Tabu Search - Basic Description

Basic Description

Tabu search is a metaheuristic local search algorithm that can be used for solving combinatorial optimization problems (problems where an optimal ordering and selection of options is desired - an example, the traveling salesman problem, is detailed below).

Tabu search uses a local or neighborhood search procedure to iteratively move from one potential solution to an improved solution in the neighborhood of, until some stopping criterion has been satisfied (generally, an attempt limit or a score threshold). Local search procedures often become stuck in poor-scoring areas or areas where scores plateau. In order to avoid these pitfalls and explore regions of the search space that would be left unexplored by other local search procedures, tabu search carefully explores the neighborhood of each solution as the search progresses. The solutions admitted to the new neighborhood, are determined through the use of memory structures. Using these memory structures, the search progresses by iteratively moving from the current solution to an improved solution in .

These memory structures form what is known as the tabu list, a set of rules and banned solutions used to filter which solutions will be admitted to the neighborhood to be explored by the search. In its simplest form, a tabu list is a short-term set of the solutions that have been visited in the recent past (less than iterations ago, where is the number of previous solutions to be stored - is also called the tabu tenure).

The memory structures used in tabu search can be divided into three categories:

• Short-term: The list of solutions recently considered. If a potential solution appears on this list, it cannot be revisited until it reaches an expiration point.
• Intermediate-term: A list of rules intended to bias the search towards promising areas of the search space.
• Long-term: Rules that promote diversity in the search process (i.e. regarding resets when the search becomes stuck in a plateau or a suboptimal dead-end).

One example of an intermediate-term memory structure is one that prohibits solutions that contain certain attributes (e.g., solutions to the traveling salesman problem which include undesirable arcs) or a memory structure that prevents certain moves (e.g. an arc that was added to a TSP tour cannot be removed in the next moves). Selected attributes in solutions recently visited are labeled "tabu-active." Solutions that contain tabu-active elements are banned.

Short-term memory alone may be enough to achieve solution superior to those found by conventional local search methods, but intermediate and long-term structures are often necessary for solving harder problems. Intermediate and long-term structures primarily serve to intensify and diversify the search (the short-term memory also intensifies the search by temporarily locking in certain locally attractive attributes, i.e., those belonging to moves recently evaluated to be "good").

One major issue with Tabu Search is that it is only effective in discrete spaces. It is rare that a search would visit the same real-value point in space multiple times, making a tabu list worthless. One possible solution is to apply a similarity measure and reject solutions that violate this similarity threshold.

Another problem with Tabu Search is that if the search space is very large or of high dimensionality, it is easy to remain within a small area of the search space. To work around this pitfall, some implementations of tabu search create a tabu list consisting of the attributes of a solution, rather than entire candidate solutions. Tabu lists containing attributes (rather than whole solutions) can be more effective for some domains, although they raise a new problem. When a single attribute is marked as tabu, this typically results in more than one solution being tabu. Some of these solutions that must now be avoided could be of excellent quality and might not have been visited. To mitigate this problem, "aspiration criteria" are introduced: these override a solution's tabu state, thereby including the otherwise-excluded solution in the allowed set. A commonly used aspiration criterion is to allow solutions which are better than the currently-known best solution.

Tabu search is often benchmarked against other local search methods - such as Reactive search optimization, Hill climbing, Guided Local Search, or greedy randomized adaptive search procedure - or other metaheuristic methods - such as Simulated annealing, genetic algorithms, or Ant colony optimization algorithms.