Population　synthesis　is　the　foundation　of　the　agent-based　social　simulation.　Current　approaches　mostly　consider　basic　population　and　households,　rather　than　other　social　organizations.　This　article　starts　with　a　theoretical　analysis　of　the　iterative　proportional　updating　(IPU)　algorithm,　a　representative　method　in　this　field,　and　then　gives　an　extension　to　consider　more　social　organization　types.　The　IPU　method,　for　the　first　time,　proves　to　be　unable　to　converge　to　an　optimal　population　distribution　that　simultaneously　satisfies　the　constraints　from　individual　and　household　levels.　It　is　further　improved　to　a　bilevel　optimization,　which　can　solve　such　a　problem　and　include　more　than　one　type　of　social　organization.　Numerical　simulations,　as　well　as　population　synthesis　using　actual　Chinese　nationwide　census　data,　support　our　theoretical　conclusions　and　indicate　that　our　proposed　bilevel　optimization　can　both　synthesize　more　social　organization　types　and　get　more　accurate　results.