1. Presenter: Leo, Shih-Chang, Lin Advisor: Frank, Yeong-Sung, Lin 1 2015/12/16

2. Agenda  What is Tabu search?  Heuristic search  Tabu search  Characteristic  Elements definition  Tabu search process  Algorithm  Application ： TSP  Related study 2 2015/12/16

3. What is Tabu Search?  Proposed by Fred Glover in 1989  A kind of heuristic search  Used for solving combinatorial optimization problems  Short term  Get the local optimum  Long term  Intensification and diversification  Leave the local optimum to get global optimum 3 2015/12/16

4. Heuristic Search(1/2)  Characteristic:  or “experienced search”  not always find the best solution  guarantee to find a good solution in reasonable time.  By sacrificing completeness it increases efficiency.  Useful in solving tough problems 4 2015/12/16

5. Heuristic Search(2/2)  Steps 1. Generate a possible solution which can either be a point in the problem space or a path from the initial state. 2. Test to see if this possible solution is a real solution by comparing the state reached with the set of goal states. 3. If it is a real solution, return. Otherwise repeat from 1. 2015/12/16 5

6. Tabu Search(1/7)  Characteristic  Capability of getting global solution instead of local solution  Tabu list can avoid repeating trivial search  Update tabu list to speed up searching 6 2015/12/16

7. Tabu Search(2/7)  Elements Definition  Neighborhood solution ： a solution which must exist in a set of feasible solution, and which is not in the tabu list.  Move ： change the current solution to its neighborhood solution. 7 2015/12/16

8. Tabu Search(3/7)  Tabu List ： a short-term memory which records the solutions that have been visited in the recent past. In this way, we can avoid repeating search. In general, tabu list has a fixed size to memorize, and it follows FIFO to maintain the list.  Aspiration Criteria ： when a solution in the tabu list is better than the currently-known best solution, the solution is permitted to replace the currently-known solution with the best solution. 8 2015/12/16

9. Tabu Search(4/7)  Stopping Criteria ： the stopping conditions 。  Maximum iterative numbers  Maximum times which counts when object function’s value doesn’t improve  The longest default execution time of CPU  When object function’s output is acceptable 9 2015/12/16

10. Tabu Search(5/7)  Algorithm 2015/12/16 10

11. Tabu Search(6 / 7)  Process 11 2015/12/16

12. Tabu Search( 7 / 7) 12 2015/12/16

13. Application(1/7)  Traveling Salesman Problem (A Comparative Study of Tabu Search and Simulated Annealing for Traveling Salesman Problem by Sachin Jayaswal, University of Waterloo)  a problem where starting from a node it is required to visit every other node only once in a way that the total distance covered is minimized. 13 2015/12/16

14. Application(2/7)  Tabu Search for TSP  Solution Representation ：  A feasible solution is represented as a sequence of nodes, each node appearing only once and in the order it is visited. The first and the last visited nodes are fixed to 1. 2015/12/16 14 35247681

15. Application(3/7)  Initial Solution  A good feasible, yet not-optimal, solution to the TSP can be found quickly using a greedy approach.  Starting with the first node in the tour, find the nearest node.  Each time find the nearest unvisited node from the current node until all the nodes are visited. 2015/12/16 15 35247681

16. Application(4/7)  Neighborhood solution  A neighborhood solution to a given solution is defined as any other solution that is obtained by a pair wise exchange of any two nodes in the solution.  If we fix node 1 as the start and the end node, for a problem of N nodes, there are C n-1 2 such neighborhoods to a given solution. 2015/12/16 16 35247681

17. Application(5/7)  Tabu List  Initially, it is empty  the attribute stored in the Tabu list is a pair of nodes that have been exchanged recently.  Aspiration criteria  The criterion used for this to happen in the present problem of TSP is to allow a move, even if it is in tabu list, if it results in a solution with an objective value better than that of the current best-known solution. 2015/12/16 17

18. Application(6/7)  Termination criteria  The algorithm terminates if a pre-specified number of iterations is reached. 2015/12/16 18

19. Application(7/7)  Computational Experience 2015/12/16 19 #NodesMin DistMax Dist Optimum (GAMS) Tabu Search Object% Gap 1010010003043 0 15502001167 0 202001200622364363.42 40200200022244235135.70 52N/A 1182821250455.72 127N/A 75428667.8314.93

20. Related study ( 禁忌搜尋法則求解推銷員旅行問題, 吳泰熙 and 張欽智,1997)  Different parameters set in Tabu search affect the quality of optimum  The size of Tabu list ：  n is the amount of cities, x is the coefficient of Tabu list  0.5n <(0.5+(2.5x)/4)n < 3n  2.375n as x = 3  The maximum of iteration ：  If n = 2000  If n >50, iteration >= 4000 2015/12/16 20

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