Combining Multi-objective Genetic Algorithm And Neural Network Dynamically For The Shape Optimization Of Cavities In Accelerators

There are many complex optimization problems in physics,many of which contain common characteristics and can be classified into a class of multi-objective optimization problems containing constraints and requiring computationally complex evaluation to obtain the concerned indicators,such as the optimization of cavity in accelerator,the design of radio frequency antenna,and even the shape optimization of aircraft.Taking the optimization of the shape of the accelerator cavity as an example.To obtain the various indicators of the cavity,the distribution of the electromagnetic field should be calculated firstly,then these indicators can be further calculated according to the electromagnetic field.This process is very complicated and requires a huge amount of calculation.Therefore,when using advanced multi-objective optimization algorithms to handle this kind of problem,these algorithms often fail to converge under limited computing resources.As a result,the most commonly used method to handle this question at present is still the inefficient artificial optimization method which is difficult to find the global optimal solutions.As a common method for predicting regression problems,neural network(NN)can solve the above problems by predicting a large number of solutions.When these solutions are put into the multi-objective optimization algorithm,the convergence rate of this optimization algorithm can be greatly improved.However,the training of NN still needs a large number of samples.When strict constraints in these problems requiring extremely accuracy of NN than constraints exist(such as equality constraints),the NN that cannot meet the accuracy requirements can only play a very limited role in the optimization algorithm,and even make the performance of the optimization algorithm worse.In this dissertation,Dynamically Used NN-based Multi-objective Genetic Algorithm(DNMOGA)is proposed for handling the multi-objective optimization problems in physics.In this algorithm,a penalty operation that can be progressively stricter over generations is executed in fitness function to fulfill constraints gradually.Meanwhile,NN is included in an operator.This operator not only produces several individuals to be further evaluated,just like the operators of mutation and crossover do,but also screens in a great number of estimated individuals internally.The performance of these operators is different when the penalty changes,so the number of individuals that come from these operators to be further evaluated is dynamically redistributed.In addition,accessibility algorithm is proposed as a new idea to deal with preference in NSGA-Ⅱ,which doesn’t depend on extra reference points that are set manually in other algorithms to lead the nondominated front to approach them.In the experiments,the differences of performance between the DNMOGA and common multi-objective optimization algorithms are first explored based on the 499.65 MHz normal conducting spherically shaped(SS)cavity,and the influence of the setting of various parameters in DNMOGA on the results is also explored.Subsequently,this algorithm is further applied to optimize the 500 MHz superconducting ellipsoidal cavity and the more geometrically complex 325 MHz superconducting double-gap spoke cavity.By comparing with the results of artificial optimization,DNMOGA obtains many individuals similar to the artificially optimized superconducting ellipsoidal cavity,and acquires some individuals better than the artificially optimized superconducting doublegap spoke cavity.DNMOGA can be used to solve the multi-objective optimization problems in other complex physics problems.