The measurement of transuranic isotopes in spent nuclear fuel is a crucial technique for nuclear material accounting and nuclear non-proliferation. In a pebble bed high-temperature gas-cooled reactor, numerous fuel spheres circulate through the reactor core multiple times, making it unfeasible to document the power histories of individual fuel spheres. This complexity renders it impossible to employ traditional methods, such as solving the forward burnup equations used in conventional reactors, to calculate the transuranic isotopes.In this approach, optimization algorithms were coupled with the data obtained from the BUrnup Measurement System to establish a power history inversion model, which was used to solve for the power history of fuel spheres and subsequently calculate the transuranic isotopes.The paper also compared the pros and cons of coupling the inversion model with different optimization algorithms and evaluated models using various schemes of activity vector. This process helped determine the most suitable optimization algorithm and scheme of activity vector. Sensitivity analysis revealed that the established inversion model exhibited a degree of tolerance to noise in input data and the underlying physical model.