Solving the Vehicle Routing Problem with Multiple Multi-Capacity Vehicles

1
Solving the Vehicle Routing Problem withMultiple
Multi-Capacity Vehicles

• Michael Sanders

2
Overall Goals

• Create a program that given
• List of delivery points
• Number and capacity of vehicles
• List of roads
• Return a list of routes that most efficiently
  utilize vehicles
• Efficiency undefined, but probably will be
  product delivered over distance traveled

3
Current Goals

• Create a program that given
• List of roads w/ geographic coordinates and
  address information
• Returns the quickest route between those two
  points

4
Scope

• Heuristics
• In both aspects of program
• A search
• Used to find shortest route between two locations
• Will use heuristic based on geographical
  coordinates

5
Previous Research

• Vehicle Routing Problem (VRP)
• Extensively researched
• Solutions
• Agent architecture
• Used agents to represent vehicles and
  auctioneer that assigned customers to routes
• Ant colony optimization
• Could solve variants of VRP

6
Variants of VRP

• Variants
• VRP with Time Windows (VRPTW)
• Requires deliveries to be in specific time ranges
  for each delivery
• Multi-Depot VRP (MDVRP)
• Multiple origins for vehicles

7
Components

• Route finder
• Given two intersections, find shortest-time route
  between the two
• Delivery route creator
• Using list of delivery points and quantity to be
  delivered, utilizes other component to most
  efficiently deliver the product

8
Route Finder

• Program responsible finding quickest route
• Uses A search with a geographic heuristic
• Will use latitude and longitude coordinates to
  help find best route
• Will use speed limit information as well to find
  quickest route as well
• Uses Fairfax Cty and Census data

9
Distance Method

• def find_dist coord1, coord2
• dLatcoord10.to_f-coord20.to_f
• dLongcoord11.to_f-coord21.to_f
• dLat 69.1703234283616 Convert to miles
• dLong (Math.cos(coord10.to_f
  0.0174532925199433) 69.1703234283616)
• dist Math.hypot(dLat, dLong)
• return dist
• end

10
Timeline

• Breadth-first search version of route finder is
  working
• Next goal implement heuristic
• Route creator will follow after that
• Aiming to be done early spring in time for
  volunteer groups delivery day to test program

11
Testing

• Currently running route finder and evaluating
  answer against what I know to be best route
• As heuristic is implemented, results can be
  compared against commercially available mapping
  programs such as Google Maps

12
Other Information

• Language
• Ruby
• Problems
• Road data
• Not complete in certain fieldsaddresses,
  coordinates, speed limits, etc.
• Delivery data is not standardized
• Road names not standard throughout list

13
Source of Road Data

• US Census Bureau
• Sample data line11106 75990609 A Great Neck
  Ct A41 3701 3899
  3700 389800002230922309
  51510590599478394783 54144541444160004160
  0030103010 -7709633938714921 -7709897738714251

14
Things Learned

• Use of hash tables and array storage
• Inprocessing of data

15
Testing Analysis

• Route finder is currently successful so far
• Is capable of finding route between two addresses
  very close to each other
• However, is very inefficient
• Breadth-first search
• Given complexity of local road network, finding a
  route between intersections that are far away can
  take days

16
Main Points

• Importance of the route finder
• Crucial to the route creators ability to
  function
• Ways of implementing a heuristic in the route
  creator
• Some ideas from literature research