Multicriteria Interval Goal Optimization in the Regulation of Lake-River Systems

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Multicriteria Interval Goal Optimization in the
Regulation of Lake-River Systems

• Raimo P. Hämäläinen and Otso Ojanen
• Systems Analysis Laboratory
• Helsinki University of Technology
• www.hut.fi/Units/SAL
• raimo_at_hut.fi

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Lake Päijänne and River Kymijoki in Finland
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Päijänne-Kymijoki lake river system

• 4th largest in Finland
• Control Outflow from Päijänne to the river
  Kymijoki
• Inflows forecasted
• Regulation policies Water levels at six time
  points

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Need for modelling

• Development of feasible regulation strategies is
  a dynamic control problem
• No intuitive solutions
• Planning againts long historical inflow data
• Interest in optimal regulation
• Interactive analysis of impacts
• Many interest groups
• Interactive dynamic multicriteria optimization

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Goal programming

• Goal Utopia point/set
• Problem Find a point in the feasible set closest
  to the goal point/set
• minimize distance d
• New aspects
• Dynamic problem
• Goal interval (set)

Goal point/set
d
cost function
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Why goal programming ?

• Economic, social and environmental impacts
• 19 primary 27 secondary 48 different impacts
• For example Power production, flood damages,
  number of destroyed loon nests
• Some impacts are interdependentenergy produced
  and the value of energy
• Direct use of tradeoff comparisons is difficult

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Modeling Principles

• Lake dynamics
• Optimization against four year history data
• Lower dam regulation by a given rule
• Regulator uses a rolling two goal optimization
  strategy
• Adjustment rules

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Interactive decision support
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Goals in water levels

• Users give desired water levels at
• six different points during one year
• ideal level acceptable interval (min, max)

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• Dynamics of the lake Päijänne

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Constraints

• Outflow from Päijänne
• Min/max flow
• Fixed and hard
• Max change in outflow
• Soft penalty
• Water level in the
• midstream lake Pyhäjävi
• Fixed rule based regulation
• Part of the dynamics

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Criteria and penalty functions

• Criterion for goal levels
• Quadratic cost for differences of goal points
  from regulated water levels
• Penalty outside the goal interval
• Quadratic difference from the limits (min or max)
• Penalty for violation of change in outflow rate
• Quadratic cost outside the maximum flow limit,
  otherwise zero

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Cost function minimized Sum of deviations from
goal penalty outside goal intervals
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Benefits of the interval goal formulation

• Relaxation of the rigidity of fixed target points
• Allows dynamic flexibility to the solution
• Softer solutions with smaller changes in the flow
  rate
• Can increase risk and sensitivity to unpredicted
  deviations in the inflows

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Generation of the optimal regulation strategy
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ISMO - spreadsheet software

• Minimizes deviations from goal levels and goal
  intervals
• Satisfies flow constraints
• Simulates the regulators operating principles
• Preference model
• Set of goal levels acceptability intervals
• Optimization againts history data for a selected
  four year period
• Modifiable parameters
• Flow constraints in the river
• steepness of the penalty function

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Use of models in ISMO
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Inflows years 1980-1984
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Utopia solution
Water level
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Utopia solution
Outflow
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Realistic solution
Water level
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Realistic solution
Outflow
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Utopia and Realistic Solutions years 1980-1984
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Impacts

• Nature
• Spawning areas for pike fish
• Water level when ice melts
• number of destroyed loon nests
• Social
• Recreational losses
• Professional fishing Reduction of the water
  level during 10-Dec and 28-Feb
• Economic
• Power production
• Flood damages
• Days infavourable for log floating

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• Comparison of impacts

• User evaluates and modifies goal levels

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Spreadsheet modelling works

• ISMO is implemented in MS Excel 7.0
• Solver provides optimization routines
• 10-20 minutes for one solution
• Benefits
• Rapid development
• Simple data input, model modification,
  visualization and printing
• Users accept easily
• Excel is a commonly used office program

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Further development

• Other optimization criteria
• Energy
• Other impacts
• Different information patterns
• Iterative optimization of the goal levels to
  produce maximum amount/value of the energy
• Now used to develop new regulation policies.
  Could ISMO be developed for everyday operational
  regulation ?

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References

• Hämäläinen R.P., Mäntysaari J., A Dynamic
  Interval Goal Programming Approach to the
  Regulation of a Lake-River System,
  Multi-Criteria Decision Analysis, Vol. 10, Issue
  2, March-April (2001).
• Hämäläinen, R.P., Mäntysaari J., Dynamic
  Multiobjective Heating Optimization, European
  Journal of Operational Research, 142, (2002).
• Hämäläinen R.P., Kettunen E., Marttunen M.,
  Ehtamo, H., Evaluating a Framework for
  Multistakeholder Decision Support in Water
  Resources Management, Group Decision and
  Negotiation, Vol. 10, No. 4, (2001).
• Marttunen M., Hämäläinen R.P., The Decision
  Analysis Interview Apporach in the Collaborative
  Management of a Large Regulated Water Course,
  Environmental Management, Vol. 42 6 (2008).
• Schniederjans M.J., Goal Programming
  Methodology and Applications, Kluwer Academic
  Publishers, (1995).