Presenter: Leo, Shih-Chang, LinAdvisor: Frank, Yeong-Sung, Lin

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Agenda

What is Tabu search? Heuristic search Tabu search

Characteristic Elements definition Tabu search process Algorithm

Application ： TSP Related study

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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

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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

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Heuristic Search(2/2)

Steps1. 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.

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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

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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.

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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.

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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

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Tabu Search(5/7)

Algorithm

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Tabu Search(6 / 7)

Process

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Tabu Search( 7 / 7)

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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.

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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.

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3 5 2 4 7 6 8 1

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.

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3 5 2 4 7 6 8 1

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-1

2 such neighborhoods to a given solution.

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3 5 2 4 7 6 8 1

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.

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Application(6/7)

Termination criteria The algorithm terminates if a pre-specified

number of iterations is reached .

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Application(7/7)

Computational Experience

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#NodesMin Dist

Max Dist

Optimum

(GAMS)Tabu Search

Object % Gap

10 100 1000 3043 3043 0

15 50 200 1167 1167 0

20 200 1200 6223 6436 3.42

40 200 2000 22244 23513 5.70

52 N/A N/A 118282 125045 5.72

127 N/A N/A 7542 8667.83 14.93

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 <50, iteration >= 2000 If n >50 , iteration >= 4000

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