— We study the complexity of a spectrum of design problems for optical networks in order to carry a set of demands. Under wavelength division multiplexing (WDM) technology, demands sharing a common fiber are transported on distinct wavelengths. Multiple fibers may be deployed on a physical link. Our basic goal is to design networks of minimum cost, minimum congestion and maximum throughput. This translates to three variants in the design objectives: 1) MIN-SUMFIBER: minimizing the total amount of fibers deployed to carry all demands; 2) MIN-MAXFIBER: minimizing the maximum amount of fibers per link to carry all demands; and 3) MAX-THRUPUT: maximizing the carried demands using a given set of fibers. We also have two variants in the design constraints: 1) CHOOSEROUTE: Here we specify both a routing path and a wavelength for each demand; 2) FIXEDROUTE: Here we are given demand routes and we specify wavelengths only. The FIXEDROUTE variant allows us to study wavelength assignment in...