PSO algorithms for Generalized Multi-depot VRP with pickup & delivery requests Pandhapon Sombuntham

 Background  Proposed Approaches  Experiment  Summary  Q&A Contents

Transportation of Material Right Time Route Planning Right Place Right Quantity ?

Background Location A Location B Depot otb-games.com To ATo B VRP (Vehicle Routing Problem ) Shipment Done Shipment Done To Depot VRPSPD (Vehicle Routing Problem with simultaneous pickup & delivery ) Shipment Done To B No direct shipment between Locations (except depot) No direct shipment between Locations (except depot)

Background Depot otb-games.com Location A Location B To B PDP (Pickup & Delivery Problem) Finished Shipment Empty truck Vehicle Station Direct shipment 3 Roles of Locations Pickup Location Delivery Location Vehicle Station One role for a location Direct shipment 3 Roles of Locations Pickup Location Delivery Location Vehicle Station One role for a location To B clipartof.com Delivery Location Pickup Location

Background Location A Location B 1 1 To A 2 2 To B Location C 7 7 To A Allow … Direct shipment … Can pickup more than 1 item from a location to deliver to more than one destinations. … Location can play multiple roles Allow … Direct shipment … Can pickup more than 1 item from a location to deliver to more than one destinations. … Location can play multiple roles 6 6 To D 3 3 To B 4 4 To C To B GVRP – MDPDP Generalized Vehicle Routing problem for multi-depot with pickup and delivery requests Location D Any location can play multiple roles

Deliver Background Depot (Supply Node) Customer ( Demand Node) VRP (Vehicle Routing Problem ) PDP (Pickup & Delivery Problem) GVRP – MDPDP Generalized Vehicle Routing problem for multi-depot with pickup and delivery requests Pickup Deliver Vehicle Station Pickup Location Deliver Location Location with Vehicle Location w/o Vehicle Allow Multiple roles for each location Many pickups at a location

 Limousine service at Airport in Big city Example mitchellslimousines.net Airport To C clipartof.com To B clipartof.com To A clipartof.com A B C Airport Station Many pickups at airport Airport is both pickup and delivery location

Pooling Vehicle SME Location A Location B 1 1 To A 2 2 To B Location C 7 7 To A 6 6 To D 3 3 To B 4 4 To C To B GVRP – MDPDP Generalized Vehicle Routing problem for multi-depot with pickup and delivery requests Location D SME Sharing Fleet of vehicles Among alliances Any location can play multiple roles + Many Pickups at locations

Daily operation  100s items  Consider ? VRP     Vehicle capacity Heterogeneous vehicle On-Time delivery Maximum Route time Direct shipments Many pickups items at any locations Multiple-role locations PDP      GVRP-MDPDR        Experience Poor Utilization

Proposed Approach Based on Particle Swarm Optimization (PSO) framework for solving the vehicle routing problems,i.e. CVRP VRPSPD,and VRPTW (Ai & Kachitvichyanukul, 2009a,2009b,2009c) PSO with multiple social learning terms of Pongchairerks & Kachitvichyanukul [10],[11] PSO rigasturists.lv istockphoto.com Initialize particles with random position and zero velocity Evaluate fitness value Update pbest and gbest Meet stopping criterion? Update velocity and position Start End YES NO

Thesis Framework GVRP-MDPDR GLNPSO Application Encoding (Solution representation) Encoding (Solution representation) Decoding SD1 SD2 SD3 Preliminary TestEffect on Time Appropriate Swarm size & steps Comparison algorithms

Test Instances  PDPTW (Li & Lim,2001)  Special cases of GVRP-MDPDR  Newly Generated Instances  locations with items involved Half-random-half-clustered Randomly distributed Clustered

Test on PDPTW Case Best known solution Best of 5 Replications Average NVDistanceNVDistanceNVDistance lc lc lc lc lc lc lc lc lc lc lc lc lc

Application on Real case Vehicle capacity Heterogeneous vehicle On-Time delivery Maximum Route time Direct shipments Many pickups items at any locations Multiple-role locations  128 items  Consider        Vehicle ID27 Items18 No. of Visit12 Route Time534 Sequence Location Visit Pickup ItemsDeliver Items , ,57, ,61, ,

Application with Multi-Objective PSO (MOPSO) GVRP-MDPDR GLNPSO Application Encoding (Solution representation) Encoding (Solution representation) Decoding MOPSO w 1 x Cost 1 x NV + w 2 x Cost 2 x Total distance = Total Cost

Multi-Objective PSO  Two objective functions  Number of Vehicle used  Total distances  MOPSO  Trade-off solutions  Pareto front optimality  (Nguyen et al., 2010)

Multi-Objective PSO Erc1 ParameterValue No. of Particle 50 Iteration500 No. of Neighbors 5 Cp1.3 Cg1.3 Cl1 Cn2 Inertia weight 0.9 to 0.4 Provide Alternatives for the decision maker to analyze the tradeoff.

 More Generalized case of VRP  Add practical consideration  Extend PSO Framework  Experiments  Application with Real-word  Decision Supports tools Summary Vehicle capacity Heterogeneous vehicle On-Time delivery Maximum Route time Direct shipments Many pickups items at any locations Multiple-role locations       

 Further study  Develop encoding and decoding Procedure Randomness & Logical methods  Analyze more about properties of the problem  More Practical consideration  MOPSO More objectives to considered  Adaptive PSO Recommendation

Q&A

Best Wishes For your attentions

Output Vehicle ID27 Items18 No. of Visit12 Route Time534 Sequence Location Visit Waiting TimePickup ItemsDeliver Items , ,57, ,61, ,