Tabu Search--- part II

報告者 : 王 敬 育

Short-term memory

• Handled by treating the tabu list as a circular list

• size ： t

• Perform effectively for driving the search beyond local optima and obtaining progressively improved solutions

• Aspiration criteria

Long-term memory

• Endow the memory structures with a flexibility to choose the “most attractive” moves by evaluation function

• Doesn’t restrict evaluations to measures of “ascent” and “descent” ， but more adaptive and varied measures

Tabu List Strategies for Single Attribute Moves

TL is a vector of attributes which impart a tabu classification to moves that contain these attributes

TL = (e(1) ， e(2) ，… e(q))

Identify the list of solutions (x(1) ， x(2) ，… x(q)) such that ， for each i ， e(i) is the attribute associated with the move applied to x(i) to prevent this move from being reversed to return to x(i)

Tabu List Strategies for Single Attribute Moves

• e(i) & e(i)

ex ： if x(i) → x(i+1) ， e(i) set xj =1

and x(i+1) → x(i) ， e(i) set xj =0

• in the sequence e(p) ，… e(q) ， if any e(r) is followed by an element e(s) such that e(r) = e(s) the e(r) is said to be canceled by the first such e(s)

Tabu Status Based on Cancellation Sequences

•active tabu list ， ATL ， consists only of the element

of TL that have not been canceled

ATL = (e(p) ，… e(q))

•An element e(p+1) is added to ATL ， where e(q+1) =

e(q) ， and e(q+1) cancle an earlier element e(i) of

ATL as a result of e(q+1) = e(i)

Tabu Status Based on Cancellation Sequences

•The structure of ATL ， upon adding e(q+1) but

berore dropping e(i) ， may be depicted as follows ： ATL = (e(p) ，… e(h) ， e(i) ， e(j)… e(q) ， e(q+1) )

•Cancellation Sequence ， or C-Sequence ： lies between the canceling element e(q+1) and the

canceled element e(i)

Tabu Status Based on Cancellation Sequences

•startseq(e) & endseq(e)

startseq(e) denote the element f on ATL that

starts the C-Sequence terminated by e

endseq(e) denote the element g on ATL that

end the C-Sequence initial by e

ATL before Cancellation

ATL after Cancellation

New C-Sequence Dominated by old

Later ATL before creating Tabu Element

Later ATL after creating Tabu Element

Tabu List Management by the Reverse Elimination Method

Tabu List Management by the Reverse Elimination Method

Bounded Variable Specialization of the Reverse Elimination Method

Bounded Variable Specialization of the Reverse Elimination Method

Handling Paired Attribute Moves by the Reverse Elimination Method

Handling Paired Attribute Moves by the Reverse Elimination Method