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Lecture 13

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Unformatted text preview: permuta1on: •  Applying a Swap Operator to a permuta1on: –  (a, d, g, b, e) + SO(1,2) = (d, a, g, b, e) •  Apply a sequence of SO (SS) to a permuta1on: –  SS=(SO(1,2,), SO(5,4), SO(5,1)) –  (a, d, g, b, e) + SS  ­> (d,a,g,b,e)  ­> (d,a,g,e,b)  ­> (b,a,g,e,d) Subtract Two Permuta1ons •  A: (a, c, d, e, b), B: (c, a, b, e, d) •  There is a SS that transforms A to B. –  a is in posi1on 1 in A and 2 in B: SO1(1,2) –  A+SO1=A’= (c,a,d,e,b) –  b is in posi1on 5 in A’ and 3 in B: SO2(5,3) –  A’+SO2=(c,a,b,e,d)=B •  SS=(SO1(1,2), SO2(5,3)) •  A ­B = SS 4 2/25/14 TSP ­PSO algorithm Par1cle Velocity Update  ­ Con1nued Each velocity is a swap sequence (SS). v(t) = v(t ­1) α*(pbest ­x(t ­1)) β*(gbest ­x(t ­1)) α, β are probability between 0 and 1. α * (pbest ­x(t ­1)) means when a generated random number is > α , all swap operators in swap sequence (pbest – x(t ­1)) are included in the updated velocity. The same applies to β and (gbest ­x(t ­1)). •  Other work has improved this simple scheme. •  •  •  •  Exercise a b c d e f x 16.47 16.47 20....
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