
Glover, F. 1986. Future Paths for Integer Programming and Links to Artificial Intelligence. Computers and Operations Research. Vol. 13, pp. 533549

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Glover, F. 1986. Future Paths for Integer Programming and Links to Artificial Intelligence. Computers and Operations Research. Vol. 13, pp. 533549. Hansen, P. 1986. The Steepest Ascent Mildest Descent Heuristic for Combinatorial Programming. Congress on Numerical Methods in Combinatorial Optimization, Capri, Italy.
3 main strategies [7]: 3 main strategies [7]:  Forbidding strategy: control what enters the tabu list
 Freeing strategy: control what exits the tabu list and when
 Shortterm strategy: manage interplay between the forbidding strategy and freeing strategy to select trial solutions
Local search procedure Local search procedure Neighborhood structure Aspiration conditions Form of tabu moves Maximum size of tabu list Stopping rule
A chief way to exploit memory in tabu search is to classify a subset of the moves in a neighborhood as forbidden (or tabu) [1]. A chief way to exploit memory in tabu search is to classify a subset of the moves in a neighborhood as forbidden (or tabu) [1]. A neighborhood is constructed to identify adjacent solutions that can be reached from current solution [8]. The classification depends on the history of the search, and particularly on the recency or frequency that certain move or solution components, called attributes, have participated in generating past solutions [1]. A tabu list records forbidden moves, which are referred to as tabu moves [5]. Tabu restrictions are subject to an important exception. When a tabu move has a sufficiently attractive evaluation where it would result in a solution better than any visited so far, then its tabu classification may be overridden. A condition that allows such an override to occur is called an aspiration criterion[1].
Step 1: Choose an initial solution i in S. Set i* = i and k=0. Step 1: Choose an initial solution i in S. Set i* = i and k=0. Step 2: Set k=k+1 and generate a subset V* of solution in N(i,k) such that neither one of the Tabu conditions is violated or at least one of the aspiration conditions holds. Step 3: Choose a best j in V* and set i=j. Step 4: If f(i) < f(i*) then set i* = i. Step 5: Update Tabu and aspiration conditions. Step 6: If a stopping condition is met then stop. Else go to Step 2.
Some immediate stopping conditions could be the following [4]: Some immediate stopping conditions could be the following [4]: N(i, K+1) = 0. (no feasible solution in the neighborhood of solution i) K is larger than the maximum number of iterations allowed. The number of iterations since the last improvement of i* is larger than a specified number. Evidence can be given that an optimum solution has been obtained.
Minimum spanning tree problem with constraints.  Minimum spanning tree problem with constraints.
 Objective: Connects all nodes with minimum costs
New cost = 75 (iteration 2) New cost = 75 (iteration 2) ( new best so far solution)
* A tabu move will be considered only if it would result in a better solution than the best trial solution found previously (Aspiration Condition) * A tabu move will be considered only if it would result in a better solution than the best trial solution found previously (Aspiration Condition) Iteration 3 new cost = 85
* A tabu move will be considered only if it would result in a better solution than the best trial solution found previously (Aspiration Condition) * A tabu move will be considered only if it would result in a better solution than the best trial solution found previously (Aspiration Condition) Iteration 4 new cost = 70 Override tabu status
Optimal Solution Cost = 70 Additional iterations only find inferior solutions
Long term memory Long term memory We’ll see how this information is used in a minute
When search not going well; e.g., haven’t found an improving neighbor in some iterations When search not going well; e.g., haven’t found an improving neighbor in some iterations New best solutions become rare
Intensify search in promising regions When to intensify vs. diversify: interesting; further topic we will not cover
Pros: Pros:  Allows nonimproving solution to be accepted in order to escape from a local optimum (true too for GA, SimAnn, AntColOpt)
 The use of Tabu list (helps avoid cycles and move reversal)
 Can be applied to both discrete and continuous solution spaces
 For larger and more difficult problems (scheduling, quadratic assignment and vehicle routing), tabu search obtains solutions that rival and often surpass the best solutions previously found by other approaches [1].
Cons:  Too many parameters to be determined
 Number of iterations could be very large
 Global optimum may not be found, depends on parameter settings (also true of GA, SimAnn, AntColOpt)
[1] Glover, F., Kelly, J. P., and Laguna, M. 1995. Genetic Algorithms and Tabu Search: Hybrids for Optimization. Computers and Operations Research. Vol. 22, No. 1, pp. 111 – 134. [1] Glover, F., Kelly, J. P., and Laguna, M. 1995. Genetic Algorithms and Tabu Search: Hybrids for Optimization. Computers and Operations Research. Vol. 22, No. 1, pp. 111 – 134. [2] Glover, F. and Laguna, M. 1997. Tabu Search. Norwell, MA: Kluwer Academic Publishers. [3] Hanafi, S. 2001. On the Convergence of Tabu Search. Journal of Heuristics. Vol. 7, pp. 47 – 58. [4] Hertz, A., Taillard, E. and Werra, D. A Tutorial on Tabu Search. Accessed on April 14, 2005: http://www.cs.colostate.edu/~whitley/CS640/hertz92tutorial.pdf [5] Hillier, F.S. and Lieberman, G.J. 2005. Introduction to Operations Research. New York, NY: McGrawHill. 8th Ed. [6] Ji, M. and Tang, H. 2004. Global Optimizations and Tabu Search Based on Mamory. Applied Mathematics and Computation. Vol. 159, pp. 449 – 457. [7] Pham, D.T. and Karaboga, D. 2000. Intelligent Optimisation Techniques – Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. London: SpringerVerlag. [8] Reeves, C.R. 1993. Modern Heuristic Techniques for Combinatorial Problems. John Wiley & Sons, Inc.
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