T ABU S EARCH Ta-Chun Lien

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

O UTLINE History Descent Method Memory Framework

H ISTORY 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

D ESCENT M ETHOD 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 stops 4) Otherwise, designate x ’ to be the new x and go to step2.

D ESCENT M ETHOD ( 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

M EMORY Short Term Memory Long Term Memory Each type of Memory is accompanied by its own special strategies. However, the effect of both types of memory may be viewed as modifying the Neighborhood N(x) of the current solution x. N*(x) :modified neighborhood

S HORT -T ERM M EMORY 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

T ABU T ENURE 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.

A SPIRATION C RITERIA 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

T ABU OR NOT T ABU 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

T ABU D ECISION T REE Move Does the move contain tabu-tenure attributes? Is the move tabu? Does the move satisfy the aspiration criteria? Move is admissibleMove is not admissible Yes No

L ONG T ERM M EMORY Intensification Strategies Diversification Strategies Path Relinking

I NTENSIFICATION S TRATEGIES 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 optimally and combining the partial solutions leads to an optimal solution.

D IVERSIFICATION S TRATEGIES 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.

P ATH R ELINKING 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

R ELINKING S OLUTIONS Initiating solution Guiding solution Original path Relinked path

T ABU S EARCH F RAMEWORK Stop Heuristic procedure Modified choice rules for diversification or intensification Generate initial solution and initialize memory structures Construct modified neighborhood Select best neighbor Execute specialized procedures Tabu restrictions Aspiration criteria Path relinking Update memory structures Update best solution More iterations? Short and long term memory Yes No

A CKNOWLEDGEMENT Sz-Cheng Chen

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