MultiObjective Optimization for Finite Element Analysis ITSS 2010

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

Presentation schedule q Objectives and motivation q Techniques of MO algorithms (state-of-the-art) q Experiments q Results q Conclusions page 2 xkadle 19@stud. feec. vutbr. cz

Objectives and motivation Objective: - 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 page 3 xkadle 19@stud. feec. vutbr. cz

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 (f 1 = x 1, f 2=(x 1+x 2)/x 1, - … 0. 1<x <1, 0<x <5, 20 agents, 200 iterations) 1 page 4 2 xkadle 19@stud. feec. vutbr. cz

Experiment – FEM mesh optimization - Algorithm: NSGA (non-dominated sorting, niching) - Structure: waveguide R 100 - Mesh: regular [Nx, Ny ] Ny = 3 y x Nx = 4 Fig. 2: Regular mesh discretization - Decision space: Nx, Ny varying from 2 to 25 - Objectives: - Conflict: minimal error vs. minimal CPU demands page 5 xkadle 19@stud. feec. vutbr. cz

Results (1) Fig. 3: Decision space (100 agents, 200 iterations, 5 075 FEM analyses) page 6 xkadle 19@stud. feec. vutbr. cz

Results (2) Fig. 4: Solution space (100 agents, 200 iterations) page 7 xkadle 19@stud. feec. vutbr. cz Tab. 1: Percentage hit rate of NSGA algorithm for various values of iterations and agents

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 1 600 FEM analyses) - Future work: - Improve efficiency of current techniques - Implement new promising algorithms page 8 xkadle 19@stud. feec. vutbr. cz

Contact Thank you for your attention! xkadle 19@stud. feec. vutbr. cz Department of Radio Electronics, Brno University of Technology Purkynova 118, 612 00 Brno, Czech Republic Tel: +420 541 149 117 Fax: +420 541 149 244 page 9 xkadle 19@stud. feec. vutbr. cz

This work was supported by the project CZ. 1. 07/2. 3. 00/09. 0092 Communication Systems for Emerging Frequency Bands