  We propose a scheme for investigating the correlation and trade-off among
target variables using a multi-objective Bayesian optimization (MBO). We
discuss the features of the Pareto front (PF) of ThMn12-type compounds, (R,
Z)(Fe,Co,Ti)12 (R = Y, Nd, Sm; Z = Zr, Dy) in terms of magne- tization, Curie
temperature, and a price index by using data from first-principles
calculations, and we extract the trade-off relations from the analysis. We show
that the trade-off relationships can be used to determine changes in the
controllable variables by using partial least squares regression. For example,
the tendency toward low cost and high Curie temperature is related to the
reduction in Dy and increase in Co. We also discuss the efficiency of MBO as a
practical scheme to obtain the features of the PF. We show that MBO can offer
an approximated set for the PF even when obtaining the true PF is difficult.
