Tabu Search Review: Branch and bound has a “rigid” memory structure (i.e. all branches are completed or fathomed). Simulated Annealing has no memory structure. Relies on randomization to search the solution space.

Tabu Search Primary Features of Tabu Search: Adaptive memory - remembers features of good/bad solutions that you encounter). Responsive exploration – exploration based on past exploration.

Tabu Search Basic Algorithmic Features: Always move to the best available neighborhood solution, even if it is worse than the current solution. Maintain a list of solution points that must be avoided (not allowed) or a list of move features that are not allowed. Referred to as the tabu list. Update the tabu list based on some memory structure (short-term memory). Remove tabu moves after some time period has elapsed (tenure). Allow for exceptions from the tabu list (aspiration criteria). Expand the search area, modify tenure or size of tabu list.

Tabu Search Tabu Search Short-Term Memory Component (F. Glover, 1990): Begin with a Starting Current Solution Obtain the solution from initialization or from An intermediate or long-term memory component Create a Candidate List of Moves (If applied, each move would generate a new solution from the current solution) Choose the Best Admissible Candidate (Admissibility is based on the tabu restrictions and aspiration criteria.) Designate the solution obtained as the new current solution. Record it as the new Best Solution if it improves on the previous best. Stopping Criterion Stop if a specified number of iterations has elapsed In total or since the last Best Solution was found. Stop Continue Terminate Globally or Transfer A transfer initiates an intensification or Diversification Phase embodied in an intermediate or long-term memory component. Update Admissibility Conditions Update tabu restrictions and Aspiration criteria.

Tabu Search Issue 1: What is a tabu list? How is it generated? How does is it incorporate memory? See handout. Issue 2: How can a tabu list be used to expand the search area?

Tabu Search Issue 3: What is an aspiration criteria? Criteria which allows a tabu moved to be accepted under certain conditions. Most common aspiration criterion, if the move finds a new best solution, then accept the move even if the move is tabu.

Tabu Search Issue 4: Algorithm for selecting best admissible candidate (Glover). Evaluate Each Candidate Move Does the move yield a higher evaluation Than any other move found admissible so far? NO YES Check Tabu Status Is the move tabu? YES NO Check Aspiration Level Does move satisfy Aspiration criteria? YES Move is Admissible Designate as best Admissible candidate. NO Candidate List Check Is there a good probability of better moves left, or should candidate list be extended? YES NO Make the Chosen Best Admissible Move

Tabu Search Example of Tabu Search – See handouts