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G5BAIM
Artificial Intelligence Methods
Tabu Search
G5BAIM Tabu Search
Characteristics of SA (review)
• Random selection of a neighbouring
solution
• Probabilistic acceptance of non-improving
solutions;
• The best solution is recorded:
– Lack of memory of history of search;
– All the information found during the search is lost;
G5BAIM Tabu Search
Tabu Search
Proposed independently by Glover(1986) and
Hansen(1986);
• Tabu search is “a meta-heuristic
superimposed on another heuristic. The
overall approach is to avoid entrapment in
cycles by forbidding or penalizing moves
which take the solution, in the next
iteration, to points in the solution space
previously visited (hence tabu).”
G5BAIM Tabu Search
Tabu Search (continued)
• Accepts non-improving solutions
deterministically in order to escape from
local optima (where all the neighbouring
solutions are non-improving) by guiding a
steepest descent local seach (or steepest
ascent hill climbing ) algorithm;
• Uses of memory to:
– prevent the search from revisiting previously visited
solutions;
– explore the unvisited areas of the solution space;
Is memory useful during the search?
G5BAIM Tabu Search
Uses of memory during the search?
• Intelligence needs memory!
• Discouraging some patterns in solution: e.g.
in clustering example, selection of some
stores as warehouses or their assignment of
some stores to a specific warehouse may be
considered taboo (forbidden).
• Information on characteristics of good
solutions (or bad solutions!)
G5BAIM Tabu Search
Dangers of memory
• Exhaustive usage of memory resources:
– Design of efficient data structures to record and access the
recorded data efficiently;
• Collecting more data than could be handled:
– Clear understanding of which attributes of solutions are crucial;
– Limited selection of attributes of solutions to be memorised;
– Clear strategy on usage of information or their disposal when not
needed;
• Memorising information which should not be
remembered:
– Misguiding patterns in local optima which are very different from
global optimum;;
G5BAIM Tabu Search
Tabu Search algorithm
Function TABU_SEARCH(Problem) returns
a solution state
• Inputs: Problem, a problem
• Local Variables: Current, a state
• Next, a state
• BestSolutionSeen, a state
• H, a history of visited states
G5BAIM Tabu Search
Tabu Search algorithm (continued)
• Current = MAKE-NODE(INITIALSTATE[Problem])
• While not terminte
– Next = a highest-valued successor of Current
– If(not Move_Tabu(H,Next) or Aspiration(Next)) then
• Current = Next
• Update BestSolutionSeen
• H = Recency(H + Current)
– Endif
• End-While
• Return BestSolutionSeen
G5BAIM Tabu Search
Elements of Tabu Search
• Tabu List (short term memory): to record a
limited number of attributes of solutions
(moves, selections, assignments, etc) to be
discouraged in order to prevent revisiting a
visited solution;
• Tabu tenure: number of iterations a tabu
move is considered to remain tabu;
• Aspiration criteria: accepting an improving
solution even if generated by a tabu move
– Similar to SA in always accepting improving solutions,
but accepting non-improving ones when there is no
improving solution in te neighbourhood;
G5BAIM Tabu Search
Elements of Tabu Search (continued)
Long term memory): to record attributes of
elite solutions to be used in:
• Intensification: giving priority to attributes
of a set of elite solutions (usually in
weighted probability manner)
• Diversification: Discouraging attributes of
elite solutions in selection functions in order
to diversify the search to other areas of
solution space;
G5BAIM Tabu Search
Example of use of memory
In our example of selecting warehouses, following
information could be recorded:
• Short term memory:
– Maintain a list of t stores and prevent them from being selected as
warehouse or prevent their assignments to specific selection of
warehouses for a number of iterations;
• Long term memory:
– Maintain a list of t stores which have been selected as warehouses
in the last k best solution and encourage (or discourage) their
selection in future solutions by using their frequency of appearance
in set of elite solutions and the quality of solutions which they have
appeared in our selection function;
• Which stores have been selected as warehouses in our elite solutions?
• Which assignment of stores to warehouses in our elite solutions;
G5BAIM Tabu Search
References
• 1. Glover, F. 1989. Tabu Search – Part I. ORSA
Journal on Computing, Vol. 1, No. 3, pp 190-206.
• 2. Glover, F. 1990. Tabu Search – Part II. ORSA
Journal on Computing, Vol. 2, No. 1, pp 4-32.
• 3. Glover, F., Laguna, M. 1998. Tabu Search.
Kluwer Academic Publishers
• 4. Rayward-Smith, V.J., Osman, I.H., Reeves,
C.R., Smith, G.D. 1996. Modern Heuristic Search
Methods, John Wiley & Sons.
• 5. Russell, S., Norvig, P. 1995. Artificial
Intelligence A Modern Approach. Prentice-Hall
G5BAIM
Artificial Intelligence Methods
End of Tabu Search