Transcript Tabu Search

TABU SEARCH
Presenter: Leo, Shih-Chang, Lin
Advisor: Frank, Yeong-Sung, Lin
2015/4/13
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Agenda
 What is Tabu search?
 Heuristic search
 Tabu search
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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 optimum
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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)
 Steps
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.
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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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 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.
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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 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
#Nodes
Min 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
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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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