PWR core loading pattern optimization with adaptive genetic algorithm


Chairman Kim Jong Il said:

"Along with this any scientific and technological problems relating to the construction of hydroelectric-and thermal-power stations and atomic power plants that are suited to the conditions in our country should be solved."

The goal of loading pattern optimization (LPO) for the operation of the nuclear reactor is to determine the loading patterns (LPs) for producing full power with adequate safety margins.

Because the LPO problem is a complex combinatorial optimization problem, achieving the optimal LP is very difficult and efficient optimization methods are needed.

Genetic algorithms (GAs), which is one of stochastic optimization methods, have been widely applied to the LPO and yielded outstanding results. However, due to the low local search capability, the performance of the conventional GA (CGA) is not so good as those of other optimization methods. Therefore, in the use of GAs, it is very important to improve the local search capability and increase the convergence rate of the algorithm.

One way to increase the convergence rate of Gas is to adjust the crossover and mutation probabilities adaptively according to the fitness of the individual.

In GAs for the LPO, the adaptive probabilities have mainly employed in the mutation process, and have been not applied to the crossover process. In addition, most of the adaptive probabilities employed in the mutation were relative to the generation number. The advantage of adaptive GA (AGA) is that the crossover and mutation probabilities are adjusted according to the fitness of the individual to improve the convergence. However, the original AGA has the disadvantage that premature convergence can occur easily.

Hence, we have proposed a new adaptive genetic algorithm for the loading pattern optimization of PWR. The proposed algorithm is applied to optimize the first cycle pattern for the core of PWR with an electrical power rating of 1000MW, and its performance is compared with those of CGA and the original AGA. The research solution is as follows.

First, for the LP analysis of pressurized water reactor (PWR), the core simulation code, TPSQ/AGANGC, which can calculate the critical boron concentration and the radial power peaking factor (RPPF) of the core corresponding to the given LP and evaluate its fitness, was developed. AGANGC, the Adaptive Genetic Algorithm Nodal Green's function Code, is based on solving two dimensional (2D) and three dimensional (3D) multi-group neutron diffusion equations by the nodal Green's function method on Neumann boundary condition (Hu Y.M et al., 1998). TPSQ, the Transmission Probability code for Square assemblies, is a lattice physics code, which performs homogeneous calculations for fuel and non-fuel cells and the fuel assembly by the collision probability method and the transmission probability method. The multi-group constants at different burn-up, different fuel and coolant temperatures and different boron concentrations for nine types of fuel assemblies calculated by TPSQ are input to AGANGC code.

Second, a new AGA which is based on the encoding by integers, the tournament selection, the two-point crossover and the mutation based on randomly swapping positions between two fuel assemblies (FAs) was proposed. The objective function for LPO is to minimize the maximum RPPF at the equilibrium of Xe under the constraint condition which the cycle length must be satisfied. New calculation formulae are introduced to adjust effectively the crossover and mutation probabilities according to the fitness value of the individual.

Finally, the LPO for the first core of the 1000MWe PWR was implemented by employing the proposed AGA. The constraint condition for the LPO is that the cycle length must be equal to or longer than 13764.2MWd/tU of the reference LP proposed by the designer. The maximum RPPF of the obtained LP is decreased than 1.281 of the reference LP. The results show that the proposed AGA is effective to improve the convergence rate of genetic algorithms (GAs) in the LPO. Both the population size and the maximum generation number were selected as 100. The good results by the proposed AGA were achieved with Pc,max = 0.9 and Pm,max = 0.4. The cycle burn-up and the maximum RPPF at the equilibrium of Xe of the obtained optimal LP are 13873.4MWd/tU and 1.272, respectively. 50 experiments of each of the proposed AGA, CGA and the original AGA were carried out and the mean and standard deviation of the maximum RPPF of the best LPs found after each experiment in each algorithm were compared. Those obtained by the proposed AGA are smallest, and the convergence rate of proposed AGA is also much faster than others.

Our results were published in the SCI International Journal "Annals of Nuclear Energy " (159 (2021) 108331) under the title of the "PWR core loading pattern optimization with adaptive genetic algorithm" (