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

1. 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@hut.fi

2. Lake Päijänne and River Kymijoki in Finland

3. Päijänne-Kymijoki lake river system 4:th largest in Finland Control: Outflow from Päijänne to the river Kymijoki Inflows: forecasted Regulation policies:Water levels at six time points

4. 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

5. Goal programming Goal point/set • 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) d cost function

6. 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 interdependent:energy produced and the value of energy • Direct use of tradeoff comparisons is difficult

7. 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

8. Interactive decision support

9. Goals in water levels Users give desired water levels at: • six different points during one year • ideal level + acceptable interval (min, max)

10. Dynamics of the lake Päijänne

11. 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

12. 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

13. Cost function minimized =Sum of deviations from goal + penalty outside goal intervals

14. 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

15. Generation of the optimal regulation strategy

17. ISMO - spreadsheet software Minimizes deviations from goal levels and goal intervals Satisfies flow constraints Simulates the regulator’s 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

18. Use of models in ISMO

20. Inflows years 1980-1984

21. Utopia solution Water level

22. Utopia solution Outflow

23. Realistic solution Water level

24. Realistic solution Outflow

25. Water level Water level Outflow Outflow Utopia and Realistic Solutions years 1980-1984

26. 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

27. Comparison of impacts: • User evaluates and modifies goal levels

28. 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

29. 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 ?

30. 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).