This　article　introduces　an　effective　stochastic　operation　framework　for　optimal　energy　management　of　the　shipboard　power　systems　including　large,　nonlinear　and　dynamic　loads.　The　proposed　framework　divides　the　ship　power　system　into　several　agents,　which　coordinate　with　each　other　based　on　their　demands/supplies　until.　The　alternating　direction　method　of　multipliers　(ADMM)　is　deployed　as　the　multi-agent　framework　to　solve　the　reformulated　distributed　energy　management　problem　in　the　ship.　Two　types　of　turbo-generators　are　considered　in　the　proposed　system　model,　including　single-shaft　and　twin-shaft　models,　to　increase　the　part-load　efficiency　in　certain　times　when　facing　variable　speed　operation.　The　proposed　distributed　framework　is　equipped　with　a　recursive　mechanism,　which　helps　the　ship　system　for　running　optimal　load　scheduling　when　facing　insufficient　power　generation.　In　order　to　model　the　uncertainty　effects　associated　with　the　forecast　error　in　the　interval-ahead　load　demand,　a　stochastic　framework　based　on　unscented　transform　is　devised　which　can　work　in　the　nonlinear　and　correlated　environments　of　shipboard　power　systems.　Due　to　the　nonlinear　cost　function　in　each　agent,　a　powerful　optimization　algorithm　based　on　modified　θ-firefly　algorithm　(Mθ-FOA)　is　proposed.　This　is　a　phasor　algorithm,　which　helps　for　escaping　from　premature　convergence　and　getting　trapped　in　local　optima.　The　appropriate　performance　of　the　proposed　stochastic　model　is　examined　on　the　real　dataset　of　a　ship　power　system.　The　simulation　results　show　the　high　robustness,　guarantied　consensus,　economic　operation　and　feasible　solution　when　power　generation　shortage　based　on　load　shedding　in　the　system.　©　2020　Elsevier　Ltd