Snow Removal Algorithms for the city of Regina'

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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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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.

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Solution Attempts

• 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

• 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

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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) ).

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• 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

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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.
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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.

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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.

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• 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

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• 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.

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Agents

• Environment

Individuals
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
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Plow problem

• Environment

Individuals
Be aware of others
Communicate status to others
Include all streets with hierarchy
Avoid visit streets already plowed
Lanes
Road rules
Human issues
etc
Experience data
priority
Decision making module
Knowledge
etc
Communication protocol
Sensing module
Map (graph)
Environment
Other agents
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Thank you