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Editorial Team
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Asked: 2026-05-23T02:41:49+00:00

Could you please help me understand this Tabu search page 7 example: TS is

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Could you please help me understand this Tabu search page 7 example:

TS is a mathematical optimization method,
belonging to the class of trajectory
based techniques. Tabu search enhances
the performance of a local search
method by using memory structures that
describe the visited solutions: once a
potential solution has been
determined, it is marked as “taboo”
(“tabu” being a different spelling of
the same word) so that the algorithm
does not visit that possibility
repeatedly. Tabu search is attributed
to Fred W. Glover

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I do not understand why an upper triangle is used, and why is this :

The tabu structure now shows that
swapping the positions of modules 4
and 5 is forbidden for 3 iterations.
The most improving move at this step
is to swap 3 and 1 for a gain of 2.

Could you please explain why the triangle and why is it the above statement?

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1 Answer

  1. Editorial Team

    The statement

    In the exemple of the powerpoint they chose a duration of 3. Each time one swap is made it will be tabu for the next 3 moves.

    That’s why at step 1 (note: I start at step 0) you have the following statement:

    The tabu structure now shows that
    swapping the positions of modules 4
    and 5 is forbidden for 3 iterations.
    The most improving move at this step
    is to swap 3 and 1 for a gain of 2.

    Swapping 3 and 1 at this step is the best move to increase value.

    After your last step (step 3) they actually swap 4 and 5 even if it is tabu because of the aspiration criterion. (20 > 18 which is best value so far).

    The triangle

    The representation is a triangle because the swapping manipulation is symetric. So you don’t need more than an upper triangle to represent your tabu structure.

    In each cell of the tabu structure you have the remaining tenure (the duration left for the move to be tabu) of the pair (x,y) = (y,x).

    I don’t know much about tabu search, but I hope it helps.

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