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Snow Removal Algorithms for the city of Regina.

Snow Removal Algorithms for the city of Regina. Norberto Flores CIMAT, Mexico Nikolas Karalis National Technical University of Athens, Greece Notice Ringa University of Guelph Ortho Flint University of Western Ontario Under the supervision of : Dr. Edward Doolittle.

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Snow Removal Algorithms for the city of Regina.

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  1. Snow Removal Algorithms for the city of Regina. • Norberto Flores CIMAT, Mexico • Nikolas Karalis National Technical University of Athens, Greece • Notice Ringa University of Guelph • Ortho Flint University of Western Ontario Under the supervision of : Dr. Edward Doolittle

  2. Historical Perspective The Konigsberg Problem Given the city of Konigsberg with its seven bridges, is it possible to go for a walk, starting and ending the same place and passing each of the bridges exactly once? or equivalently : The Euler Tour Problem Given a connected graph G = (N,E) find a tour that visits every edge in E exactly once, or determine that no such tour exists. The Chinese Postman Problem (CPP). Given a connected graph G = (N,E,C) with distances on the edges, find a tour, which passes through every edge at least once and does this in the shortest possible way. The Capacitated Arc Routing Problem (CARP). Given a connected undirected weighted graph G = (N,E,Q), where Q is a demand matrix, and given a number of identical vehicles each with capacity W (where W max qij), find a number of tours such that 1) Each arc with positive demand is serviced by exactly one vehicle, 2) The sum of demand of those arcs serviced by each vehicle does not exceed W, and 3) The total cost of the tours is minimized.

  3. Solution Attempts • Meta Heuristics • Simulated Annealing, Eglese 1994 • Tabu Search, Hertz et al. 2000 • Memetic Algorithm, Lacomme et al. 2001 • Ant Colony System, Doerner et al. 2003 • Guided Local Search, Buellens et al. 2003 Heuristics • Construct-Strike Algorithm, Christofides 1973 • Augment-Merge Algorithm, Golden and Wong 1981 • Path-Scanning Algorithm, Baker et al. 1983 • Parallel-Insert Algorithm, Chapleau et al. 1984 • Augment-Insert Algorithm, Pearn 1991

  4. Optimal Solutions • Branch and Bound, Hirabayashi et al. 1992 • Cutting Plane (LP Relaxation), Belenguer and Benavent 2003 • Branch, Cut and Price algorithm (not applied to the CARP, but useful for combinatorial optimization problems such as Vehicle Routing Problems (VRP) ).

  5. Calculations • 5 Plow Machines • 50.8 km. in total • 106.4 km. will be traversed. • Average Speed (worst case estimation) when plowing : 1km/h • Average Speed (worst case estimation) when traversing a clean road : 20km/h

  6. Generalization for the whole city of Regina REALLY ROUGH estimations Worst Case Senario based on the simplest algorithm We take into account the first 4 categories. 415 km to be cleaned. They will traverse about 415 km. 20 km to be serviced by each plow machine. 20 km to be traversed. 20 hours of servicing + 1 hour of traversing per plow.

  7. Cost Estimations • 20 plow machines X 1 hour of traversing X 10 times per year = 200 hours of traversing per year • 40 people X 200 hours per year = 8,000 hour per year. • 50-100 $/hour X 8000 = 40,000 – 80,000 $ per year. • In a more realistic concept, the actual cost is about 10,000 $ per year.

  8. Another approach… Softcomputing Set of computational techniques of computer science, artificial intelligence, machine learning and some engineering disciplines. Study, model, and analyze very complex phenomena: those for which more conventional methods have not yielded low cost, analytic, and complete solutions. More complex systems from biology, medicine, the humanities, management, etc, often remained intractable to conventional mathematical and analytical methods.

  9. Areas of softcomputing include: Neural networks (NN) Fuzzy systems (FS) Evolutionary computation (EC) Evolutionary algorithms (Genetic A.) Harmony search Memetic algorithms Agents theory (Ant colony) Simulated annealing

  10. Soft computing techniques resemble biological processes more closely than traditional techniques, which are largely based on formal logical systems, such as sentential logic and predicate logic, or rely heavily on computer-aided numerical analysis (as in finite element analysis). • Soft computing techniques often complement each other. Main idea: Softcomputing techniques exploit the tolerance of imprecision, partial truth, and uncertainty for a particular problem.

  11. Individuals Agents Environment rising order of complexity → Observable Partially observable Deterministic Stochastic Episodic Sequential Static Dynamic Discrete Continuous Single-agent Multiple agent Rules of behavior Communication protocol GOALS

  12. Individuals Plow problem… Be aware of others Communicate status to others Include all streets with hierarchy Avoid visit streets already plowed Lanes Road rules Human issues Environment etc……… Experience data priority etc……… Decisionmaking module Knowledge Map (graph) Communicationprotocol Sensing module Other agents Environment

  13. Thank you

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