Presentation of our work on modeling pheromone dispensers at the Workshop on Symbolic Regression and Modeling (thursday 9th july), part of the Genetic and Evolutionary Computation Conference GECCO 2009, Montreal, Canada.

1. Multiobjective Genetic Programming Approach for a Smooth Modeling of the Release Kinetics of a Pheromone DispenserEva Alfaro-Cid, Anna Esparcia-Alcázar, Pilar Moya, J.J. Merelo, Beatriu Femenia-Ferrer, Ken Sharman, Jaime Primo

3. Introduction: mating disruption

4. Problem description

5. Genetic programming

6. Modeling results

8. Mating disruption technique Mating disruption by sexual confusion is an agricultural technique that intends to substitute the use of insecticides for pest control. Sexual confusion is achieved by the diffusion of large amounts of sexual pheromone, so that the males are confused and mating is disrupted. How? -> using pheromone dispensers )

9. Pheromone dispensers The Centro de Ecología Química Agrícola (CEQA) of the Universidad Politécnica de Valencia has developed biodegradable dispensers which work effectively during the whole flight period of the pest.

11. Problem description Let the residual r be the percentage of product that has not been released into the atmosphere For a given dispenser, find a function r (t), where t = time The available data are a sequence of points (r, t) obtained in field conditions. Since measuring r is costly, there are very few measurements available and they are not equally spaced in time (there are more measurements initially, when the speed of emission is faster).

13. Genetic programming

14. Multi-objective genetic programming 1: A(0) = ; 2: P(0) = init_random(); 3: g = 1; 4: eval (P (g-1)); 5: eval (A (g-1)); 6: A(g) = save( P(g-1), A(g-1)); 7: truncate (A(g)); 8: if g>g_max then stop; 9: M(g) = select(A(g)); 10: P(g) = cross&mut(M(g)); 11: g = g+1; 12: go to Step 4;

15. Mono vs. Multi-objective GP Mono-objective GP Cost function: Mean Squared Error (MSE) MSE = 1/n * Sn (rcalculated - rmeasured)2 Multi-objective GP Cost function (2 obj.): Obj1 = MSE Obj2(“Smoothness”) = M (rcalculated (t+1) – rcalculated (t))/t Cost function (“leave-one-out”): Obji = |rcalculated (i) – rmeasured (i)|

16. Comparison of results

17. Mono-objective best result

18. Mono-objective best result

19. 2-objectives best result

20. 2-objectives best result

21. “Leave-one-out”bestresult

22. “Leave-one-out”bestresult

23. Conclusions Genetic programming has proven to be capable of finding functions that fit well the performance of the dispensers. The mono-objective approach obtained the smallest MSE for the training data. However, both multi-objective approaches evolved models that predicted the validation data more accurately. Probably it is a case of overfitting. Regarding the “smoothness” of the resulting models, it can be seen that both multi-objective approaches obtained models that did not show discontinuities in their behaviour, specially the bi-objective model. This results showthe utility of including an extra objective to minimize the “jumps” in the models when dealing with problems where the experimental data are scarce.

24. Future work Modeling the distributionof pheromone in the environment. This has great economic interest, as: it would allow the optimisation of the placement of dispensers in the plot, hence minimising the number of dispensers needed to guarantee an efficient pest control. It would help support the claim that the amount of pheromone in the air is harmless to humans, which is needed to get governmental authorisation

25. Thanks! aesparcia@iti.upv.es