1. Multiple-criteria Optimization Lecture 11 (5/11/2016)

2. Multi-criteria Optimization Goal Programming (pre-emptive, non-pre- emptive) Pareto-set generating methods

3. Timber and Non-Timber Tradeoffs Tóth et al. (2006): For. Sci. 52(1):93-107 Tóth-McDill (2008): Environ. Model. Assess. 13:1-15

4. The Concept of Pareto-Optimality and Dominance Pareto- or Efficient Frontier Non-dominated or efficient alternatives Solutions below the frontier are dominated and of no interest to the decision makers The ideal solution is unattainable due to conflict in objectives

5. Pareto-Optimality Cont. A management alternative is efficient or Pareto-optimal with respect to a set of competing management objectives if no improvement is possible in achieving any of the objectives without compromising another one (the concept is due to Pareto 1908)

6. The Weighted Objective Functions Method

7. The ε - Constraining Method

8. Decomposition based on the Tschebyseff Metric

9. The Alpha-Delta Method

10. The Triangles Method

11. Solution Times

12. The Alpha-Delta Method with 3 objectives Iteration 2Iteration 1

13. The Weighted-Method in 3D

14. Bundle 3 Bundle 28 Bundle 31 Bundle 43 Bundle 1 Bundle 31 Bundle 3 Example#1: Pack Forest

15. Example#2: Tauranga-Taupo Catchment in New Zealand