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Greedy Random A Novel Algorithm for Vehicle Routing Optimization Dominik R. Rabiej 39 th National Junior Science and Humanities Symposium Orlando, Florida April 28, 2001

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2 Overview Vehicle Routing Introduction Ten Artificial Intelligence Algorithms Greedy Random: Best-Performing Why is Greedy Random successful? Analysis and Conclusion

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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

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Key Central Depot Customer Vehicle Route Closed Open

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5 Algorithm & Engine Inspiration: Human-Guided Simple Search Engine: Problem-Specific Optimization Algorithm –Problem-Independent –Drives Engine –Evaluates Situation, Determines Next Step

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Set ParametersSelect Algorithm Run AlgorithmRun CVRTW Engine Done? Yes No Pre-computed Solution with Parameters Optimized Solution

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7 Initial Experiment Ten Distinct Algorithms –Multiple Runs on Standard Benchmarks Which will optimize best? –Best Fewest Vehicles Used Tie-Breaker: Aggregate Distance Why?

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Key Central Depot Customer Vehicle Route Closed Open Random Circle Random Routes

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9 Initial Experiment Results

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10 Greedy Random Significantly better at 95% confidence How and why?

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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

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12 Investigative Experiments Analyze GR’s performance Experiments –Feasible/Infeasible –Variable Priorities –Multiple Initial Random Moves –Steepest Greedy Random

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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

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14 Feasible/Infeas. Results

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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

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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

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17 Results Comparison

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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

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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

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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

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21 Further Information http://dominik.net/research/gr/ Pending Publication in an Artificial Intelligence Journal

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