Tabu Search: More Advanced Concepts

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Tabu Search More Advanced Concepts
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Links with AI

• First works specifically made a link
• Heuristic uses memory, learns, and reacts during
  the search
• Target analysis is an off-line process to provide
  a means to determine adaptive triggers
• Conduct detailed analysis of search process
• Propose and test new search constructs
• Implement with memory structures

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Target Analysis(extended discussion)
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Overview of TA

• Links tabu search and artificial intelligence
• Provides some ability for heuristic to learn
  what rules are best
• Most rules have evolved
• Used by someone and deemed to work well
• Legacy use promotes overall satisfaction with
  approach
• Why might legacy rules not be the best?

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Simple Greedy Example

• For an example why legacy approaches may not be
  the best, consider the following example from
  current research
• Greedy approaches function like steepest ascent
  procedures
• The Chu and Beasley repair operation was a greedy
  heuristic
• General approach is to develop an effective
  gradient that accounts for constraints

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Toyoda

• Primal Effective Gradient Method Start with all
  items removed from the knapsacks
• Compute an effective gradient for each
  candidate item not currently in the knapsacks
• Add highest scoring element knapsack, retaining
  feasibility

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Toyoda Details
Pj vector of variable j resources required Pu
vector of constraint resources used so far
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Senju and Toyoda

• Dual Effective Gradient Method Start with all
  items designated as contained in the knapsacks
• Compute an effective gradient for each element
• Drop lowest scoring item, until problem
  feasibility is achieved
• Re-consider any dropped elements for re-inclusion
  if all constraints have slack available

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S T Details
R sum of constraint coefficients S Each R
less RHS value
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Loulou and Michaelides

• Modified version of Toyodas approach
• Primal Effective Gradient Method
• - Same steps as Toyoda
• Only difference is in defining Effective
  Gradient
• - Emphasis is on tightest constraint

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L M Details
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Thirty Years of Results

• The Senju-Toyoda approach one of the earliest
• Influenced tabu search efforts, however,
• Not as popular within heuristics community
• Heuristics are tested against test problems
• Real problems (limited numbers)
• Synthetic or artificial problems
• Benchmark test sets
• Performance conclusions only as good as the
  sample population

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Problems with Problems

• Real world problems limited and not a thorough
  representative
• Synthetic problems hard to duplicate among
  researchers and requires probability assumptions
  for generation
• Benchmark test sets can take on a life of their
  own
• Great for comparative purposes
• What if set is not really that good?

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Problems with Beasley Set

• Varies number of variables and constraints
• Total of 5, 10 and 30 constraints
• Varies RHS ratio along good range
• Every constraint constructed exactly the same
• Even with 30 constraints the resource limit in
  every constraint is exactly the same ratio to the
  sum of the coefficients within the problem
• Sort of like solving a single constraint problem!
• Thus, problems are not very representative

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Consider Sample Problem
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Recall Beasleys Problems
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Representative of Problems
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Consider an Alternative Set

• Vary constraint settings
• Tight
• Loose
• Mixed
• Just 2 constraints in this set

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Comparisons
Coding, 1tight constraint, 2loose constraint
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So What?

• The immediate question that should come to mind
  is why does the S-T approach do so well?
• Any why had this not been uncovered before?
• The answer is the form of the effective gradient
• The dual method provides a trajectory that favors
  the most restrictive constraint
• The next question is how to allow the heuristic
  to learn from this
• The answer is a modified primal heuristic

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Explaining the Behavior
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Explaining the Behavior

• L M is an improved version of TOYODA
• S T was the best when the constraint slackness
  levels were mixed
• Combined characteristics of S T into L M
• New heuristic is extended from L M heuristic
  based on our knowledge of S T
• New effective gradient

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Results of New Heuristic
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Results with Benchmarks
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Change Benchmarks Slightly
Benchmark modified so there is a tight constraint
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Purpose of Excursion

• Legacy approaches may not be a best approach
• Deeper knowledge of problem and solution approach
  performance on that problem is required
• This deeper knowledge is not obvious
• Run experiments
• Collect and analyze data
• Conjecture and test
• Basically, a Target Analysis approach!

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Target Analysis
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Target Analysis Questions

• Which decision rules should be selected to guide
  the search?
• Which parameter values should be chosen to
  implement the decision rule?
• What attributes are most relevant for determining
  tabu status?
• what associated tabu restrictions, tabu tenures
  and aspiration criteria should be used?

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More Questions

• What weights should be assigned to create
  penalties (e.g., as a function of frequency-based
  memory) and what thresholds should govern their
  application?
• Which measures of quality and influence are most
  appropriate?
• which combinations of these lead to the best
  results in different search phases?

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And Still More Questions

• What features of the search trajectory disclose
  when to focus more strongly on intensification
  and when to focus more strongly on
  diversification?
• For Example
• How should the search trajectory change to best
  accommodate realistic problems?
• What is the difference between legacy
  trajectories?
• Can these good trajectories be exploited?

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In general, target analysis replaces the
inefficient legacy approach with a systematic
approach to create hindsight before the fact, and
then undertakes to reverse engineer the types
of rules that will lead to good solutions.
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Some Final Thoughts
Many times we in the Analytical community fit
problems into our (favorite) solution technique.
With a technique like Tabu Search our analytical
paradigm becomes one of fitting the solution
technique to the specific problem.
Next class we will examine the application of
many of these tabu search concepts to the general
form of the MKP via the application article
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Questions?