TABU SEARCHTa-Chun Lien

REFERENCE

Fred G., Manuel L., Tabu Search, Kluwer Academic Publishers, USA(1997)

OUTLINE

History Descent Method Memory Framework

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

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.

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

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

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

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.

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

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

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

LONG TERM MEMORY

Intensification Strategies Diversification Strategies Path Relinking

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.

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.

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

RELINKING SOLUTIONS

Initiating solutionGuiding solution

Original pathRelinked path

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

ACKNOWLEDGEMENT

Sz-Cheng Chen

THANKS FOR YOUR ATTENTION