1 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Classical Exploration Methods for Design Space Exploration (multi-criteria decision making) Ernesto Wandeler 7. January 2005

2 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory The Multi-Objective Optimization Problem (MOOP)

3 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Solutions to the MOOP MOOPs without conflicting objectives lead to a single optimal solution MOOPs with conflicting objectives lead to more than one solution: Pareto optimal solutions Mathematically, every Pareto optimal solution is an equally acceptable solution Generally, a single solution is needed Selecting a single solution needs information that is not contained in the objective functions

4 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory The Analyst and the Decision Maker Analyst: Person or computer program responsible for the mathematical side of the solution process. Decision Maker: Person who has better insight into the problem. This person can choose a solution out of several Pareto optimal solutions.

5 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Classification of Exploration Methods No-Preference Methods A Posteriori Methods A Priori Methods Interactive Methods

6 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory No-Preference Methods Working order: 1) analyst The opinions of the decision maker are not taken into consideration. The analyst solves the MOOP using some method and a solution is presented to the decision maker. The decision maker accepts or rejects the solution.

7 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Method of Global Criterion ideal criterion vector Can not find all Pareto optimal solutions.

8 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Working order: 1) analyst, 2) decision maker The analyst generates a set of Pareto optimal solutions. The decision maker selects the most preferred among the alternatives. A Posteriori Methods

9 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Weighting Method (see also Value Function) Can not find all Pareto optimal solutions.

10 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory  - Constraint Method Can find all Pareto optimal solutions!

11 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Hybrid Method Can find all Pareto optimal solutions!

12 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Working order: 1) decision maker, 2) analyst The decision maker specifies his preferences, hopes and opinions. The analyst generates a solution. A Priori Methods

13 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Value Function Method contour of U

14 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Lexicographic Ordering

15 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory (Weighted) Goal Programming reference point (goal)

16 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory (Weighted) Goal Programming 1-Dim

17 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Interactive Methods Working order: 1) analyst, 2) decision maker, 3) analyst,... The analyst finds an initial feasible solution. Analyst interacts with the decision maker. The analyst finds a new solution. If this solution is acceptable stop, else iterate.

18 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Some Interactive Methods Interactive Surrogate Worth Trade-Off (ISWT) Step Method Reference Point Method GUESS Method Light Beam Search and many more...

19 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Review of Classical Methods Only one Pareto-optimal solution can be expected to be found in one simulation run of a classical algorithm. Not all Pareto-optimal solutions can be found by some algorithms in non-convex MOOP. All algorithms require some problem knowledge, such as suitable weights or  or target values.