Are there any applications of choice modelling to romantic relationships?
Speed dating seems to provide an ideal setting for the type of study you seek. There are several relevant papers (see References below and Google search human mate preferences speed dating).

There is no consensus among researchers, but here's a sampling of some of the supposed findings:


Buston &amp; Emlen claim that people choose mates from their league, i.e., those they think have comparable traits, which lie in four categories: "wealth and status, family commitment, physical appearance, and sexual ﬁdelity".
Todd et al. claim support for parental investment theory because "men chose women based on their physical attractiveness, whereas women ... chose men whose overall desirability as a mate matched the women's self-perceived physical attractiveness"



  References
  
  
  Buston, P. M. &amp; Emlen, S. T. (2003) Cognitive processes underlying human mate choice: the relationship between self-perception and mate preference in Western society. PNAS 100: 8805-8810. [pdf]
  Todd, P. M., Penke, L., Fasolo, B., &amp; Lenton, A. P. (2007) Different cognitive processes underlie human mate choices and mate preferences. PNAS 104: 15011-15016. [pdf]