Empirical ’ backward ’ galaxy evolution models for IR-bright galaxies are constrained using multiband IR surveys . A new Monte-Carlo algorithm is developed for this task . It exploits a large library of realistic Spectral Energy Distributions ( SEDs ) of 837 local IR galaxies ( IRAS 25 \mu m selected ) from the UV ( 1000Å ) to the radio ( 20cm ) , including ISO-measured 3–13 \mu m unidentified broad features ( UIBs ) . The basic assumption is that the local correlation between SEDs and Mid-Infrared ( MIR ) luminosities can be applied to earlier epochs of the Universe , an assumption which will be strongly tested by SIRTF . By attaching an SED appropriately drawn from the SED library to every source predicted by a given model , the algorithm enables simultaneous comparisons with multiple surveys in a wide range of wavebands . Three populations of IR sources are considered in the evolution models . These include ( 1 ) starburst galaxies , ( 2 ) normal late-type galaxies , and ( 3 ) galaxies with AGN . Constrained by data from the literature , our best-fit model ( ‘ Peak Model ’ ) predicts that since z=1.5 the population of starburst galaxies undergoes a very strong luminosity evolution ( L = L _ { 0 } \times ( 1 + z ) ^ { 4.2 } ) and also strong density evolution ( \rho = \rho _ { 0 } \times ( 1 + z ) ^ { 2 } ) , the normal late-type galaxy population undergoes a passive luminosity evolution ( L = L _ { 0 } \times ( 1 + z ) ^ { 1.5 } ) , and the galaxies with an AGN undergo a pure luminosity evolution similar to that of optical QSOs ( L = L _ { 0 } \times ( 1 + z ) ^ { 3.5 } ) . Prior at z \geq 1.5 all evolution rates drop as ( 1 + z ) ^ { -3 } . The luminosity evolution results in evolution of SEDs of IR-bright sources because of the luminosity dependence of the SEDs . Predictions for number counts , confusion limits , redshift distributions , and color-color diagrams are made for multiband surveys using the upcoming SIRTF satellite . A \Lambda -Cosmology ( \Omega _ { \Lambda } = 0.7 , \Omega _ { m } = 0.3 , H _ { 0 } =75 km sec ^ { -1 } Mpc ^ { -1 } ) is assumed throughout the paper .