TABU SEARCH Presenter Leo ShihChang Lin Advisor Frank

TABU SEARCH Presenter: Leo, Shih-Chang, Lin Advisor: Frank, Yeong-Sung, Lin 2020/11/27 1

Agenda What is Tabu search? Heuristic search Tabu search Characteristic Elements definition Tabu search process Algorithm Application：TSP Related study 2020/11/27 2

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 2020/11/27 3

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 2020/11/27 4

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. 2020/11/27 5

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 2020/11/27 6

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. 2020/11/27 7

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. 2020/11/27 8

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 2020/11/27 9

Tabu Search(5/7) Algorithm 2020/11/27 10

Tabu Search(6 / 7) Process 2020/11/27 11

Tabu Search( 7 / 7) 2020/11/27 12

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. 2020/11/27 13

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. 3 5 2 4 7 6 8 2020/11/27 1 14

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. 3 5 2 4 7 6 8 2020/11/27 1 15

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 Cn-12 such neighborhoods to a given solution. 3 5 2 4 7 6 8 2020/11/27 1 16

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. 2020/11/27 17

Application(6/7) Termination criteria �The algorithm terminates if a pre-specified number of iterations is reached. 2020/11/27 18

Application(7/7) Computational Experience #Nodes Min Dist Max Dist Optimum (GAMS) Tabu Search Object % Gap 10 1000 3043 0 15 50 200 1167 0 20 200 1200 6223 6436 3. 42 40 2000 22244 23513 5. 70 52 N/A 118282 125045 5. 72 127 N/A 7542 8667. 83 14. 93 2020/11/27 19

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. 5 n <(0. 5+(2. 5 x)/4)n < 3 n 2. 375 n as x = 3 The maximum of iteration： If n <50, iteration >= 2000 If n >50 , iteration >= 4000 2020/11/27 20

Thanks for your attention. 2020/11/27 21

Q&A 2020/11/27 22