In certain situations, such as elections in the Euclidean domain, it is possible to specify clear requirements for the operation of a multiwinner voting rule, for it to provide committees that correspond to some desirable intuitive notions (such as individual excellence of the committee members or their diversity). We formally describe several such requirements, which we refer to as "utopias". Supplied with such utopias, we develop an optimization-based mechanism for constructing committee scoring rules that provide results as close to these utopias as possible; we test our mechanism on weakly separable and OWA-based rules. In particular, using our method we recover some connections between known multiwinner voting rules and certain applications.