lect 6 ts

Department of Biomedical, Human Factors, & Industrial Engineering1

Tabu Search: Fundamentals


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?


Scenario #2:

You have misplaced your car keys.

Challenge:

How might you go about locating them?


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


Background

• According to Fred Glover, these were concepts he uncovered– Arose from an AI project course as a student– Trying to get the computer to emulate (human)

problem solving– His scenario involved fellow students solving an

optimization problem– Found they followed a fairly systematic approach


Motivation for Tabu Search

Escaping Trap of Local Optimality


Tabu Search - An Abstract

• A Meta-Heuristic

–Can be used to guide subordinate methods

• Employs adaptive memory functions

–Avoid repeat solutions using a “tabu list”

–Intensifies the search in local regions

• Employs a responsive exploration function

–Diversifies to new areas of search space


Why Memory

• Memory-less searches– Genetic algorithms– Simulated annealing– No explicit use or exploitation of memory

• Rigid memory methods– Branch and bound methods– The solution approach completely dictated

• Inherited memory– Evolutionary methods (genetic algorithms)


Resistance to Memory

• TS use of memory not immediately accepted

• Provides many more degrees of freedom– Result is approaches harder to prove– Not as mathematically tractable

• Use of memory also brings pitfalls– Proper use of memory is not immediately known

• Large part of the tabu search research now is finding integrating principles that provide guidelines for best use of memory


Tabu Search Functions

ShortTerm

LongTerm

IntermediateTerm

Glover, 1990

MEMORY FUNCTIONS

Current Focus


Purpose of Functions

AggressiveExploration

Diversification Intensification

Glover, 1990

STRATEGIC COMPONENTS


Short-Term Tabu Search

Tabu Move

Tabu Search moves among neighborhoodsTabu Search moves among neighborhoods


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 There are common moves, but generally moves aremoves arespecific to the application area. specific to the application area. Moves Moves define the neighborhood for the problem.define the neighborhood for the problem.


Definition of Terms

• Tabu – Characteristic provided a move, or attributes of a

move, that put that move “off limits”

• Tabu list– Memory structure of move attributes that are

currently in “off limits” status

• Tabu tenure– Number of iterations for which a move, or its

attributes, remain on the tabu list


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 The Tabu restriction simply prevents revisiting, or cycling which is a non-revisiting, or cycling which is a non-productive process. Needed to escape the productive process. Needed to escape the local optima trap.local optima trap.


Definition of Terms

• Attributes of solutions– Those aspects that define a solution– A move between solutions can be defined as a

change to some defined set of attributes of the solution

• Attributive memory– Stores information about solution attributes that are

changed implementing a move

• Explicit memory– Records the actual solution


Still More Definitions

• Aggressive exploration– Make the best move possible subject to the tabu

restrictions in place

• Cycling– Cycling occurs when, after a series of moves, the

search returns to a previously visited solution and assumes the same search trajectory as previously explored

• Neighborhood– Defined within the context of the application


Interesting Concepts

• Dynamic tabu tenure– Change the tabu tenure for any attribute– Can have each entry in tabu list have varied tenures– Can change the tenure based on knowledge gleaned

from the search• Called a reactive tabu search strategy

• Aspiration criteria– Means to override tabu status– Do not want to miss good solutions– Provides additional flexibility in the search


More on Aspiration Criteria?

• Motivation - do NOT pass on good solutions

• Typical criteria:

–Best-so-far

–Best found in some set of solutions

–Best according to some other criteria

• Multiple types of aspiration criteria are fine


Short-Term Tabu Search• Sufficient for many problems

– Hands-on will only focus on short-term aspects

• Tabu tenure can provide enough of an escape mechanism for an effective search–Concept of non-improving moves forces route out of

local optimality basin–Reactively increasing the tabu tenure improves the

escape mechanism• The more difficult problems require additional tabu

search constructs


A Simple Example

(use the spreadsheet provided)


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)


Consider Simple Model


• Move - Toggle a variable to 1 and another to 0

• Selected Move - Largest change, to include non-improving moves–All moves will remain feasibility

• Tabu list - prohibit variable toggled to 0 from toggling back to 1 again for 4 iterations

Simple Case One


Problems with Simple Case

• 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


• Move Part 1 - Toggle a variable to 1–Pick largest improvement as the move–Allow solution to become infeasible–Consider allowing infeasibility for multiple

steps

• Move Part 2 - Toggle a variable to 0–Continue until feasibility achieved–Drop item from most violated constraint whose

constraint coefficient is largest

A Better Simple Case


• Better initial solutions to start the search• Move and solution attributes you might

want 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


Questions?

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