Greedy RandomA Novel Algorithm for Vehicle Routing Optimization

Dominik R. Rabiej

39th National Junior Science and Humanities Symposium

Orlando, Florida

April 28, 2001

2

Overview

• Vehicle Routing Introduction

• Ten Artificial Intelligence Algorithms

• Greedy Random: Best-Performing

• Why is Greedy Random successful?

• Analysis and Conclusion

3

Vehicle Routing

• CVRTW: Capacitated Vehicle Routing with Time Windows– Customers: Location, Time Windows, Demand– Vehicles: Capacity, Travel on Routes– Central Depot: Start & Finish for Vehicles

• NP-Hard Problem

Key

Central Depot

Customer

Vehicle Route

Closed

Open

5

Algorithm & Engine

• Inspiration: Human-Guided Simple Search

• Engine: Problem-Specific

• Optimization Algorithm– Problem-Independent– Drives Engine– Evaluates Situation, Determines Next Step

Set Parameters Select Algorithm

Run AlgorithmRun CVRTW Engine

Done?

Yes

No

Pre-computed Solution with Parameters

Optimized Solution

7

Initial Experiment

• Ten Distinct Algorithms– Multiple Runs on Standard Benchmarks

• Which will optimize best?– Best

• Fewest Vehicles Used• Tie-Breaker: Aggregate Distance

• Why?

Key

Central Depot

Customer

Vehicle Route

Closed

Open

Random Circle

Random Routes

9

Initial Experiment Results

Rank Algorithm Vehicles Distance1 GR 12.81 13802 ANY 13.13 13983 RSS 13.33 13934 SC 13.38 13985 RPGR 13.44 14476 RR 13.50 14567 RP 13.54 14058 RAR 13.65 14159 RCP 13.99 1457

10 HI 14.65 1572

10

Greedy Random

• Significantly better at 95% confidence

• How and why?

2. Greedy Random will move a random customer from route A to B.

1. Initial Solution.

1

B

A

3. Moving that customer causes B’s vehicle to arrive late at another customer.

3

B

A

4. The CVRTW Engine re-optimizes, improving upon the initial solution.

4

B

A

2

B

A

12

Investigative Experiments

• Analyze GR’s performance

• Experiments– Feasible/Infeasible– Variable Priorities– Multiple Initial Random Moves– Steepest Greedy Random

13

Feasible/Infeasible

• Feasibility– All customers receive their complete

shipments within their time windows and no vehicle runs out of product

• Hypothesis– Greedy Random derives its success from

use of infeasible space: temporarily invalidated solution space

14

Feasible/Infeas. Results

BenchmarkVehicles Distance Vehicles Distance

RC101 15 1652 15 1681RC102 13.5 1492 14 1500RC103 11 1375 11 1365RC104 10 1196 10 1200RC105 14 1566 14 1568RC106 12 1431 12 1437RC107 11 1271 11 1259RC108 11 1184 11 1182Scores 12.19 1395.88 12.25 1399.00

Infeasible GR Feasible GR

15

Experiment Summary

• Feasible/Infeasible– Infeasibility must be moderate

• Variable Priorities– High/Medium is better than Low

• Multiple Initial Random Moves– One initial random move is best

• Steepest Greedy Random– Search technique independence

16

Discussion

• GR derives success from a single catalytic initial random move

• Initial random moves that resulted in improvements made significantly less change in infeasibility than those that did not

17

Results Comparison

BenchmarkVehicles Distance Vehicles Distance Vehicles Distance

RC101 15 1641 15 1662 14 1669RC102 13 1478 12 1569 12 1555RC103 11 1264 11 1224 11 1110RC104 10 1156 10 1136 10 1136RC105 14 1541 13 1691 13 1637RC106 12 1391 11 1475 11 1432RC107 11 1241 11 1236 11 1231RC108 11 1135 10 1185 10 1140Scores 12.13 1355.88 11.63 1397.25 11.50 1363.75

Greedy Random Human Guided Best Ever Found

18

Conclusion

• Greedy Random Created and Analyzed

• Single Catalytic Initial Random Move– Non-drastic, shifts search space

• Highly Portable– Separation of Algorithm & Engine– Easily applicable to other areas of

optimization

19

Future Work

• Other Applications of Greedy Random– Job Shop Scheduling

• Integration of Neural Networks– Adaptive evaluation of random moves– Increase Greedy Random’s efficiency

20

Acknowledgements

• Dr. Neal Lesh, Mitsubishi Electric Research Laboratory, Cambridge, MA

• Mitsubishi Electric Research Laboratory

• 2000 Research Science Institute at the Massachusetts Institute of Technology

• Dr. Daniel Mihalko, Western Michigan University, Mathematics & Statistics

21

Further Information

• http://dominik.net/research/gr/

• Pending Publication in an Artificial Intelligence Journal