08.12.30 林世昌 Tabu Search

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

AgendaWhat is Tabu search?Heuristic searchTabu searchCharacteristicElements definitionTabu search processAlgorithmApplicationTSPRelated study

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What is Tabu Search?Proposed by Fred Glover in 1989A kind of heuristic searchUsed for solving combinatorial optimization problemsShort termGet the local optimum Long termIntensification and diversificationLeave the local optimum to get global optimum**

Heuristic Search(1/2)Characteristic:or experienced searchnot 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)StepsGenerate a possible solution which can either be a point in the problem space or a path from the initial state. Test to see if this possible solution is a real solution by comparing the state reached with the set of goal states. If it is a real solution, return. Otherwise repeat from 1.

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Tabu Search(1/7)CharacteristicCapability of getting global solution instead of local solutionTabu list can avoid repeating trivial searchUpdate tabu list to speed up searching**

Tabu Search(2/7)Elements Definition

Neighborhood solutiona solution which must exist in a set of feasible solution, and which is not in the tabu list.

Movechange the current solution to its neighborhood solution.

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Tabu Search(3/7)Tabu Lista 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 Criteriawhen 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 Criteriathe stopping conditionsMaximum iterative numbersMaximum times which counts when object functions value doesnt improveThe longest default execution time of CPU When object functions output is acceptable

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Tabu Search(5/7)Algorithm**

Tabu Search(6 / 7)Process**

Tabu Search( 7 / 7)**

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.**

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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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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Application(4/7)Neighborhood solutionA 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.

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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 criteriaThe 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 .**

Application(7/7)Computational Experience**

#NodesMin DistMax DistOptimum(GAMS)Tabu SearchObject% Gap1010010003043304301550200116711670202001200622364363.4240200200022244235135.7052N/AN/A1182821250455.72127N/AN/A75428667.8314.93

Related study(, and ,1997)Different parameters set in Tabu search affect the quality of optimumThe size of Tabu listn is the amount of cities, x is the coefficient of Tabu list0.5n 50 , iteration >= 4000

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