1. Multi-Objective Optimization for Finite Element Analysis
ITSS 2010, Metz
Petr Kadlec
Supervisor: Zbynek Raida
Brno University of Technology

2. Presentation schedule
Objectives and motivation
Techniques of MO algorithms (state-of-the-art)
Experiments
Results
Conclusions

3. Objective: Motivation: Objectives and motivation
Stochastic multi-objective optimization of EM structures
Motivation:
- Trade-off between conflicting objectives
- Unknown analytical solution
Pareto front of optimal solutions: solutions optimal from conflicting viewpoints

4. State-of-the-art Algorithms: GA, PSO, simulated annealing…
Two problems: 1. Find optimal solutions
2. Maintain diversity between solutions
Techniques used :
Domination
Niching
Mating restrictions
Fitness sharing
External archive …
Fig. 1: Min-min NSGA optimization (f1 = x1, f2=(x1+x2)/x1, 0.1<x1<1, 0<x2<5, 20 agents, 200 iterations)

5. Experiment – FEM mesh optimization
- Algorithm: NSGA (non-dominated sorting, niching)
- Structure: waveguide R100
Mesh: regular [Nx, Ny ]
Decision space: Nx, Ny varying from 2 to 25
Objectives:
- Conflict: minimal error vs. minimal CPU demands
Nx = 4
Ny = 3 x y
Fig. 2: Regular mesh discretization

6. Results (1)
Fig. 3: Decision space (100 agents, 200 iterations, FEM analyses)

7. Results (2)
Tab. 1: Percentage hit rate of NSGA algorithm for various values of iterations and agents
Fig. 4: Solution space (100 agents, iterations)

8. Conclusions Better results with more agents vs. more iterations
Optimal results for the mesh with the ratio Nx/Ny = 1.68
Percentage hit rate only 40 % for 100 agents, 10 iterations (550 FEM analyses) against 576 analyses for every possible [Nx, Ny ]
Poor efficiency of NSGA (80 % for FEM analyses)
Future work:
Improve efficiency of current techniques
Implement new promising algorithms

9. Thank you for your attention!
Contact
Thank you for your attention!
Department of Radio Electronics, Brno University of Technology
Purkynova 118, Brno, Czech Republic
Tel:
Fax:

10. This work was supported by the project CZ. 1. 07/2. 3. 00/09
This work was supported by the project CZ.1.07/2.3.00/ Communication Systems for Emerging Frequency Bands