Simulated Annealing and Other Algorithms to Optimally or Non-Optimally Solve the Traveling Salesperson Problem (TSP) by James Pate Williams, Jr.

In the Fall Semester of 2000 I took an industrial engineering course at Auburn University. The course was Industrial Systems 6700 and was taught by Professor and Chair Alice E. Smith. The course was entitled “Search Methods for Optimization”. The first two papers that Professor Smith handed out dealt with physical and computerized simulating annealing and were: “Equation of State Calculations by Fast Computing Machines” by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, and Augusta H. Teller Los Alamos Scientific Laboratory, Los Alamos, New Mexico Edward Teller Notice that the inventor of the hydrogen bomb Edward Teller was involved with the paper and Optimization by Simulated Annealing | Science. The first paper dates from the year I was born namely 1953 and the second paper 1983, the latter year was the year that I flunked out of the Georgia Institute of Technology.

Our first assignment dealt with optimization via computerized simulating annealing (SA) and Professor Smith gave the class her implementation of the algorithm. By the way, over the last 22 years I have reused Smith’s algorithm in many of my own computer applications (C, C++, and C# computer languages).

SA gained the favor of Federal Express in 1983 and the Science paper mentioned above details the delivery service corporations use of the algorithm. The state of the art in solving the traveling salesperson problem (TSP) is the Concorde program written by scholars at the University of Waterloo in Canada: The traveling salesman problem | Mathematics | University of Waterloo (uwaterloo.ca). I believe Concorde uses linear programming.

With my software I am only able to solve small in size instances of the TSP. My implementations in a single computer application to solve toy random instances of the TSP for 3 to 25 number of locations are: brute force (3 to 9 cities), steepest descent local search (SDLS) from http://www.cs.bham.ac.uk/~wbl/biblio/gecco2007/docs/p1226.pdf, tabu search, evolutionary hill climber (EHC), genetic algorithm (GA), simulated annealing, some hybrid methods, minimum spanning tree, etc.

Steepest Descent Local Search

Tabu (Taboo) Search

Evolutionary Hill Climber

Genetic Algorithm

Simulated Annealing (Probably Optimal)

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Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

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