Ebook Operations research an introduction (10/E): Part 2
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Ebook Operations research an introduction (10/E): Part 2
CHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2ure radar mounted on an aircraft to obtain high-resolution images of up to 20 rectangular swaths of land. Originally. Hight path covering a sequence of swaths was done visually using time-consuming and usually suboplimal mapping software. Subsequently, a TSP-based software was developed to plan miss Ebook Operations research an introduction (10/E): Part 2ions with up to 20 swaths. The new software can plan a mission in less than 20 seconds, compared with 1 hr using the visual process. Additionally, theEbook Operations research an introduction (10/E): Part 2
average mission length is 15% less than the one obtained manually.* 1 211.1SCOPE OF THE TSPClassically, the TSP problem deals with finding the shorteCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2el is defined by two pieces of data:1Tbc number of cities, n.2The distances djj between cities i and i (dịị — ■» if cities i and ị arc not linked).Ibc maximum number of lours in an //-city situation is (n I)! if the network is directed (i.e., dịị A ilji) and half that much if it is not.In reality. T Ebook Operations research an introduction (10/E): Part 2SP applications extend well beyond the classical definition of visiting cities. The real-life application given at the start of this chapter describesEbook Operations research an introduction (10/E): Part 2
mission'Details of the study can be found in D. Panion and A. Elberx. "Mission Planning for Synthetic Aperture Radar Surveillance.” Interfaces, Vol. CHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2.The Aha! Moment below describes a noted TSP application in the late nineteenth century that ushered the first known use of mathematical modeling in archaeology (a field mainly dominated by art historians and linguists). A brief list of other TSP applications is given in Problem 11-1. Additional app Ebook Operations research an introduction (10/E): Part 2lications are also given in Problems 11-2 to 11-14.Aha! Moment: Earliest Mathematical Model in Archaeology, or How to "Seriate" Ancient Egyptian GraveEbook Operations research an introduction (10/E): Part 2
s Using TSP2In 1894. the eminent British Egyptologist l linders Petrie (1853-1942) excavated a vast site of predynastic graves west of the Nile in NaqCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2e built. The method employs classifications of lime-based changes of artifacts, such as Slone tools and pottery fragments.The Naqada tomb site boasted an abundance of potteries used to store essentials Ancient Egyptians thought necessary for the afterlife. Petrie kept meticulous records of the potte Ebook Operations research an introduction (10/E): Part 2ries in each grave, but needed a systematic process to translate the data into a chronological order of the time the graves were constructed. I le staEbook Operations research an introduction (10/E): Part 2
rted with some 900 promising graves, classify ing their potteries into 9 principal styles. He then designed (narrow) paper slips each comprised of 10 CHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2e were entered in their proper columns. A column is left blank if its style is not found in the grave. In the end. a column entry in a slip is viewed in a 0-1 (binary) fashion representing the absence or presence of a potterystyle in the grave.The data slips allowed the determination of a numeric sc Ebook Operations research an introduction (10/E): Part 2ore representing the closeness (in lime) of two graves: a count of the entries that differ from one another among all nine pottery styles, l or examplEbook Operations research an introduction (10/E): Part 2
e, the following two slips yield a score of 4 as shown by the underlines:Grave 1: absent, present, present, present, absent, present, present, absent,CHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2ikely built within the same era: otherwise, large scores suggest the graves originated in distinct eras. Using this line of reasoning. Petrie physically ordered the slips vertically so that graves with similar scores were placed close to one another (ci. Nearest Neighbor heuristic. Section 11.4.1) a Ebook Operations research an introduction (10/E): Part 2nd was thus able to infer a chronological order of the relative times the graves were constructed. Petrie noted that his seriativn problem could be soEbook Operations research an introduction (10/E): Part 2
lved by finding the arrangement of all graves that minimizes the sum of their associated scores.In today's terminology. Petrie's seriation problem is CHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2onstructed. Though Petrie described his model in archaeological terms (rather than mathematically), it is clear that he had an exceptional mathematical mind. Remarkably, using the binary code he developed in the late nineteenth century to represent2Thomas L. Gcrtzen and Martin Grotschel, Hinders Pet Ebook Operations research an introduction (10/E): Part 2rie (1853-1942), the Travelling Salesman Problem, and the Beginning of Mathematical Modeling in Archaeology. Documenta Mathematical Extra Vol. ISMP. pEbook Operations research an introduction (10/E): Part 2
p. 199-210,2012.www.downloadslide.net11.2TSP Mathematical Model 437(absence-presence of) a pottery style in a grave site. Petrie’s numeric score is thCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2ecause of the similarity between the seriation problem and the TSP. Petrie is credited with ushering in the use of the first "mathematical" model in archaeology.As a historical note. Petrie had no formal schooling and his knowledge in mathematics included two self-taught courses in algebra and trigo Ebook Operations research an introduction (10/E): Part 2nometry at age 24. Yet. his discoveries as an archaeologist resulted in a prestigious professorship in Egyptology al University College London. AmongEbook Operations research an introduction (10/E): Part 2
Petrie’s students was Howard Carter who later discovered the tomb of "boy king" Tutankhamun in 1922. Petrie remained committed to scientific discoveryCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertu Ebook Operations research an introduction (10/E): Part 2ellectual abilities. The Petrie Museum of Egyptian Archaeology in London houses more than 80.000 pieces and ranks fourth in Egyptian artifacts after the Cairo Museum, the British Museum, and the Agyplischcs Museum. Berlin.11.2TSP MATHEMATICAL MODELAs staled in Section I 1.1. a I SP model is defined Ebook Operations research an introduction (10/E): Part 2by the number of cities n and the distance matrix |i/jj||. Thc definition of a lour disallows linking a city lo itself by assigning a very high penallEbook Operations research an introduction (10/E): Part 2
y lo the diagonal elements of lhe distance matrix. A T SP is sy inmetric if dij — dji for all /■ and /: else it is asymmetric.Define{I. if city j is rCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertuCHAPTER 11Traveling Salesperson Problem (TSP)Real-Life ApplicationThe Australian Defence Sciences and Technology Organisation employs synthetic apertuGọi ngay
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