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 Working route finder  Return a list of routes that efficiently utilizes vehicles  Efficiency defined as distance traveled over product delivered

Scope

 Select/develop a working heuristic for solution finder   Several possibilities from previous research Decided on a genetic algorithm

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  Solution finder  Using list of delivery points and quantity to be delivered, utilizes other component to most efficiently deliver the product

Route Finder

   Had attempted to write own route finder program Failed due to data reliability Researched free commercial options

Solution Creator

 Uses three types of genetic operations to find better solutions   Creates a set of Route objects  Each has unique vehicle assigned  The whole set has deliveries to entire customer list Route objects are “genes” that are operated on

Genetic Operations

 Swap  Two deliveries on two different routes are switched  Randomize  The points on a route are randomly reordered

Genetic Operations

 Insert  A delivery point from one route is deleted from that route and added to another

Testing

  Following slide will show percentages Percentages represent the final solution’s total distance traveled, as a percentage of the original, randomly-created solution’s total distance traveled

10,000 Generations

Swap 0.921

Insert 0.833

Rand.

0.93

Swap +Insert 0.89

Swap +Rand.

0.933

Insert +Rand. All 0.884

0.901

0.92

0.905

0.875

0.863

0.92

0.938

0.915

0.892

0.901

0.937

0.894

0.924

0.904

0.913

0.935

0.862

0.945

0.85

0.89

0.92025 0.85825 0.93325 0.88675 0.91525

0.944

0.929

0.9115 0.91175

Test Code

gen_algs $swap1, true, false, false gen_algs $rand1, false, false, true gen_algs $swapRand1,true, false, true gen_algs $insertRand1,false, true, true gen_algs $insert1,false, true, false gen_algs $insert2,false, true, false gen_algs $swapInsert1,true, true, false gen_algs $swapInsert2,true, true, false gen_algs $all1, true, true, true gen_algs $all2, true, true, true

Results

 Most efficient method:  Use two arrays using insert method  Average of 85.75% distance traveled versus original solution

Other Information

 Language  Ruby  Problems  Route finder  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  More genetic operations are not necessarily better  Using all genetic operations usually resulted in moderate results

Extensions

 Addition of working route finder  Will result in fully functional program  Further optimization of genetic algorithms   Increase or decrease chance of mutation Implement different operations