wright university tabu search part1

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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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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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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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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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?

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