1. An Evolution Strategy for Improving the Design of Phased Array Transducers Stephen Chen, York University Sarah Razzaqi, University of Toronto Vincent Lupien, Acoustic Ideas Inc.

2. July 21, 2006CEC 2006 Phased Array Transducers  A non-mechanical way to direct an energy beam  Useful for Non-Destructive Evaluation

3. July 21, 2006CEC 2006 Continuum Probe Designer™  Product of Acoustic Ideas Inc.  Automated design tool that creates an optimized probe for a given inspection task  Removes “art” of design

4. July 21, 2006CEC 2006 Continuum Probe Designer™ Components  Cost function generator uses exclusive patent- pending technology to design an optimized probe

5. July 21, 2006CEC 2006 Optimization Solver  The optimized probe is developed for a given probe geometry  Finding the best probe geometry is another optimization task  In this paper, the probe designer is treated as a “cost function generator”

6. July 21, 2006CEC 2006 Optimization Objective  Probe costs are directly related to the number of elements used in a design  Existing instrumentation can only control 32 independent channels at a time

7. July 21, 2006CEC 2006 Benchmark Optimization Solver  Cost function generator is implemented in MATLAB®  fmincon from MATLAB® Optimization Toolbox initially used for the optimization solver  fmincon uses gradient descent  fmincon performs very inconsistently

8. July 21, 2006CEC 2006 An Evolution Strategy for the Optimization Solver  Standard (1+λ)-ES  fmincon uses about 300 function evaluations on average  Want about 100 generations to allow for convergence  Therefore, λ = 3

9. July 21, 2006CEC 2006 Evolution Strategy Development  Tested σ = 0.001 to 0.01  Consistently better with larger sigma

10. July 21, 2006CEC 2006 Evolution Strategy vs. fmincon  Tested on one expert guess and 29 random start points  ES results are vastly superior and more consistent  ES results are still not good enough fmincon (1+λ)-ES 76.232.5 70.83.9 518

11. July 21, 2006CEC 2006 Independent Parallel Runs  High standard deviation suggests that using multiple runs will lead to easy improvements  Results are better, but still not good enough (1+λ)-ES Four parallel 32.531.3 3.92.9 1822

12. July 21, 2006CEC 2006 “Smart” start points  High correlation between ES solution and quality of random start point  Use random search to find “smart” points  Better results again Four parallel “Smart” start pts 31.330.1 2.93.2 2225

13. July 21, 2006CEC 2006 Current Work  Need to get to 30/30 feasible solutions Make Continuum Probe Designer™ suitable for non-expect users – i.e. feasible solutions from any random/non-expert start point  Using WoSP to find “smart” start points

14. July 21, 2006CEC 2006 WoSP  Waves of Swarm Particles  Each wave finds/explores another local optima  Standard particle swarm explores one optima exhaustively  WoSP works well with a local optimizer Use local optimizer to “finish” each wave

15. July 21, 2006CEC 2006 Summary  Evolution Strategy works better than gradient descent in very noisy search spaces  Effect of sigma on ES convergence rate suggests a noisy search space  Relationship between quality of start and end points supports using “smart” start points