t abu s earch ta-chun lien. r eference fred g., manuel l., tabu search, kluwer academic publishers,...
TRANSCRIPT
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TABU SEARCHTa-Chun Lien
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REFERENCE
Fred G., Manuel L., Tabu Search, Kluwer Academic Publishers, USA(1997)
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OUTLINE
History Descent Method Memory Framework
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HISTORY
A very simple memory mechanism is described in Glover (1977)
Glover (1986) introduces tabu search as a “meta-heuristic” superimposed on another heuristic
Glover (1989a) and (1989b) provide a full description of the method
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DESCENT METHOD
1) Choose x X to start the process.2) Find x’ N(x) such that f(x’)<f(x).3) If no such x’ can be found, x is the local
optimum and the method stops4) Otherwise, designate x’ to be the new x and
go to step2.
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DESCENT METHOD(CONT’D)
The evident shortcoming of a decent method is that such a local optimum in most cases will not be a global optimum
The version of a descent method called steepest descent scans the entire neighborhood of x. It is guaranteed to yield globally optimal solutions for some problem, but impractical for computational expensive
Mechanisms of tabu search are introduced to go beyond the locally optimal termination point of a locally optimal termination point of a descent method by creating good neighborhood structure
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MEMORY
Short Term Memory Long Term Memory
Each type of Memory is accompanied by its own
special strategies. However, the effect of bothtypes of memory may be viewed as modifying
theNeighborhood N(x) of the current solution x.N*(x):modified neighborhood
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SHORT-TERM MEMORY
The main goal of the STM is to avoid reversal of moves and cycling
The most common implementation of the STM is based on move attributes and the recency of the moves
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TABU TENURE
Tabu list: memorize local optimum and its neighbor to forbid move to this place again. Avoiding repeatedly search.
Tabu tenure: a simplified Tabu list. Only memorize solution’s attribute.
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ASPIRATION CRITERIA By Objective
A Tabu move becomes admissible if it yields a solution that is better than an aspiration value
By Search Direction A Tabu move becomes admissible if the direction
of the search (improving or non-improving) does not change
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TABU OR NOT TABU
Only moves can be tabu. Attributes are never tabu.
A move may be tabu if it contains one or more tabu attributes
The classification of a move (as tabu or not tabu) is determined by the Tabu tenure
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TABU DECISION TREE
Move
Does the move containtabu-tenure attributes?
Is the move tabu?
Does the move satisfythe aspiration criteria?
Move is admissible Move is not admissible
Yes
Yes
YesNo
NoNo
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LONG TERM MEMORY
Intensification Strategies Diversification Strategies Path Relinking
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INTENSIFICATION STRATEGIES
Intensify the search in promising regions
Ways for intensifying the search are the use of more elaborate heuristics or even exact methods or the enlargement of the neighborhood
Some optimization problems can be partitioned into
subproblems. Solving these subproblems optimallyand combining the partial solutions leads to anoptimal solution.
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DIVERSIFICATION STRATEGIES
Avoiding a large region of the solution space remains completely unexplored
The simplest way to do it is to perform several random restarts or penalize frequently performed moves or solutions often visited.
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PATH RELINKING This approach generates new solutions
by exploring trajectories that connect elite solutions
The exploration starts from an initiating solution and generates a path in the neighborhood space that leads to a guiding solution
Choice rules for next move are designed to incorporate attributes contained in the guiding solution
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RELINKING SOLUTIONS
Initiating solutionGuiding solution
Original pathRelinked path
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TABU SEARCH FRAMEWORK
Stop
Heuristicprocedure
Modified choice rules for diversification or intensification
Generate initial solution and initialize memory
structures
Construct modifiedneighborhood
Select bestneighbor
Execute specializedprocedures
Tabu restrictionsAspiration criteria
Path relinking
Update memorystructures
Update best solution
More iterations?
Short and long term memory
YesNo
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ACKNOWLEDGEMENT
Sz-Cheng Chen
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THANKS FOR YOUR ATTENTION