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# Hybrid Genetic Algorithm for Solving Multi Constraint Vehicle Routing Problem

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This presentation is my grad school's thesis seminar (September 2012). Still discuss about Vehicle Routing Problem (VRP), but with additional solving methods. The last presentation (discuss about VRPSPD) was only solved with Genetic Algorithm, however, in this presentation additional Local Search also used to help GA solved the problem faster and more efficient. That's why we call it "Hybrid Genetic Algorithm". The constraint itself also added, beside Simultaneous Pickup and Delivery (SPD), Time Window and Multi Trips are included.

Hopefully this simple presentation could enhance your knowledge about VRP and Genetic Algorithm.

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### Hybrid Genetic Algorithm for Solving Multi Constraint Vehicle Routing Problem

1. 1. Hybrid Genetic Algorithm for Solving Multi Constraint Vehicle Routing Problem Carry Prameswari 23611001
2. 2. Outline Introduction Previous Work Hybrid Genetic Algorithm Multi-Constraint VRP Analysis Conclusion and Future Work
3. 3. Introduction
4. 4. Introduction: Vehicle Routing Problem Find the minimum total traveling distance with CONSTRAINTS that must be fulfilled
5. 5. Introduction: Vehicle Routing Problem VRP in our daily life Airline business Shuttle Travel Logistic Supply chain Package delivery Networking Communication
6. 6. Previous Work
7. 7. Previous Works • Capacitated • Simultaneous Pickup and Delivery VRP Case Study • Max. 12 Destination Point • Genetic Algorithm • Prins Splitting Procedure Method
8. 8. BP B A C D E A: B: C: D: E: Previous Works VRP with Simultaneous Pick-up & Delivery Constraint
9. 9. BP B A C D E A: B: C: D: E: Previous Works VRP with SPD and Vehicle spec. constraint
10. 10. Previous Works Genetic Algorithm BP B A C D E A B C D E 1 2 3 4 5
11. 11. Genetic Algorithm Initialization Evaluation & Selection Crossover Mutation Evaluation Selection: Roulette Wheel Procedure Novel Order Cross Over 1 22 33 44 5566 77 8 9 1100 10 9 8 7 6 5 4 3 2 1 10 9 7 Inversion Mutation 1 2 33 44 55 66 77 88 99 1100 Swapping Mutation 1 2 3 44 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
12. 12. Current Research C VRP SPD GA + Prins Slitting Procedure Local Search Multi-Trips Time Window Previous Work Add. Solving Method Additional Constraints SCOPE : Basic constraint  CVRP-SPD. VRP TW only consider about travelling and service time .
13. 13. Hybrid Genetic Algorithm
14. 14. Hybrid Genetic Algorithm GA Local Search Hybrid Genetic Algorithm Position-Oriented Genes Exchange Static Move Descriptor (SMD): a. 1-0 Exchange Move b. 1-1 Exchange Move c. 2-opt Move
15. 15. Hybrid Genetic Algorithm Local Search: Position-Oriented Genes Exchange 1 2 3 4 5 2 1 3 4 5 2 1 3 4 5 1 2 3 4 5 3 2 1 4 5 1 3 2 4 5 4 2 3 1 5 1 4 3 2 5 5 2 3 4 1 1 5 3 4 2
16. 16. 1 2 3 4 5 Hybrid Genetic Algorithm Local Search: 1-0 Exchange Move 1 2 3 4 5 1 3 2 4 5 1 2 5 3 4 New Chromosomes From 1-0 Exchange Move LS procedure 2 1 3 4 5 3 2 1 4 5 4 2 3 1 5 5 2 3 4 1 1 3 2 4 5 1 4 3 2 5 1 5 3 4 2 1 2 4 3 5 1 2 5 4 3 1 2 3 5 4
17. 17. Hybrid Genetic Algorithm Local Search: 1-1 Exchange Move 1 2 3 4 5 1 2 3 4 5 3 2 1 4 5 1 5 3 4 2 New Chromosomes From 1-1 Exchange Move LS procedure 1 3 2 4 5 1 4 2 3 5 1 5 2 3 4 1 2 4 3 5 1 2 5 3 4 1 2 3 5 4
18. 18. 1 2 3 4 5 1 2 3 4 5 Hybrid Genetic Algorithm Local Search: 2 - opt Exchange Move 3 4 5 1 2 1 4 5 2 3 New Chromosomes From 2-opt Exchange LS procedure 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 1 3 4 5 2 1 4 5 2 3 1 5 2 3 4 1 2 4 5 3 1 2 5 3 4 1 2 3 5 4
19. 19. Multi-Constraint VRP
20. 20. Multi-Constraint VRP BP A B C A: B: C: Vehicle Capacity : 5 pax Multi-Trips Solution: 1st trip: Base – A – B – C – Base 2nd trip: Base – B – Base
21. 21. Multi-Constraint VRP Multi-Trips Steps taken to tackle this constraint Point A B C Deliv 2 7 1 Pickup 6 4 2 Point A1 A2 B1 B2 C Deliv 2 0 5 2 1 Pickup 5 1 4 0 2 Solution: 1st trip: Base – A – B – C – Base 2nd trip: Base – A – B – Base Exist demand that excess vehicle capacity? Reconstruct pick-up and delivery demand Associate pick-up and delivery demand matrix Reconstruct coordinate points matrix according to the new demand matrix Go to GA process Go directly to the GA process N Y Associate point coordinates to the basic
22. 22. Multi-Constraint VRP Case Execution Multi-Trips Destination Point 1 2 3 4 5 6 7 8 9 10 B Delivery Demand 5 3 16 4 2 2 20 1 2 4 - Pickup Demand 4 1 18 3 1 1 18 2 4 3 - Coordinate X 6 8 9 10 7 4 1 0 0 2 5 Coordinate Y 9 10 8 7 6 8 9 8 7 7 5 Vehicle Capacity 15 pax Trip Sequence Delivery Pick-up 1st trip: base – 1 – 2 – 3 – 4 – 5 – base 2nd trip: base – 3 – base 3rd trip: base – 7 – base 4th trip: base – 6 – 7 – 8 – 9 – 10– base Point 1 : 5 Point 2 : 3 Point 3 : 1 Point 4 : 4 Point 5 : 2 Point 3 : 15 Point 7 : 15 Point 6 : 2 Point 7 : 5 Point 8 : 1 Point 9 : 2 Point 10 : 4 Point 1 : 4 Point 2 : 1 Point 3 : 3 Point 4 : 3 Point 5 : 1 Point 3 : 15 Point 7 : 15 Point 6 : 1 Point 7 : 3 Point 8 : 2 Point 9 : 4 Point 10 : 3
23. 23. Multi-Constraint VRP Time Window time interval, given an earliest arrival time and latest arrival time. considering service time and total traveling time. determine the optimal route for both customer’s delivery and pick-up demand to destination point which have specified time Key point
24. 24. Multi-Constraint VRP Time Window Add initial input: vehicle speed and service time matrix Change the matrix of distance into travel time matrix Fitness function adjustment Time calculation  the main object of the calculation Final display adjustment: present the departure and arrival time at each point of the optimal route obtained Steps taken to tackle this constraint
25. 25. Multi-Constraint VRP Destination Point 1 2 3 4 B Coordinate X 40 45 60 65 50 Coordinate Y 70 90 80 60 50 Service time (minutes) 10 10 10 10 10 Earliest Arrival (EA) 7.00 7.00 7.30 6.00 ~ Latest Departure (LD) 8.30 8.30 9.00 7.30 ~ Time Window Case Execution Total Dist : 128.68 Total Dist 128.68
26. 26. Multi-Constraint VRP Case Execution Time Window Destination Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B Delivery Demand 30 20 10 20 0 10 30 10 10 10 20 20 20 10 10 - Pickup Demand 30 10 10 10 10 10 10 20 40 10 30 40 30 10 20 - Coordinate X 68 66 65 65 63 60 60 67 65 62 62 60 60 58 55 40 Coordinate Y 60 55 55 60 58 55 60 85 85 82 80 80 85 75 80 50 Service time (minutes) 20 40 40 20 30 30 30 20 10 30 10 10 20 10 30 -
27. 27. Analysis
28. 28. Analysis Local Search Placement Analysis Local Search Comparison Analysis Local Search Performance Analysis
29. 29. Analysis
30. 30. Analysis
31. 31. Analysis Case Study Destination Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B Delivery Demand 30 20 10 20 0 10 30 10 10 10 20 20 20 10 10 - Pickup Demand 30 10 10 10 10 10 10 20 40 10 30 40 30 10 20 - Coordinate X 68 66 65 65 63 60 60 67 65 65 62 60 60 58 55 40 Coordinate Y 60 55 55 60 58 55 60 85 85 82 80 80 85 75 80 50 Parameters: Vehicle capacity (Q) = 150 Max. distance (D) = 4000 Number of vehicle (H)= 2 Penalty Function (PF) = 1000000 Population Size = 40 Max Generation = 100 Crossover Probability = 0.85 Muatation Probability = 0.05 Optimal Fitness Value : 189.651
32. 32. Local Search as a Fitness Function Selected chromosome Calculate distance using Prins Splitting Procedure For 1 to number of Genes: Performed Local Search Find better chromosome? Y Save N End Generate initial population Evaluate each chromosome (Procedure on the next flowchart) Population converged or Max. Generation reached? Selection Reproduction (Procedure on the next flowchart)
33. 33. Select two parent chromosomes Crossover (probability)? Child = Parent 1 N Y Mutation (probability)? Child = Parent 1 Perform Crossover N Y Performed Local Search Calculate distance using Prins Splitting Procedure Find better chromosome? Y Child = New chromosome Child = Parent 1 Local Search as a Mutation Procedure
34. 34. Analysis Local Search Placement Analysis No. Placement of Local Search Mean Fitness Value No. of Vehicle Computational Time (second) 1 As a Fitness Function 201.21 2.2 714.88 2 As a Mutation Procedure 190.83 2.3 43.14
35. 35. Analysis Local Search Comparison Analysis No. Type of Local Search Mean Fitness Value No. of Vehicle Computational Time (second) 1 PLS 190.83 2.3 43.13 A 1-1 exchange move 190.99 2.34 28.93 B 1-0 exchange move 190.66 2.37 28.55 C 2-2 opt exchange move 192.23 2.42 13.67 2 A+B 202.24 2.25 65.34 3 A+C 192.56 2.38 22.73 4 B+C 197.21 2.5 30.79 5 A+B+C 200.73 2.26 63.47
36. 36. Analysis Local Search Performance Analysis 15 point 20 point 25 point 30 point 35 point Q=120; Q=140; Q=230; Q=200; Q=250; D=1000; D=1000; D=1000; D=1000; D=1000; H=10; H=10; H=10; H=10; H=10; PF=1000000; PF=1000000; PF=1000000; PF=1000000; PF=1000000; PopSize = 80; PopSize = 100; PopSize = 150; PopSize = 200; PopSize = 100; MaxG = 300; MaxG = 300; MaxG = 500; MaxG = 550; MaxG = 600; Pcrsovr = 0.9; Pcrsovr = 0.9; Pcrsovr = 0.9; Pcrsovr = 0.9; Pcrsovr = 0.9; Pmut = 0.1; Pmut = 0.1; Pmut = 0.1; Pmut = 0.1; Pmut = 0.1;
37. 37. Analysis Local Search Performance Analysis Optimal Route: Base-11-14-15-13-12-Base Base-7-10-6-3-2-Base Base-1-5-8-9-4-Base Fitness Value: 71.8003 Number of Vehicle used: 3 Computational Time: 97.799 sec Optimal Route: Base-17-20-19-15-14-Base Base-1-5-8-9-6-Base Base-2-3-10-7-4-12-Base Base-18-16-13-11-Base Fitness Value: 95.4184 Number of Vehicle used: 4 Computational Time: 397.873217 sec
38. 38. Analysis Local Search Performance Analysis Optimal Route: Base-16-17-20-19-15-14-13-7-Base Base-2-5-3-6-10-9-8-4-1-Base Base-21-22-24-25-23-28-12-11-Base Fitness Value: 95.1245 Number of Vehicle used: 3 Computational Time: 1670.22 sec Optimal Route: Base-6-8-9-10-7-4-Base Base-13-11-2-23-24-5-3-1-12-Base Base-16-18-17-19-20-14-15-Base Base-30-22-25-26-29-28-27-21-Base Fitness Value: 133.29 Number of Vehicle used: 4 Computational Time: 5204.85 sec
39. 39. Analysis Local Search Performance Analysis Optimal Route: Base-7-6-9-3-21-23-2-5-8-10-Base Base-4-1-12-16-17-Base Base-18-20-19-15-14-13-11-Base Base-33-32-31-34-35-30-28-29-22-26-Base Fitness Value: 149.3730 Number of Vehicle used: 5 Computational Time: 4089.0482 No. Number of Point Destination on Test Case Mean Mean of Fitness Value−Optimal Fitness Value (Δ) Fitness Value No. of Vehicle Computational Time (second) 1 15 71.9201 3.2 99.0231 0.1198 2 20 97.8146 4.3 402.9787 2.3962 3 25 101.4521 3.5 1967.54 6.3276 4 30 165.956 4.4 5823.72 32.666 5 35 210.6423 5.5 4892.143 61.2703
40. 40. Conclusion & Future Works
41. 41. Conclusions and Future Works Conclusions Hybrid Genetic Algorithm that combines Local Search and GA has been successfully developed to solve multi constraint vehicle routing problems From 4 type of LS method, 1-0 exchange move is the most preferable method to be combined with GA VRP with time window and multi-trips constraint could be solved without causing major change in basic Hybrid GA solver Future Works There are still a lot of constraints in VRP problem to be included, for instance: Multi vehicle, multi depot, split delivery Comparison between GA with other heuristic method.
42. 42. Thank You