Liu, C. J. Lin, S. C. Yao, Y. T. Shen, Y. C. Lin

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In₀.₁₈Al₀.₈₂N/AlN/GaN metal-oxide-semiconductor heterostructure field-effect transistors (MOS-HFETs) having Al₂O₃ gate-dielectric and backside metal-trench structure are investigated. The Al₂O₃ gate oxide was formed by using a cost-effective non-vacuum ultrasonic spray pyrolysis deposition (USPD) method. In order to enhance the heat dissipation efficiency, metal trenches were etched 3-µm deep and evaporated with a 150-nm thick Ni film on the backside of the Si substrate. The present In₀.₁₈Al₀.₈₂N/AlN/GaN MOS-HFET (Schottky-gate HFET) has demonstrated improved maximum drain-source current density (IDS, max) of 1.08 (0.86) A/mm at VDS = 8 V, gate-voltage swing (GVS) of 4 (2) V, on/off-current ratio (Ion/Ioff) of 8.9 × 10⁸ (7.4 × 10⁴), subthreshold swing (SS) of 140 (244) mV/dec, two-terminal off-state gate-drain breakdown voltage (BVGD) of -191.1 (-173.8) V, turn-on voltage (Von) of 4.2 (1.2) V, and three-terminal on-state drain-source breakdown voltage (BVDS) of 155.9 (98.5) V. Enhanced power performances, including saturated output power (Pout) of 27.9 (21.5) dBm, power gain (Gₐ) of 20.3 (15.5) dB, and power-added efficiency (PAE) of 44.3% (34.8%), are obtained. Superior breakdown and RF power performances are achieved. The present In₀.₁₈Al₀.₈₂N/AlN/GaN MOS-HFET design with backside metal-trench is advantageous for high-power circuit applications.

Keywords: backside metal-trench, InAlN/AlN/GaN, MOS-HFET, non-vacuum ultrasonic spray pyrolysis deposition

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Ocotlán Díaz-Parra, Jorge A. Ruiz-Vanoye, Alejandro Fuentes-Penna, Beatriz Bernabe-Loranca, Patricia Ambrocio-Cruz, José J. Hernández-Flores

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The Maritime Platform Transport Problem of Solid, Special and Dangerous Waste consist of to minimize the monetary value of carry different types of waste from one location to another location using ships. We offer a novel mathematical, the characterization of the problem and the use CPLEX to find the optimal values to solve the Solid, Special and Hazardous Waste Transportation Problem of offshore platforms instances of Mexican state-owned petroleum company (PEMEX). The set of instances used are WTPLib real instances and the tool CPLEX solver to solve the MPTPSSDW problem.

Keywords: oil platform, transport problem, waste, solid waste

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Cagri Memis, Muzaffer Kapanoglu

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The school bus routing problem (SBRP) is a variant of the Vehicle Routing Problem (VRP) classified as a location-allocation-routing problem. In this study, the SBRP is decomposed into two sub-problems: (1) bus route generation and (2) bus stop selection to solve large instances of the SBRP in reasonable computational times. To solve the first sub-problem, we propose a genetic algorithm to generate bus routes. Once the routes have been fixed, a sub-problem remains of allocating students to stops considering the capacity of the buses and the walkability constraints of the students. While the exact method solves small-scale problems, treating large-scale problems with the exact method becomes complex due to computational problems, a deficiency that the genetic algorithm can overcome. Results obtained from the proposed approach on 150 instances up to 250 stops show that the matheuristic algorithm provides better solutions in reasonable computational times with respect to benchmark algorithms.

Keywords: genetic algorithm, matheuristic, school bus routing problem, vehicle routing problem

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

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

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

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Authors: Miriam Palomo-Nieto, Adrian Agricola, Rudolf Psotta, Reza Abdollahipour, Ludvik Valtr

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The importance of vision and the visual control of movement have been labeled in the literature related to motor control and many studies have demonstrated that children with low motor competence may rely more heavily on vision to perform movements than their typically developing peers. The aim of the study was to highlight the effects of different visual conditions on motor performance during walking in children with different levels of motor coordination. Participants (n = 32, mean age = 8.5 years sd. ± 0.5) were divided into two groups: typical development (TD) and low motor coordination (LMC) based on the scores of the Movement Assessment Battery for Children (MABC-2). They were asked to walk along a 10 meters walkway where the Optojump-Next instrument was installed in a portable laboratory (15 x 3 m), which allows that all participants had the same visual information. They walked in self-selected speed under four visual conditions: full vision (FV), limited vision 100 ms (LV-100), limited vision 150 ms (LV-150) and non-vision (NV). For visual occlusion participants were equipped with Plato Goggles that shut for 100 and 150 ms, respectively, within each 2 sec. Data were analyzed in a two-way mixed-effect ANOVA including 2 (TD vs. LMC) x 4 (FV, LV-100, LV-150 & NV) with repeated-measures on the last factor (p ≤.05). Results indicated that TD children walked faster and with longer normalized steps length and strides than LMC children. For TD children the percentage of the single support and swing time were higher than for low motor competence children. However, the percentage of load response and pre swing was higher in the low motor competence children rather than the TD children. These findings indicated that through walking we could be able to identify different levels of motor coordination in children. Likewise, LMC children showed shorter percentages in those parameters regarding only one leg support, supporting the idea of balance problems.

Keywords: visual information, motor performance, walking pattern, optojump

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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: 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: 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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