...Graphing Applications and the TSP Name: Institution: Graphing Applications and the TSP Question 1 A Hamiltonian cycle is a closed loop within a graph that visits all its vertices exactly once. An example of the Hamiltonian cycle is the Travelling salesman problem. The solution to the minimum length of a Hamiltonian cycle is an NP complete problem that cannot be computed in polynomial time. This means that the minimum possible path cannot be computed by a deterministic machine. When completing a Hamiltonian cycle, one has to make sure that there are only two edges getting in and out of a vertex. In addition one has to ensure that there are no sub-cycles in the cycle. In a Hamiltonian cycle with n vertices, the number of different cycles that can be completed is (n-1)! /2 in a complete undirected graph and (n-1)! In a complete directed graph (Narasimhan, 2009). Question 2 A Euler cycle is a path that passes through all the edges of a graph exactly once. It usually starts and ends at the same vertex. For one to construct a Euler cycle all the vertices in the graph must have an even degree. Therefore, one can conclude that any graph with all vertices of an even degree connected is a Euler cycle. Unlike the Hamiltonian cycle, the Euler cycle can be computed in polynomial time. The Euler cycle can be constructed using the Fleury’s or Hierholzer’s algorithm. Question 3 The minimum length of a Hamiltonian cycle is the shortest path that can...
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...Technology Vol:7 2013-06-25 Optimization Using Simulation of the Vehicle Routing Problem International Science Index Vol:7, No:6, 2013 waset.org/Publication/15351 Nayera E. El-Gharably, Khaled S. El-Kilany, and Aziz E. El-Sayed Keywords—Discrete event system simulation, optimization using simulation, vehicle routing problem. points or require a solution to be found quickly. Computational time on the fastest computers for optimization methods has been too long for many practical problems. Cognitive, heuristic, or combination heuristic-optimization solution procedures have been good alternatives [8]. The aim of this work is threefold; to present a new mathematical formulation of the VRP problem that uses fewer decision variables, to show how to model the TSP problem as a discrete event simulation model, and to employ the developed simulation model in finding the optimum/near optimum solution of the problem. This paper is organized as follows: in Section II, the basic concepts of VRP and the solution techniques found in literature will be briefly discussed. In Section III, proposed problem formulations will be presented followed by the simulation model development and optimization using simulation in sections IV and V. Finally, in section VI, the conclusions drawn from this work are presented. I. INTRODUCTION II. LITERATURE REVIEW HE vehicle routing problem (VRP) is one of the most intensively studied problems in operations research, and this is due to its structural charm as well...
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...Demo Script Parallel Computing on Azure - Travelling Salesman Demo Demo version: 1.0.0 Last updated: 12/7/2011 Contents Overview 3 Key Messages 4 Key Technologies 4 Prerequisites 4 Time Estimates 5 Setup and Configuration 6 Demo Flow 7 Opening Statement 9 Step-by-Step Walkthrough 10 Segment #1: Scaling-Up Windows Azure Applications using a Single Instance 10 Segment #2: Scaling-Out Windows Azure Applications using Multiple instances 17 Summary 24 * Overview This demo highlights how to scale-up Web Applications on Windows Azure, using the .NET Task Parallel Library (TPL) classes from .NET Framework 4.0. This library efficiently utilizes multiple processors within Windows Azure roles, where the size of the Virtual Machine instance is greater than Small (i.e. where there are multiple processors available). Additionally, the demo shows how to scale-out applications taking advantage of Technical Computing across multiple role instances, using a Job scheduling algorithm. The work is distributed to all the available instances, maximizing the CPU processing of each. Travelling Salesman demo is using a “genetic” algorithm to quickly solve the problem that would ordinarily require very many conventional interactions to solve. The problem and its real–life applications are widely documented (for example, see http://www.tsp.gatech.edu/index.html). The algorithm used in this demo was taken from http://www.heatonresearch.com/online/introduction–neural–networks–cs–edition–2/chapter–6...
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...partial fulfillment for the award of the degree Bachelor of Technology in “Computer Science engineering” J.N.T.U Hyderabad during the year 2010. Y.V.S Pragathi M.Tech Head of CSE Department 3 Abstract Ant Colony Optimization (ACO) has been successfully applied to those combinatorial optimization problems which can be translated into a graph exploration. Artificial ants build solutions step by step adding solution components that are represented by graph nodes. The existing ACO algorithms are suitable when the graph is not very large (thousands of nodes) but is not useful when the graph size can be a challenge for the computer memory and cannot be completely generated or stored in it. In this paper we study a new ACO model that overcomes the difficulties found when working with a huge construction graph. In addition to the description of the model, we analyze in the experimental section one technique used for dealing with this huge graph exploration. The results of the analysis can help to understand the meaning of the new parameters introduced and to decide which parameterization is more suitable for a given problem. For the experiments we use one real problem with capital importance in Software Engineering: refutation...
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...Introduction TSP (Travelling salesman problem) is an optimization problem that it is difficult to solve using classical methods. Different Genetic Algorithm (GA) have been right to solve the TSP each with advantages and disadvantages (Davis, 2005) In this research paper, I highlight a new algorithm by merging different genetic Algorithm results to the better solution for TSP. In amalgam algorithm, appropriateness of algorithm and traveled distance for TSP has been considered. Results obtained suggest that it does not quickly establish in the local optimum and enjoys a good speed for an inclusive answer (Fogel, 2010). New methods such as GAs, refrigeration algorithms, Artificial Neural Networks, and ACO (Ant Colony Optimization) to solve TSP problem, in recent past have been suggested. Both ACO and GAs is centered on repetitive (Goldenberg, 2005) ACO system was unfilled for the first time by Dorigoat al. to solve TSP. In ACO algorithms, people work together to find the solution. In collective intelligence algorithms, it uses the real life of creatures without putting in consideration the complex mechanisms in run their day to day life in all aspects as best as possible. GA is an iterative procedure that contains a population of individuals or chromosomes. Coding of randomly or heuristic by a string of symbols as a gene in possible solution is done. All possible solution in this search space is examined. When search space is large, GAs usually are used. People can select an...
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...Vehicle Routing Problem with Restocking Professor : O.Univ.Prof.Dr. Richard Hartl Vienna,2014 Student: Shkodran Ahmeti 0851254 Table of contents Table of contents List of figures 1.Introduction 1.2. Problem Presentation 2. Stochastic Vehicle Routing Problem With Optimal Restocking 3. Single Vehicle Routing Problem 4. Multiple Vehicle Routing 4.1. Heuristic Algorithms 4.1.1. Route-First-Cluster-Next Heuristic Algorithm 4.1.2. Cluster-First- Route- Second Algorithm 4.1.3. Improving the Heuristic Solution 5. Computational Study and Results 5.1. Set – partitioning problem formulation 5.2.Test of Algorithms over Problem Sizes and Expected Route Length Limits 5.3. Comparison of the Algorithms over Demand Variations 5.4. Comparison with a Deterministic Method 6. Summary References List of figures Figure 1 A desired truck route with restocking action of returning to the depot when a stockout occurs or in anticipation of a stockout Figure 2 The two updating Strategies a and b Figure 3 Defined or particular route of a single vehicle Figure 4 Expected costs of going directly to the next node Figure 5 Expected costs of the restocking action Figure 6 Monotonicity of function fj(q) Figure 7 Choosing the unused vehicle Figure 8 Forming the clusters Figure 9 Routing through the clusters Figure 10 Cyclic transfer Figure 11 String cross Figure 12 String exchange Figure 13 String relocation ABSTRACT This paper presents a Stochastic Vehicle Routing Problem SVRP, where just...
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...OPERATION RESEARCH “PENGEMBANGAN METODE TRANSPORTASI DALAM OPERASI PENELITIAN” TYPE II – COMPARE & CONTRAST IQBAL TAWAKKAL - 1506694736 PROGRAM MAGISTER TEKNIK INDUSTRI - SALEMBA UNIVERSITAS INDONESIA 1. INTRODUCTION A special class of linear programming problem is Transportation Problem, where the objective is to minimize the cost of distributing a product from a number of sources (e.g. factories) to a number of destinations (e.g. warehouses) while satisfying both the supply limits and the demand requirement. Because of the special structure of the Transportation Problem the Simplex Method of solving is unsuitable for the Transportation Problem. The model assumes that the distributing cost on a given rout is directly proportional to the number of units distributed on that route. Generally, the transportation model can be extended to areas other than the direct transportation of a commodity, including among others, inventory control, employment scheduling, and personnel assignment. Transportation was one of the earliest application areas of operations research, and important transportation problems, such as the traveling salesman problem, vehicle routing problem, and traffic assignment problem, contributed to fundamental knowledge in operations research. Transportation remains one of the most important and vibrant areas of operations research. The transportation model has some rigid characteristic, which are: * A product is transported from a number...
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...Local Search Heuristics for the Vehicle Routing Problem Chris Gro¨r1 e Oak Ridge National Laboratory, 1 Bethel Valley Rd, Oak Ridge, TN 37831 cgroer@gmail.com Bruce Golden R.H. Smith School of Business, University of Maryland, College Park, MD 20742, USA, bgolden@rhsmith.umd.edu Edward Wasil2 Kogod School of Business, American University, Washington, DC 20016, USA, ewasil@american.edu The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. Real-world instances of the VRP can contain hundreds and even thousands of customer locations and can involve many complicating constraints, necessitating the use of heuristic methods. We present a software library of local search heuristics that allow one to quickly generate solutions to VRP instances. The code has a logical, object-oriented design and uses efficient data structures to store and modify solutions. The core of the library is the implementation of seven local search operators that share a similar interface and are designed to be extended to handle additional options with minimal code change. The code is well-documented, straightforward to compile, and is freely available online. The code contains several applications that can be used to generate solutions to the capacitated VRP. Computational results indicate that these applications are able to generate solutions that are within about one percent of the best-known solution on benchmark problems. Key words: vehicle routing; optimization; heuristics;...
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...The piece of technology I will be adding to the story The Notorious Jumping Frog of Calaveras County is anabolic steroids.They will arrive in this story by a travelling salesman who was passing through the town, carrying a ‘miracle drug’, promising that it can boost performance and do other amazing things. Anabolic steroids are a synthetic version of testosterone and can be used to enhance a person's performance, boost muscle growth, and decrease the amount of rest muscles need to recover. The steroids will be given to the frog by Jim Smiley to boost his performance so that he can bet on him and always win. Anabolic steroids are a synthetic version of the male hormone testosterone and can be used to enhance a person’s performance. They are used to treat to treat hormone problems in men, though using them to boost performance is illegal and can cause damage to the body. Anabolic steroids affect the skeletal muscles by activating cells to produce more protein to build more muscle cells. They also inhibit glucocorticoids, which decreases the time your muscles need...
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...of the tragedy are related to ancient Greece. A Greek tragedy is a sad story, which represents a character with a tragic flaw leading to his downfall. In addition, in traditional tragedy, the main character falls from high authority and often it is predetermined by fate, while the audience experiences catharsis (Bloom 2). Arthur Miller’s play Death of a Salesman is considered to be a tragedy because this literary work has some of the main characteristics of the tragedy genre. In this play, the main character Willy Loman possesses such traits and behaviors that lead to his downfall, and the audience experiences catharsis. Willy Loman as a real tragic hero comes to the decision to commit suicide because of serious financial problems of his family (Phelps 79). This play has already been criticized by a number of literary critics who represented different opinions on the plot of the book. The major goal of this paper is to critically evaluate the play Death of a Salesman written by the well-known American writer Arthur Miller, paying special attention to the play’s characteristics of a tragedy. In the play Death of a Salesman, the author investigates human nature and represents his main character as a person whose dissatisfaction with his own life leads to his tragic end. The plot of this literary work is rather simple. The play consists of two acts. In the first act, Willy Loman, the main character of Miller’s play returns home from New York. It is found that his goal was to...
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...Introduction to Transportation Problem Re-cap of linear programming, Classic transportation problem, LP formulation, Solution using MS Excel Text: BRS 5.1, 5.2, 5.3 Class 2: Transportation Problem (cont.) Basic feasible solution of TP, properties, Analysis of Excel output, Sensitivity analysis Text: BRS 5.1, 5.2, 5.3 Class 3: Transshipment problem Formulation of LP model, different variations (unbalanced case, combining with production scheduling, multi-modal and multi-SKU transportation), Conversion of transshipment model into classic transportation model. Text: BRS 5.4, 5.5 Class 4: Assignment problem Binary ILP formulation, solution by Hungarian method Text: BRS 5.6 Class 5: Network models Shortest path problem, Minimal spanning tree Text: BRS 5.8, 5.9 Class 6: Game theory Introduction to game theory: Types of game, Two person zero-sum game, concept of saddle point, dominance rule Text: WW 14.1, 14.2 Class 7: Game theory (contd.) Mixed startegy, Linear programming formulation Text: WW 14.2, 14.3 Class 8: Mid-term Test Class 9: Markov chain Introduction to stochastic processes, markov chains, transition probability matrix, steadystate probabilities. Text: Handouts and WW 17.1, 17.2, 17.3 Class 10: Decision theory Decision making under uncertainty, Decision criteria, Decision Tree Text: BRs 8.1, 8.2, 8.3, 8.4, 8.6 Class 11: Decision theory (contd.) Decision making under risk, EVPI, EVSI Text: 8.5, 8.8, 8.9 Class 12: Travelling Salesman Problem Optimization model formulation...
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...Fatherhood: Does the past effect the present? Did the lack of a father negatively affect Willy’s character? (Bradford,1) Willy Loman’s father left his family and was out of his childhood when Wily was only 3 years eleven months old. As a result Willy was a failure of a father to his sons. By not having his father in his life, Willy did not know or learn how to be a good father to Biff and Happy. In the play, Death of a Salesman, written by Arthur Miller, the main character Willy is a husband, father, friend, business partner and salesman. Willy is not very good at any aspects of his life, particularly parenthood. The factors in which Willy fails at parenting are numerous including, not making his family number one priority, not disciplining his sons, encouraging bad behaviours, not admitting his faults and lying. Firstly, with Willy not making his family his number one priority, he does this by constantly putting work before them. Willy has never been there for his sons, as he is travelling every week to visit customers, and he never really had the chance to get to know, and show his love for his sons. Willy does not have the father-son relationship with his children that most fathers desire to have. Willy’s love for his eldest son Biff, is based solely on Biffs achievements as a football player. Biff has been offered '...scholarships to three universities...' (Miller 20), and when he fails math, and because of poor grades does not qualify for the university...
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...Discount: Reduction from the full amount of a price. The following are the five types of discounts which we see are: Simple Discount: Offer a price reduction on a product by a percentage. For example, buy a shirt and receive 25 % off the original price. Minimum Purchase Discount: Offer a price reduction on a minimum quantity purchase. For example, buy two shirts and receive 20 % off each shirt. Buy N, Get one Free. Offer a free gift with a minimum quantity purchase. For example, buy two shirts and receive a third shirt for free• Offer a price reduction on a product if another product is purchased. For example, buy a shirt and receive Rs.10 off a pair of jeans• Paired Set Discount: Offer a price reduction on an item if a certain quantity of another item is purchased. For example, buy three shirts and receive 30 % off a pair of jeans• Order Discount: Offer a price reduction or free shipping on the order total, if a certain amount is purchased. For example, buy Rs. 5000worth of merchandise, and receive 10 % off the total order. Banking: A system of trading in money which involved safeguarding deposits and making funds available for borrowers.* what is the use of mathematics in Banking •Bank is full of transactions. In turn the transaction is nothing but mathematics •Banks are also involved in stocks and bonds. Bond calculations are mathematical. Stock options are also quite mathematical Foreign...
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...“If the proper study of mankind is man, man’s inescapable problem is himself-what he would like to be, what he is, what he is not, and yet what he must live and die with.” –John Mason Brown (Brown 207) The Two Sides of America and Willy Loman America is a madman. America became a man who fell off his rocker and is free to roam the earth to disturb the minds of those who inhabit it. The American dream is often considered a fantasy by those who criticize it. Capitalism sometimes may not be all that it is cracked up to be when you get down in the dirt and start building. Even when you begin to believe you are moving forward you can be eternally unsure of the direction you are moving. At this point, the race to the top can drive you crazy. In Arthur Miller’s play A Death of a Salesman, the central character Willy Loman embodies the American dream and he is certainly mad. In the story, Willy works as a growing salesman who is getting older and tiring from travelling for work for small returns. His hard work goes unrewarded as each paycheck goes right into the house which always needs to be serviced and mended. This house as it gets to be paid off after 25 years finally becomes owned by the family who ironically may soon not live in the house together. Willy’s family consists of his humble and caring wife, Linda, and his two handsome and able-bodied sons Happy and Biff. The story centers around the external conflict of Willy pushing Biff to be what he wants him to be and Biff’s...
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...[pic] MANAGEMENT REPORT INTRODUCTION 3 PLANNING 5 ORGANIZING 11 ANALYSIS OF THE ORGANISATION STRUCTURE 13 LEADING 17 LEADERSHIP STYLE 17 CONCLUSION 21 SWOT ANALYSIS 21 INTRODUCTION The focus of this report is basically to analyze the different management functions at Coca cola beverages Pakistan limited Karachi. These functions include planning, organizing, leading and controlling. History: International: Coca-Cola laid the foundation of the beverage industry when it was formed in May 1886 in Atlanta. However it was not until 1895 that the idea of selling coke in bottles was introduced. With the passage of time Coca-Cola gained popularity and its product began to get recognized internationally. Thus from its mere beginning in 1886 Coca-Cola has now been transformed into a strong multinational with its product being currently recognized all over the world. Coca-Cola, in fact, has now become one of the most famous and widely consumed brands in the world. It has not only established its footings in the beverage industry but is currently heading the list of the most financially sound companies in the world. Pakistan: Although Coca-Cola is not a new name for the local market, Coca-Cola Beverages Pakistan Limited (CCBPL) began its operations on 26 May 1996 in Pakistan. Coca-Cola Beverages Private LTD (CCBPL) is a joint venture between Coca-Cola International, Fraser and Neeves Singapore...
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