Genetic Algorithms : An Examination of the Traveling Salesman Problem

1. Genetic Algorithms:An Examination of the Traveling Salesman Problem Troy Cok Engineering 315 December 3, 2001

2. Basic Overview • Genetic algorithms are attempts to model evolutionary behavior • Survival of the fittest, etc. • More than mere simulations of life • Goal: Exhibit real characteristics of living things • GA’s have several uses • Problem solvers • Basis for competent machine learning • Computational models of innovation, creativity, etc.

3. Classic GA Problem • Traveling Salesman Problem (TSP) • Implications in science, engineering • Control of routing system • Constraints: • Can be in one city at a time • Each city visited once and only once • Problem: • What is the shortest route through N cities?

4. Mathematical Attempts at TSP • Testing every possibility would require N! separate additions • For a 15 city tour: • 15! = 1.31 x 1012 separate calculations • Assuming 1 million calculations per second  15.2 days • Increasing complexity…

5. Solving TSP using GA • Generates a “near-perfect” solution in minutes • Steps: • Create group of random tours • Stored as sequence of numbers (parents) • Choose 2 of the better solutions • Combine and create new sequences (children) • Problems here: • City 1 repeated in Child 1 • City 5 repeated in Child 2

6. Modifications Needed • Algorithm must not allow repeated cities • Also, order must be considered • 12345 is same as 32154 • Based upon these considerations, a computer model for N cities can be created • Gets quite detailed

7. Some Existing GA Programs

8. Final Notes • GA’s determine adequate “solution” to TSP • Much faster than sheer number-crunching • Enables efficient system control • The better the algorithm, the better the solution • Ongoing research in this area