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.
46 Cruises & Counting! Favorites: Paul Gauguin to Tahiti: Uniworld River Cruises in Europe; any of the Celebrity Solstice-class ships; Holland America for 12-nights in the Baltics & Russia; RCCL for 14-night Greek Isles, Turkey, & Croatia; Holland America for 14-day Alaska cruisetour; 10-night Canada/New England cruise; 21 days in Hawaii including a 7-night NCL cruise; Oceania for 25 days in Asia; & 3 months touring Europe by train. And many days spent in all-inclusive resorts!