Poco Loco Moco'

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Poco Loco Moco.
Local search approaches to handling preferences
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Contents

• Preference modeling.
• Preferences giving Soco
• Modeling examples.
• Problem solving approaches.
• Preferences giving Moco.
• Background
• Modeling examples.
• Elements in problem solving approaches
• Loco Moco
• Sintefs program A suggestion

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Reasons for modeling preferences

• Over-constrainedness
• De-facto over-constrainedness
• Solution preferences

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CSPs
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Problem modeling,CSP
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Problem modeling, CSP
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Problem modeling, PCSP

• Divide the constraints into hard and soft
  constraints
• C CH ? CS
• Add preference functions ?i with the following
  structure

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Problem modeling, PCSP
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Flexibility

• Value preferences
• Constraint preferences
• Max-CSP
• Free functions ?i.
• Unusal possibilities

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Example, free functionsn-settlers

• 2n variables, Xx1,,xn, Y y1,,yn.
• (xi, yi) gives the co-ordinates of piece i.

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Settlers and personal space
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Problem formulation
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Settlers and elevation
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The assignment problem
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Maximal constraint satisfaction
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Maximum constraint satisfaction
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N-cowboys
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Moco

• Set of objective functions
• Objective point z F(si) denotes the vector
• z z1,... zk f1(si),... fk(si).
• Objective space, Z z(1),,.

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Multiple objectives
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Moco

• z is attainable if there exists s in S so that
  f(s) z.
• Ideal point z min(f1),...,min(fk) over all
  s in S.
• Minimize f1(si),... fk(si) over all s in S
• Minimize f1(si),... fk(si) over all s in S

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Domination

• State s dominates s if and only if
• and
• there exists at least one fi F such that fi(s)
  lt fi(s).

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Pareto optimality
If which dominates s.

• s is
• efficient,
• Pareto optimal ,
• non-inferior,
• non-dominated,
• Pareto-admissible

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Efficient frontier

• P Problem.
• E(P) The set of efficient states.

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Objective space
Attainable points
Z
S
s
z
E(P)
Ideal points
State space
Objective space
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Max spread, min elevation n-settlers
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Real world personal space
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Elements in problem solving approaches

• Weights and scalarizing functions
• Targets
• Priorities and hierarchies
• Functional and fuzzy preferences
• Changing the problem

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Weights

• Select a suitable set of weight vectors

L
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Weights

• Specifying a set of weight vectors

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Scalarizing functions

• Select a suitable scalarizing function
• Solve the problem
• Different weight vectors give different
• points on the efficient frontier.

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Scalarizing functions

• The weighted sum
• The Chebychev function

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Weighted sum
The weighted sum cant map onto the full set
E(P).
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The Chebychev function
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Goals of a problem solver

• Find efficient points.
• Approximations of efficient points.
• Find more than one state
• (in order to give the problem solver
  alternatives).
• Good distribution over E(P).
• The size of the set of alternatives should be
  balanced against the cost of generating them,
  which again is balanced against their quality.

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Loco Moco difficulties

• Modelling a move evaluation function without a
  complete ordering relation over the states.
• The notion of distance is not obvious.
• The question of meta-strategies has to extend to
  exploring the efficient frontier
• The quality of the algorithm is a multi-criteria
  measure
• Speed,
• Distribution over AE(P).
• Distance to points on E(P)

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Move evaluations
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Loco Moco strategies

• Searching the objective space guided by
  scalarizing evaluation functions over the k
  objective functions.
• Searching the objective space guided by a
  standard evaluation function, but over a
  scalarizing objective function.

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Scalarizing objective functions
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Cache
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Sintefs program ?

• Modeling PCSPs
• Enhancing SCOOP.
• Defining some test examples.
• Testing existing and new algorithms
• Defining some papers to be written.
• Agent Moco?
• Defining a simple version of Norskog

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Testing algorithms
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Possible papers

• Comparative analysis experiments of existing
  Loco Moco algorithms.
• Trying out the NBI method in Loco Moco
• Moco P-SAT Heuristics
• Scoop A library for Loco Moco
• Multi-objective harvest scheduling