Sensitivity of differential evolution algorithms for multi-objective optimization problems in fuel assembly design

The performance of multi-objective optimization algorithms are often highly problem-dependent, and require tuning of their parameters each time to perform effectively. Algorithms which feature adaptive parameter control offer enhancements in robustness and improved convergence rates as a result. This is highly beneficial for problems which feature high dimensionality and non-linear relationships, which are commonly encountered in nuclear engineering. In this paper, the robustness of the multi-objective differential evolution algorithm MOJADE is investigated by performing a sensitivity study on its behavioural parameters: the rate of parameter adaptation and the eliteness/greediness of the selection step. Performance was measured by optimizing a uranium-plutonium mixed-oxide (MOX) fuel assembly with gadolinium burnable poisons to maximize the amount of plutonium within the assembly whilst simultaneously minimizing the power peaking factor within the assembly at the beginning of life. The design variables were the location of UPu MOX pins within the assembly, the amount of plutonium in the MOX pins, the location of the Gd pins, and the amount of Gd within the Gd pins. The reactor physics software package WIMS was used to solve the neutron transport equation. Results indicate MOJADE performance remains consistent for a wide range of both behavioural parameters, suggesting the algorithm is able to perform effectively without requiring trial and error to find the 'optimal' control parameter settings.