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Innovations in Solving the Physical Travelling Salesman Problem at GECCO 2005

The GECCO 2005 competition showcased innovative methods to address the Physical Travelling Salesman Problem (PTSP), where the objective is to visit all cities in minimum time using discrete time steps with a choice of force vectors. With 68 entries from 10 unique participants, solutions utilized various evolutionary algorithms and strategies. Notable entries included Martin Byrod's method, placing first with a route-optimizing EA, and Rok Sibanc's two-stage method utilizing force vectors. The competition highlighted the creativity in problem-solving and sparked interest in future contests focused on algorithm submissions.

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Innovations in Solving the Physical Travelling Salesman Problem at GECCO 2005

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  1. PTSP Competition SessionGECCO 2005 Session Chair: Graham Kendall Competition Organiser: Simon Lucas

  2. Physical Travelling Salesman Problem • Visit all cities in minimum time • Each time step, choice of 5 force vectors • Solutions are strings over {0,1,2,3,4}* • Secondary criteria: • Minimise non-zero forces • Given solutions of equal quality, earliest submission wins

  3. Participation • Number of entrants: • 10 (by unique email addresses) • Plus many anonymous (not necessarily different) entrants • Number of entries: 68 • No limit on the number of entries per individual

  4. Top Ten Entries • Jiaqiao Hu = umd; Jose Martin = IAI CSIC

  5. Presentations • Jose Martin • Jiaqiao Hu

  6. Rok Sibanc (2nd Place) • Best solution: 652, 652, Wed Jun 22 12:49:15

  7. Rok’s Method(Summarised by Simon Lucas with apologies for any errors) • 2-stage • Stage 1: • Optimise route (permutation of cities) • With a novel criteria • Includes angles between consecutive straight-line segments • As well as distance • And a weighting parameter to balance contribution of terms • Optimised with a population-based, mutation only EA • Tournament Selection

  8. Rok’s Force Vector Optimiser • Stage 2: for a given route • Find best set of forces • Interesting: uses only symbols 1-4 • (the unit vectors) • Never uses a zero-force step • Incremental approach: • Optimise a solution that visits just the first city, • Then the first two, then three etc… • Mutation only EA

  9. Rok’s Fitness Function • The fitness function: • iSeen+((1-(iUsed/m_iGenomeMaxLenght)))+(2.0/dNearest)+(20/(3+dLastDist)); • • iSeen is the number of visited cities • • iUsed is the number of used vectors • • m_iGenomeMaxLenght is the maximum number of vectors for a genome • • dNearest is square of the distance of last position before last visited city • • dLastDist is square of the distance of last position to the next unvisited city

  10. Rok’s Variation Operators • 1-Symbol Substitution • 1-Symbol Deletion (and insertion?) • Replace a subsequence of length n, with n copies of the same symbol • Deletion of a subsequence • Probability of these mutations such that small changes more likely than large ones

  11. Martin Byrod – 1st Place • Winning entry: 648, 636, Wed Jun 22 12:41:11

  12. Martin’s Method(Summarised by Simon Lucas with apologies for any errors) • Two stage: • Use a standard EA to optimise the route, given standard TSP cost function • Then plug in the real cost function (which may alter the TSP-estimated route) • The real cost function is determined by an EA that optimises the solution string for a given route • Population-based EA, mutation only

  13. Martin’s Fitness Function • Fitness function: • N: Number of cities visited • E: distance to next city • T: total time taken (length of string) • Optimised using a greedy sliding window approach • 0 to 100, then 10 to 110 etc. • Force Vector EA initialised with routes derived from PD Controller

  14. Key Idea: Swap Mutation • Use both Swap (right) and bit-flip (left) mutation • Swap makes much smaller changes • But bit-flip needed to make all strings reachable • Sample swap: 1234 -> 1324

  15. Bob MacCallum (6th) : GP(Summarised by Simon Lucas with apologies for any errors) • Used PerlGP to evolve a controller • Different approach to the other methods • The controller takes as input: • Current state (position, velocity) • Locations of cities that are yet to be visited • Outputs a continuous force vector at each time-step • Which is then quantised to form next solution step

  16. Bob’s Best Route

  17. Summary • PTSP: Interesting challenge that stimulated a good deal of interest • Many different approaches possible: • Some work much better than others • Simple naïve methods perform poorly • Web-based continuous league: • Interesting to observe • Psychological aspects also • Competitors showed fantastic ingenuity! • Thanks to all participants for making it a worthwhile competition • Might run a future contests where algorithms instead of solutions are submitted…

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