To improve the inherent safety and cost-effectiveness of lead-bismuth cooled fast reactors, the SPALLER-100 reactor designed by the University of South China has been selected as the research object to determine the maximum power it can produce. This is a multi-objective, complex, multi-dimensional, nonlinear, and constrained optimization problem. To maintain the transportability, material durability, and long-term operation stability of the reactor core and ensure safety under accident conditions, three steady-state limitations and three accident limitations are proposed. The platform used to calculate the maximum neutronic power produced by the reactor at different core heights has been built using Latin hypercube sampling and the Kriging proxy model. Meanwhile, the cooling power of the reactor at different core heights is calculated by considering its natural circulation capacity. Finally, a design scheme is obtained that meets the requirements of neutronic and thermal-hydraulic assessments, while producing maximum power. Consequently, during the entire life-cycle of SPALLER-100, a safety analysis of three typical accident scenarios (unprotected loss of heat sink, unprotected transient over power, and unprotected coolant inlet temperature undercooling) is performed using a Quasi-Static Reactivity Balance (QSRB) approach. The results show that the platform used to calculate the maximum neutronic power exhibits high accuracy, and that the design scheme with maximum power is safe and economical. Overall, this study can provide reference ideas for designing natural circulation reactors that can maximize power output.