wright university tabu search part1
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8/3/2019 Wright University Tabu Search Part1
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Department of Biomedical, Human Factors, & Industrial Engineering
Tabu Search: Fundamentals
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Department of Biomedical, Human Factors, & Industrial Engineering
Scenario #1:You are playing fetch with your dog
Challenge:Why does he/she not find the ball if
you throw it a different direction?
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Scenario #2:You have misplaced your car keys.
Challenge:How might you go about locating
them?
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Key Concepts of Scenario
Avoid self-defeating actions Keep a memory of search experience Thoroughly search promising areas Examine new search areas if necessary Learn from the search
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Background
According to Fred Glover, these wereconcepts he uncoveredoArose from an AI project course as a studento Trying to get the computer to emulate (human)
problem solvingo His scenario involved fellow students solving an
optimization problemo Found they followed a fairly systematic
approach
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Motivation for Tabu Search
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Tabu Search - An Abstract
A Meta-HeuristicoCan be used to guide subordinate
methods Employs adaptive memory functions
oAvoid repeat solutions using a tabu listo
Intensifies the search in local regions Employs a responsive exploration functionoDiversifies to new areas of search space
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Why Memory
Memory-less searcheso Genetic algorithmso Simulated annealingo No explicit use or exploitation of memory
Rigid memory methodso Branch and bound methodso The solution approach completely dictated
Inherited memoryo Evolutionary methods (genetic algorithms)
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Resistance to Memory
TS use of memory not immediatelyaccepted
Provides many more degrees of freedomo Result is approaches harder to proveo Not as mathematically tractable
Use of memory also brings pitfallso Proper use of memory is not immediately
known Large part of the tabu search research nowis finding integrating principles that provideguidelines for best use of memory
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Tabu Search Functions
Current Focus
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Purpose of Functions
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Short-Term Tabu Search
Tabu Search moves amongneighborhoods
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Department of Biomedical, Human Factors, & Industrial Engineering
What are Moves?
Toggle variable between 0 and 1 Swap nodes in a routing tour Swap nodes between tours Insert/delete edge operation on graph Interchange variables from basis
There are common moves, but generally moves arespecific to the application area. Moves define theneighborhood for the problem.
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Definition of Terms
Tabuo Characteristic provided a move, or attributes of
a move, that put that move off limits
Tabu listo Memory structure of move attributes that are
currently in off limits status
Tabu tenureo Number of iterations for which a move, or its
attributes, remain on the tabu list
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What is considered Tabu?
Keep recent variables from toggling Freeze in-place recently moved nodes Freeze recently moved edges Keep variables in or out of basis
The Tabu restriction simply prevents revisiting, orcycling which is a non-productive process. Neededto escape the local optima trap.
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Definition of Terms
Attributes of solutionso Those aspects that define a solutionoA move between solutions can be defined as a
change to some defined set of attributes of the
solution Attributive memory
o Stores information about solution attributes thatare changed implementing a move
Explicit memoryo Records the actual solution
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Still More Definitions
Aggressive explorationo Make the best move possible subject to the
tabu restrictions in place
Cyclingo Cycling occurs when, after a series of moves,
the search returns to a previously visitedsolution and assumes the same searchtrajectory as previously explored
Neighborhoodo Defined within the context of the application
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Interesting Concepts
Dynamic tabu tenureo Change the tabu tenure for any attributeo Can have each entry in tabu list have varied
tenureso Can change the tenure based on knowledge
gleaned from the search Called a reactive tabu search strategy
Aspiration criteriao Means to override tabu statuso Do not want to miss good solutionso Provides additional flexibility in the search
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More on Aspiration Criteria?
Motivation - do NOT pass on goodsolutions
Typical criteria:oBest-so-faroBest found in some set of solutionsoBest according to some other criteria
Multiple types of aspiration criteria arefine
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Short-Term Tabu Search
Sufficient for many problemso Hands-on will only focus on short-term
aspects
Tabu tenure can provide enough of anescape mechanism for an effectivesearchoConcept of non-improving moves
forces route out of local optimality
basinoReactively increasing the tabu tenure
improves the escape mechanism
The more difficult problems requireadditional tabu search constructs
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A Simple Example
(use the spreadsheet provided)
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Department of Biomedical, Human Factors, & Industrial Engineering
Maximize:78x1+ 73x2 + 81x3 + 68x4 + 59x5 + 48x6 + 45x7 + 22x8+ 46x9 +
96x10 + 29x11 + 56x12 + 26x13 + 74x14 + 18x15
Subject to:
29x1+ 33x2 + 28x3 + 7x4 + 6x5 + 27x6 + 6x7 + 1x8+32x9 + 38x10 + 31x11 + 22x12 + 27x13 + 1x14 + 9x15 153.5
1x1+ 10x2 + 7x3 + 14x4 + 14x5 + 13x6 + 8x7 + 13x8 +
10x9 + 7x10 + 3x11 + 11x12 + 10x13 + 8x14 + 9x15 69
32x1+ 24x2 + 26x3 + 12x4 + 14x5 + 1x6 + 34x7 + 6x8 +
3x9 + 18x10 + 20x11 + 15x12 + 8x13 + 7x14 + 36x15 128
xi = 0,1
MKP Example(should look somewhat familiar)
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Consider Simple Model
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Move - Toggle a variable to 1 andanother to 0
Selected Move - Largest change, toinclude non-improving movesoAll moves will remain feasibility
Tabu list - prohibit variable toggled to 0
from toggling back to 1 again for 4iterations
Simple Case One
P bl ith Si l
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Problems with SimpleCase
Solution does not improve very much Never really comes near the constraint
limits for feasibility A safe search, but not nearly aggressive
enough to provide good solutions
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Move Part 1 - Toggle a variable to 1o Pick largest improvement as the moveoAllow solution to become infeasibleo Consider allowing infeasibility for multiple
steps Move Part 2 - Toggle a variable to 0
o Continue until feasibility achievedo Drop item from most violated constraint
whose constraint coefficient is largest
A Better Simple Case
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Department of Biomedical, Human Factors, & Industrial Engineering
Better initial solutions to start thesearch
Move and solution attributes you mightwant to track
How might we diversify the search? What type of solutions might we
consider saving in an elite list? Could we make random moves?
Possible Extensions
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Questions?
top related