Lecture 13

# Search space n2nn12 e 3 22514 pso for

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Unformatted text preview: Conference on Machine Learning and Cyberne1cs 3 (2003) 1583–1585. Traveling Salesman Problem TSP Search Space •  The salesman must visit every city in his territory exactly once and then return home covering the shortest distance. •  Variables: x1.. xn are n city names •  Representa1on: permuta1on of n ci1es. •  5 ci1es example: (a, d, g, b, e) d a b g •  Given n unique objects, n! permuta1ons of the objects exit. Searching the shortest path is an NP ­ hard problem. •  In TSP, there are mul1ple equivalent solu1ons. –  If star1ng point is not important, and the distance from city i to j is the same as that from city j to i, each tour a ­b ­ c ­d ­e can be represented in 2n ways and give the same distance. •  Search space: n!/(2n)=(n ­1)!/2 e 3 2/25/14 PSO for TSP •  The solu1on of a par1cle is a permuta1on of n ci1es. –  Example: (a, d, g, b, e) •  The velocity of a par1cle is a sequence of swap operators (SS). •  Velocity examples: –  swap opera...
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