Multiobjective Genetic Programming Approach for a Smooth Modeling of the Release Kinetics of a Pheromone

Dispenser

Eva Alfaro-Cid, Anna Esparcia-Alcázar, Pilar Moya, J.J. Merelo, Beatriu Femenia-Ferrer,

Ken Sharman, Jaime Primo

Contents

• Objetive

• Introduction: mating disruption

• Problem description

• Genetic programming

• Modeling results

• Conclusions and future work

Objetives

• Modeling the pheromone release kinetics of an experimental dispenser developed in the Centro de Ecología Química Agrícola (CEQA) of the Universidad Politécnica de Valencia.

• To validate the use of multiobjective Genetic Programming for avoiding discontinuities in those time ranges where no measurements are available.

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

• )

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.

A few figures

• 1 kg of pheromone costs 1000 €• 1 dispenser takes 200 mg of pheromone

→ i.e. 1 dispenser costs 20 cents (+ manufacturing)

• In 1 Ha there must be 500 or 1000 dispensers (depending on the pest)– i.e cost is 100 or 200 € per Ha (+ handwork)

On the other hand,• Spraying with a classical pesticide costs

20-30 €/Ha

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).

Available data

* 2005 data

○ 2006 data

Genetic programmingAlgorithm GP, generational with elitism (0.1 %).

Inicialization Ramped half and half

Selection Tournament selection for all genetic operators

Genetic operators Replacement, crossover and mutation Tree internal nodes are selected with a probability of 0.9, terminals are selected with a probability of 0.1 and the root cannot be selected as crossover or mutation point. The resulting trees are accepted in the population only if their length is smaller than 18.

Function & terminal sets { +, -, *, /, exp, time, }

Termination criterion 51 generations (including the initial generation)

Parameters Population size, popSize = 2000Tournament size, tSize = 7Mutation rate, pM = 0.1Crossover rate, pC = 0.8Replacement rate, pR = 0.1Number of runs, n = 30

Multi-objective genetic programming

Algorithm SPEA2

Parameters Archive size, arcSize = 200

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;

Mono vs. Multi-objective GPMono-objective GP Cost function: Mean Squared Error (MSE)

MSE = 1/n * Sn (rcalculated - rmeasured)2

Multi-objective GPCost function (2 obj.):

Obj1 = MSE

Obj2 (“Smoothness”) = M (rcalculated (t+1) – rcalculated (t))/t

Cost function (“leave-one-out”):Obji = |rcalculated (i) – rmeasured (i)|

Comparison of results

Mono-objective 2-objectives Leave-one-out

MSE training(data 2005)

0.7860 25.9233 80.2972

MSE validation(data 2006)

83.9730 77.9871 25.0778

Mono-objective best result

Mono-objective best result

t

t

t

t

t

t

ttttr

44.137

2

63.90

66.1017.065.36

1081.91062.998.066.100)( 3624

2-objectives best result

2-objectives best result

60.97)027.0exp(0015.095.11

exp

)03.0exp(96.4708.067.60)(

ttt

ttttr

“Leave-one-out” best result

“Leave-one-out” best result

t

t

t

ttB

t

tttA

tBtAt

ttr

19.2

01.068.0

57.37

)94.28(07.7109.16)(

19.2

81.67)241.122(83.29)(

)()(01.050.78

62.5575.88607.89)(

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 show the utility of including an extra objective to minimize the “jumps” in the models when dealing with problems where the experimental data are scarce.

Future work

• Modeling the distribution of pheromone in the environment.

This has great economic interest, as:1. 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.

2. 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

Thanks!

aesparcia@iti.upv.es