A Genetic Solution to the Travelling Salesman Problem Ryan Honig

What is the Travelling Salesman Problem? Traveling Salesman Problem (TSP) Definition: Given a set of points, find the shortest path that visits each point exactly once and returns to the starting point.

What is the Travelling Salesman Problem? (Cont.)‏ Two Types of Problems: Symmetric Asymmetric

What is the Travelling Salesman Problem? (Cont.)‏ Symmetric AB Distance = 100

My Goal Three Things I want to do: 1.Create an algorithm that can find near- optimal solutions for symmetric TSPs. 2.Build off of the first algorithm to allow it to find near-optimal solutions for asymmetric TSPs. 3.Create a graphic Interface to run the algorithms and visualize the set of points.

Genetic Algorithm Genetic algorithm: an algorithm that has a pool of solutions, and will at random pick two solutions and combine them to create a child solution, then a fitness function is used to rank the solutions

Genetic Algorithm (Cont)‏ AABB C C D D EE Parent AParent B

AB C D E Genetic Algorithm (Cont)‏ A A A A A B B B B B Combined Path

Genetic Algorithm (Cont)‏ B AB C D E A A B B Child

Mutations Chance of 1 in 50 to introduce a mutation to the next generation (the child if it replaces a parent, or the first parent)‏ EBFDGAC R1R2 EAGDFBC

Pool Creating Heuristic AB C D E A ABA E AB C AB D A D E AB E

What I’ve done 3rd quarter First ~two weeks of the quarter spent trying to optimize my pool initializing heuristic Did some testing with the current heuristic program and the original random-pool program Worked on converting the a copy of my random pool program so that it would read in asymmetric traveling salesman problems and find near optimal solutions to them

Pool Creating Heuristic (Cont)‏ Last Quarter, I tested the program with the heuristic to initialize the pool (before my optimizing) against the program that has a random pool, and although I found the results to be slightly better, it ran a lot slower. This Quarter, I once again tested the two different versions of my program, but after I had worked for a bit on optimizing the heuristic. I found that while the heuristic program was still slightly better than the random-pool program, the time it took to run still did not justify its improvement.

Pool Creating Heuristic (Testing)‏ Average Run Time Average (of 5 runs)‏ Average Run time Average (of 5 runs)‏ Data Set / Best solution Heuristic ProgramRandom Pool Program A280: 2579 ATT48: BAYG29: 1610 BAYS29: 2020 CH130: sec 2.31 sec 1.33 sec 1.86 sec 2.76 sec 3.03 sec 4.71 sec 2.42 sec 2.81 sec 4.54 sec

What is the Travelling Salesman Problem? (Cont.)‏ Asymmetric Travelling Salesman Problem AB Distance = 100 Distance = 200

Asymmetric Travelling Salesman After a bit of testing my two programs, began work on converting the random-pool program so that it could solve asymmetric travelling salesman problems. Working with a data set that only contains 17 points, data is read in as a text file that contains the distances between points rather than the coordinates of points Currently, I can successfully read in the data, and I have converted many of the functions in my program so that they can perform on asymmetric data, but I am having a hard time converting the actual genetic algorithm Hopefully I will be able to get it working by early next quarter.

The Future of my Program Finish making the genetic algorithm compatible with asymmetric TSPs Make a GUI

Plans for a GUI Allow user to input the name of the file containing the set of points Display the set of points in a graphical representation, along with the path that the algorithm will finds for it

THE END Any Questions?