If you have the money and the time, there are a few cruises that leave from LA and end up in Singapore. For example, you might want to look at the Holland America Amsterdam on September 23rd that has a wonderful 35 night itinerary starting at around $5600 for an inside cabin (based on double occupancy).
Talk to your travel agent (preferably a Cruise Specialist) and they'll be able to assist you with all your questions.
Travel Agent/Cruise Specialist w/13 yrs exp and 48 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!