Supercritical CO2 Brayton cycles (SCO2BC) including the SCO2 single-recuperated Brayton cycle (RBC) and recompression recuperated Brayton cycle (RRBC) are considered, and flexible thermodynamic and economic modeling methodologies are presented. The influences of the key cycle parameters on thermodynamic performance of SCO2BC are studied, and the comparative analyses on RBC and RRBC are conducted. Nondominated Sorting Genetic Algorithm II (NSGA-II) is selected for the Pareto-based multi-objective optimization of the RRBC, with the maximum exergy efficiency and the lowest cost per power (k$/kW) as its objectives. Artificial neural network (ANN) is chosen to accelerate the parameters query process. It is shown that the cycle parameters such as heat source temperature, turbine inlet temperature, cycle pressure ratio, and pinch temperature difference of heat exchangers have significant effects on the cycle exergy efficiency. The exergy destruction of heat exchanger is the main reason why the exergy efficiency of RRBC is higher than that of the RBC under the same cycle conditions. RBC has a cost advantage from economic perspective, while RRBC has a much better thermodynamic performance, and could rectify the temperature pinching problem that exists in RBC. It is also shown that there is a conflicting relationship between the cycle cost/cycle power (CWR) and the cycle exergy efficiency. The optimization results could provide an optimum tradeoff curve enabling cycle designers to choose their desired combination between the efficiency and cost. ANN could help the users to find the SCO2BC parameters fast and accurately.