1. Enhancing Decision Making Emulating Human Reasoning
Matt Brunner
Sts. Peter and Paul School – California, KY
5th-8th Grade Science & Math
Samy Lafin
Scott High School – Taylor Mill, KY
9th grade Clean Energy Engineering, 10th grade Biology
RET is funded by the National Science Foundation, grant # EEC

2. Table of Contents Abstract Introduction Background Literature Review
Goals and Objectives
Research Tasks
Timeline
Research Training Received
Unit Topic, Essential Question, Challenge
Progress Made

4. Introduction Optimization Genetic Algorithms MATLAB
Traveling Salesman Problem
Define and explain the function of each of these terms in relation to the entire project

5. The Traveling Salesman Problem (TSP)1,5
“Given a set of cities along with the cost of travel between each pair of them, the traveling salesman problem, or TSP for short, is to find the cheapest way of visiting all the cities and returning to the starting point.”
Why is TSP important mathematically – NP-hard problem, even if you are given a solution it is difficult to check whether or not that is the optimal solution
(n-1)!/2 solutions – increases exponentially with number of cities
Real life – routing problems (UPS, school buses), microchips in computers
Origins of TSP are unknown, but have been seen in many places, dating back to 1832 German handbook
Circuit Riders in UK
Lincoln’s law circuit in IL
Leonhard Euler – sequence of knight’s moves in chess
Messengers, school bus routes, contests…this problem is used in so many ways
In math: Hamiltonian circuit
As the number of “cities” increases, so does the number of possibilities

6. Optimization3 Real world problem Algorithm, model, solution technique
Analysis
Validation, sensitivity analysis
Algorithm, model, solution technique
Investigates the properties of optimization
You want to get to the base issue of the problem, and get rid of any abstract or irrelevant details
This also looks at sensitivity, so once you get down to the base problem, looking at how different details can affect the outcome is sensitivity analysis.
Profit per item produced
“the final solution changes very little even with a large variation in profit per item produced.”
“the results change dramatically when the estimated profit per item produced changes very slightly”
Numerical methods
Verification
Computer implementation

7. Introduction to Genetic Algorithms2,4
Used to apply evolutionary mechanisms to computer science
Components of a genetic algorithm (GA) mimic the process of biological evolution
Fitness function
Population of chromosomes
Selection of which chromosomes will reproduce
Crossover to produce next generation of chromosomes
Random mutation of chromosomes in new generation

8. Research Training Received
Parent 1
Parent 2
Child 1
Child 2
1 2 3
4 5 6
2 1 3
6 4 5 6 1 4 2 5 3

9. Research Training Received
Parent 1
Parent 2
Child 1
Child 2
1 2 3
4 5 6
2 1 3
6 4 5
1 2 3
6 4 5
2 1 3
4 5 6 6 1 4 2 5 3

10. How we use crossover 1 2 3 4 5 6 5 4 3 1 2 5 4 3 6 Parent 1 Child 1

11. Two-Opt Algorithm

12. Abstract Determine the shortest, most efficient route to TSP.
Develop a hybrid between GA and two-opt codes.
Eventual development of artificial intelligence
This research looks into the use of an artificial intelligence to determine the shortest and most efficient route for a travelling salesman to take.  The artificial intelligence relies on a genetic algorithm to determine the best route to take.  The goal of this research project is to take a slow genetic algorithm and optimize the algorithm so that it takes less time to function.  
Our question is about creating a hybrid genetic algorithm to hasten the processing time.  Can a hybrid genetic algorithm be created that will minimize the processing time? 
A genetic algorithm is a binary code that models natural selection in evolutionary theory by crossing over code to create a new solution.  The methods used are classical research using books internet and with assistance from the assigned graduate student.  
The results that are expected are that a hybrid algorithm can be produced that will minimize the processing time for the genetic algorithm.  The average speed it takes for a number of cities to be crossed by a set number of generations then the hybrid will be applied to the code and the average speed will be taken given the same constraints. 
The scientific conclusions we hope to draw are that a genetic algorithm can be used in conjunction with another type of programming in order to create a more optimized system that is both accurate and time efficient.  This research project hopes to conclude that this is possible and prove it.

13. Objective Develop a hybrid between GA and two-opt codes
Converges faster and/or find better solution

14. Research Tasks Understand the functions and coding in MATLAB
Development of hybrid optimization program

15. Timeline Topic Week 1 Week 2 Week 3 Week 4 Week 5 Week 6
Learn MATLAB
Designing/ Writing Code
Testing
Data Analysis
Format Report
Week 1: Understand the function and coding in MATLAB
Week 2: Begin developing optimization techniques
Week 3: Develop hybrid algorithms
Week 4: Finish development, begin testing algorithms
Week 5: Test hybrid against two-opt and GA
Week 6: Finalize data and develop report
Weeks 3-6 will have writing code as well as data analysis

16. Research Training Received
MATLAB
Writing code to solve TSP

17. Progress Made

18. Verification of Code
Green lines: Verification lines that MATLAB did not produce
Red lines: MATLAB lines that were not found in verification

19. Progress Made Algorithm Additions Modified Two-opt
Nearest Neighbor (GA)
Criss-cross
Ant Colony
N-opt
Circular, Quadrants
Looking at vectors instead of scalar numbers
Neural Network

20. Nearest Neighbor
GA Hybrid
Identify closest city

21. Nearest Neighbor with Crossover
GA Hybrid
NN only performed on select cities
Switches randomly between NN and flip

22. Modified Two-Opt
Tests 3 options

23. Experimental Data NO DATA 10 Cities 50 Cities 100 Cities 1000 Cities
Distance
Time
Genetic Algorithm (MY_GA)
Mean
2.860
6.007
8.404
55.583
111.22
Standard Error
0.039
0.049
0.054
0.117
0.83
Two-Opt
2.881
6.069
8.521
41.395
21.03
0.040
0.047
0.050
0.419
0.40
Nearest Neighbor (with GA)
5.841
8.190
26.200
111.35
0.041
0.044
0.78
Modified Two-Opt
2.909
6.117
8.513
39.230
86.32
0.042
0.053
0.339
0.58
Nearest Neighbor with Crossover
5.999
39.60
8.433
578.37
0.80
10.69
NO DATA

24. Distance Data

25. Time Data

26. Comparing Distances

27. Comparing Distances

28. Comparing Distances
The basic data showed that the Nearest Neighbor hybrid with GA gave the best distance data.

29. Comparing Times

30. Comparing Times

31. Comparing Times
The basic data showed that the Nearest Neighbor with Crossover hybrid with GA gave the slowest time, but it was difficult to discern any of the other tests.

32. Remove Nearest Neighbor w/ Crossover
Highest time – why?
Two-Opt algorithms faster
At 1000 cities, no data for Nearest Neighbor w/ Crossover
NNwCrss is slower because it randomly choose between the NN and flip – the flip is easier and quicker to complete, but instead of running NN only once, we are running it 500 times with 5000 generations, which takes so much longer.
Modified 2opt takes slightly longer than 2opt because we are considering one more possibility

33. In the data for 1000 cities, it is clear that Nearest Neighbor with the genetic algorithm gives the best distance data, while the Two-Opt algorithm solves the problem in the least amount of time.

34. Conclusions Nearest Neighbor: optimal distance Two-Opt: most efficient
Application depends on situation
Forest Fire, GPS
Amazon shipping, pre-planning routes

35. Unit Topic, Essential Question, Challenge: Matt Brunner
Unit Topic: Plant Adaptations
Essential Question: What is the most effective method of grafting two or more cacti together?
Challenge: Connecting the vascular tissue of two different species of Opuntia Cactus.

36. Unit Topic, Essential Question, Challenge: Samy Lafin
Unit Topic: Human Body Systems – Organ Donation
Essential Question: How do we effectively and efficiently get donor organs to people waiting to receive a transplant?
Challenge: Develop a model of a system that could be used to determine organ donation between living donors and recipients that allows the most donors to donate and recipients to receive an organ.

37. Background Literature Review
Applegate, D. L., Bixby, R. E., Chvatal, V., and Cook, W. J. (2007). The traveling salesman problem. Princeton University Press, Princeton. Carr, J. (2014). “An Introduction to Genetic Algorithms.” < (Jun. 22, 2016). Chinneck, J.W. (2000). “Chapter 1: Introduction.” Practical Optimization: a Gentle Introduction. Dianati, M., Song, I., and Treiber, M. (2002). An Introduction to Genetic Algorithms and Evolution Strategies. An Introduction to Genetic Algorithms and Evolution Strategies, tech., Canada. Matai, R., Singh, S., and Lal, M. (2010). “Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches.” Traveling Salesman Problem, Theory and Applications. Petridis, V., Kazarlis, S., and Bakirtzis, A. (1998). “Varying fitness functions in genetic algorithm constrained optimization: the cutting stock and unit commitment problems.” IEEE Trans. Syst., Man, Cybern. B IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 28(5), 629–640.

38. The RET program funded by the National Science Foundation, Grant ID# EEC Project Faculty Mentors, Dr. Kelly Cohen and Dr. Jeff Kastner Graduate Research Assistant, Mr. Anoop Sathyan RET Project Director and Principal Investigator, Dr. Anant Kukreti RET Resource Person and Grant Coordinator, Debbie Liberi RET Resource Teacher, David Macmorine