# PTSP Competition Session GECCO 2005 by sdfwerte

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```									PTSP Competition Session
GECCO 2005
Session Chair: Graham Kendall
Competition Organiser: Simon Lucas
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
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
Top Ten Entries
Jiaqiao Hu = umd; Jose Martin = IAI CSIC
Presentations
Jose Martin
Jiaqiao Hu
Rok Sibanc (2nd Place)
Best solution: 652, 652, Wed Jun 22 12:49:15
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
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
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
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
Martin Byrod – 1st Place
Winning entry: 648, 636, Wed Jun 22 12:41:11
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
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
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
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
Bob’s Best Route
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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