Goal intervals in dynamic multicriteria problems

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Goal intervals in dynamic multicriteria problems

• The case of MOHO

Juha Mäntysaari
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Decision problem of space heating consumers

• Under time varying electricity tariff space
  heating consumers can save in heating costs by
• Storing heat in to the house during low tariff
  hours
• Trading living comfort to costs savings
• A dynamic decision problem

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Space heating problem

• Space heating consumers try to
• MIN Heating costs
• MAX Living comfort
• subject to
• Dynamic price of the electricity
• Dynamics of house
• Other (physical) constraints

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Dynamics of the house
Q(t)Q(t-1)Dtq(t-1)-d(t-1) where d(t)
aDt(T(t) - Tout(t)) Q(t) T(t)/C, (b
1/C) Þ T(t) T(t-1) bDtq(t-1) -abDt(T(t-1) -
Tout(t-1)) Units Q kWh, a kW/C, C
kWh/C
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Example houses
House 2
House 1
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Information summary
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Goal models
1. Hard constraint (pipe is hard)
2. Soft constraints (pipe is soft)Interval goal
programming
3. Hard constraint with a goal inside(pipe with
a goal)
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Hard constraints
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Soft constraints
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Hard constraints with a goal
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Goal models (summary)
1. Hard constraints
2. Soft constraints
3. Hard constraints with a goal
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MultiObjective Household heating Optimization
(MOHO)
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Idea of MOHO

• Minimize heating costs using hard lower and upper
  bounds for indoor temperature
• The case of hard constraints
• Ask How many percents would you like to
  decrease the heating costs from the current
  level?
• Solve again trying to achieve the desired
  decrease in cost by relaxing the indoor
  temperature upper bound
• The e-constraints method (upper bound must be
  active in order to succeed)

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Example House 2 (1/4)
Minimized heating costs
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Example House 2 (2/4)
Decreased costs by 5
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Example House 2 (3/4)
Decreased again by 5
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Example House 2 (4/4)
And again by 5
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Summary

• Model and parameters of the house identified
• Depending on the definition of the living
  comfort different multicriteria models can be
  used
• Benefits of the simplified approach
• Only bounds of the indoor temperature asked
• Comparison and tradeoff only with heating costs