Solving the Vehicle Routing Problem with Multiple Multi-Capacity Vehicles Michael Sanders

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

Current Goals  Continue to develop route creator  Current assigns all customers to routes  Need to randomize assignment of customers to route  Need to create catch in case route finder is unsuccessful/takes too long to find route between previous and current customer

Scope  Heuristics  In both aspects of program  A* search  Based on program’s estimate of distance to target  Route creator  Will most likely look to minimize distance traveled

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

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

Components  Route finder  Given two intersections, find shortest- distance route between the two  Not necessarily fastest route  Would need speed limit data  Delivery route creator  Using list of delivery points and quantity to be delivered, utilizes other component to most efficiently deliver the product

Route Finder  Program responsible finding quickest route  Uses US Census road data  Uses A* search with a geographic heuristic  Program moves from intersection to intersection as identified by lat/long  Afterwards, determines route taken by list of lat/long coordinates passed through

Demonstration of Route Finder 2 Search_A_clean.rb

Route Creator  In beginning stages  Goes through list of customers  Assigns everyone to routes based on vehicle capacities  Two classes  Route  Solution

tempCust=$deliveries.clone $routes=Array.new $routes << Route.new($vehicles[0]) routeCounter=0 vehicleCounter=1 while not tempCust==[] starter=true while starter currentCust=tempCust.delete_at(rand*tempCust.length-1) starter=$routes[routeCounter].add_cust(currentCust) end routeCounter+=1 $routes << Route.new($vehicles[vehicleCounter]) vehicleCounter+=1 end

Timeline  Route finder is done (except for when it doesn’t work)  Now writing route creator  Plan to use genetic algorithm to solve problem  Route class will be the “genes” of the Solution object

Testing  Easiest testing was to run route finder against personal knowledge  Program fails at longer distances  Goes for straightest path

Other Information  Language  Ruby  Problems  Data not completely standardized

Main Points  Optimum answer not necessarily goal  Finding optimum is too time-intensive  Drivers have personal knowledge of routes and can adapt as necessary