A good place to start looking for an answer is: http://en.wikipedia.org/wiki/Quality_of_life. If you mean by "utility values" "utility preferences," there is a body of economics literature that deals with the issue:http://en.wikipedia.org/wiki/Utility.

There are existing QOL surveys that have already been adapted to utility preference criteria. Attached is a paper on the SF12. I have used this extensively and it is super!

Ariel Linden's attached paper looks very interesting. It is based on empirical data with analysis of measurement properties

Thanks, Ariel and John, for your comments.

You should check first whether a mapping algorithm has been already conducted  in the literature. Attached is a systematic review of studies that had already conducted mapping technique.Check also the NICE website, they have already published a document on how to conduct mapping to EQ_5D

Some questionnaires have been designed to determine health state utilities. EQ-5D is most common of these and the Euroqol web site has extensive information. Other generic QoL instruments (like SF36) have been mapped onto the Euroqol scale. So you might be able to replicate the mapping methodology? 

Thanks for your comments, Rimal and Jonathan.

 To learn more about measuring health related quality of life (HRQoL) and how individual preferences are used to provide health-state utilities, ScHARR (U. Sheffield) run an online course on Measuring and Valuing Health:

https://www.futurelearn.com/courses/valuing-health

Also, you asked about references for mapping algorithm, so you should refer to HERC (U. Oxford) Database of Mapping Studies: 

http://www.herc.ox.ac.uk/downloads/herc-database-of-mapping-studies

... I cannot see any mapping study from QOLIE 10, so you may wish exploit your current research to conduct a mapping study (again see HERC for examples)