Lei Wu Master’s Thesis Artificial Intelligence Center University of Georgia

1. A Comparison of Nature Inspired Intelligent Optimization Methods in Aerial Spray Deposition Management Lei Wu Master’s Thesis Artificial Intelligence Center University of Georgia Major Professor: Walter D Potter Committe: Donald Nute Khaled M Rasheed

2. Presentation Overview • Introduction • Aerial Spray Deposition Problem • Genetic Algorithms • SAGA • Development of Intelligent Optimization Methods • SAGA2 (Spray Advisor using Genetic Algorithm version 2) • SAGA2NN (Spray Advisor using Genetic Algorithm version 2 with Neural Network) • SAGADO (Spray Advisor using GADO) • SASA (Spray Advisor using Simulated Annealing) • Results • Conclusion

3. Aerial Spray Deposition Problem • AGDISP (Agricultural Dispersal) aerial spray simulation model predicts the deposition of spray material released from an aircraft. • The prediction is based on a set of spray parameter values. The total combination of possible spray parameters generates a huge search space (NP hard). • AGDISP returns three spray output values: VMD (the deposition composed of Volume Median Diameter), drift fraction, and COV (the Coefficient of Variance). • The goal is to minimize the difference between the output VMD and the desired VMD, minimize the drift fraction, and minimize the COV.

4. Genetic Algorithms • Genetic algorithms are inspired by Darwin's theory of natural selection and based on the principle of survival of the fittest • Basic components of genetic algorithms • A representation of solutions to the problem • A way to create an initial population • A fitness function to evaluate the solutions • A selection mechanism to pick parents for reproduction, and crossover and mutation operators to alter the genetic composition of offspring • Values for the parameters of genetic algorithms

5. SAGA • SAGA applies the simple genetic algorithm to heuristically search for an optimal set of input parameters needed to achieve a certain aerial spray deposition. • SAGA sends a set of spray parameters to AGDISP, which is used to calculate the spray output. Based on the fitness function values mapped from the spray output values, SAGA attempts to evolve an improved set of parameters. • This is a multi-objective optimization problem, where a weighted-sum approach is applied. • Fitness = 100  [50  (1.0 – DriftFraction) + 25  (1 -COV) + 25  VMDTerm], where VMDTerm = 1.0 – abs(1.0 – VMD/VMDCenter)

6. SAGA2 • SAGA2 is developed from SAGA, and tries to get a better solution than SAGA. • The improvement of SAGA2 • SAGA2 replaces the original generational genetic algorithm with a steady-state genetic algorithm. • SAGA2 replaces the original roulette wheel selection with tournament selection. • SAGA2 combines several kinds of crossover and mutation operators, and applies them with different probabilities. • The implementation of SAGA2

7. The interface of SAGA2 the interface to customize genetic algorithm parameters the main interface the interface to preset spray parameters

8. SAGA2NN • SAGA2NN is developed from SAGA2, and tries to shorten the time required to get a useful solution. • The improvement of SAGA2NN • SAGA2NN generates the initial population from a large pool of individuals. • SAGA2NN does various crossover and mutation operations for each crossover and mutation, and selects the one with the highest fitness as the candidate. • SAGA2NN uses a neural network to approximate the fitness during the above process.

9. Neural Networks • Neural networks are inspired by the biological nervous system. • The most popular neural network is the backpropagation network. • A backpropagation network is a fully connected, layered, feedforward neural network. • A forward pass determines the network's actual output, and a backward pass determines how the weights should be changed based on the difference between the actual output and the target output. • The weight is changed in the direction where the error surface goes down most steeply, and the amount of change is determined by the learning law: ct = ct-1-(1-)dt, where ct is the current weight change, ct-1 is the previous weight change, dt is the current derivative of the error with respect to the weight,  is the learning rate, and  is the momentum.

10. The Neural Network in SAGA2NN • Data collecting • Network training • Function mapping

11. SAGADO • SAGADO is developed by applying GADO (Genetic Algorithm for Design Optimization), a general-purpose approach to solving the parametric design problem, in this problem. • A steady-state genetic algorithm is used. • The selection scheme is ranking selection. • The replacement strategy is a crowding technique. • Several crossover and mutation operators are used, in which the most important one is guided crossover. • The screen module saves time by avoiding the expensive evaluation of points that are unlikely to correspond to good designs. • An adaptive penalty method is used for handling constraints. • The implementation of SAGADO

12. SASA • SASA is developed by applying simulated annealing in this problem. • Simulated annealing is inspired by physical annealing of solids. • Basic algorithm of simulated annealing: successively generate a random move in the neighborhood of the state, accept the move if it leads to a solution with lower energy than the current solution, otherwise accept it with probability e-δ/T, where δ is the change of energy and T is the current temperature. • The implementation of SASA • The energy of a solution is the opposite of its fitness • The cooling schedule adopted is geometric cooling. The temperature is updated using the formula: Ti+1 = αTi, where α denotes the cooling factor.

13. Results • We ran these methods on several practical spray parameter specifications provided by Forest Service managers. • The maximum fitness values SAGA2 and SAGADO achieved are better than SAGA in every parameter setting. • SAGA2NN obtains much better maximum fitness value in the first few hundred evaluations. Its lead is offset later, but it takes far fewer evaluations to converge. • SAGA, SAGA2, SAGA2NN and SAGADO all greatly outperform SASA.

14. Example of Experiments

15. Evolution Process of Some Parameter Settings

16. Conclusion • Careful choice of the genetic algorithm type, the selection mechanism, and the crossover and mutation operators can boost the genetic algorithm performance. • Applying a neural network to the genetic algorithm saves time, but does not achieve a much better result. The advantage of the neural network may be counteracted by premature convergence of the genetic algorithm. • Genetic algorithms perform better than simulated annealing in an extremely complicated domain, such as aerial spray deposition management. • In aerial spray practice, if time is abundant, we recommend using SAGADO to do the optimization; if time is limited, we recommend using SAGA2NN.