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-1404766

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

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

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 http://lizardpoint.com/geography/images/maps/592x414xusa-caps-labeled.gif.pagespeed.ic.Cd8JRJohyU.png https://support.sas.com/documentation/cdl/en/ornoaug/65289/HTML/default/images/map002g.png

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

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

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

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

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

Two-Opt Algorithm

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. https://static.securityintelligence.com/uploads/2016/01/Artificial-Intelligence-Heads-to-the-Enterprise-938x535.jpg

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

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

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

Research Training Received MATLAB Writing code to solve TSP

Progress Made

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

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

Nearest Neighbor GA Hybrid Identify closest city

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

Modified Two-Opt Tests 3 options

Experimental Data NO DATA 10 Cities 50 Cities 100 Cities 1000 Cities Distance Time Genetic Algorithm (MY_GA) Mean 2.860 0.18895 6.007 0.90956 8.404 4.16206 55.583 111.22 Standard Error 0.039 0.01272 0.049 0.01628 0.054 0.08812 0.117 0.83   Two-Opt 2.881 0.00058 6.069 0.00228 8.521 0.01324 41.395 21.03 0.040 0.00036 0.047 0.00011 0.050 0.00042 0.419 0.40 Nearest Neighbor (with GA) 2.08467 5.841 3.71629 8.190 5.85383 26.200 111.35 0.04334 0.041 0.12865 0.044 0.22609 0.78 Modified Two-Opt 2.909 0.00188 6.117 0.03659 8.513 0.14772 39.230 86.32 0.042 0.00046 0.00050 0.053 0.00135 0.339 0.58 Nearest Neighbor with Crossover 1.78589 5.999 39.60 8.433 578.37 0.02066 0.80 10.69 NO DATA

Distance Data

Time Data

Comparing Distances

Comparing Distances

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

Comparing Times

Comparing Times

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.

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

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.

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

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.

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.

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.” <https://karczmarczuk.users.greyc.fr/teach/iad/gendoc/carrgenet.pdf> (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.

The RET program funded by the National Science Foundation, Grant ID# EEC-1404766 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