Comprehensive evaluation of individual and combined dietary carotenoids in Penaeus vannamei and response surface analysis for optimizing combinations

Carotenoids are essential in crustacean aquaculture, supporting pigmentation, antioxidant defense, immune function, and sensory quality. However, intensive culture restricts natural carotenoid inputs, and exclusive reliance on astaxanthin is constrained by cost and supply. Evidence to guide cost-effective formulation remains fragmented: reported optimal doses vary widely, head-to-head comparisons under a common basal diet are scarce, mixture effects are poorly defined, and rigorous multi-factor optimization is rare. In this study, <i>Penaeus vannamei</i> were fed iso-nitrogenous, iso-lipidic diets for 56 days that supplemented β-carotene, canthaxanthin, or astaxanthin individually, or all three in combination at literature-based levels. Outcomes included growth and feed efficiency; tissue carotenoid deposition and composition; antioxidant and digestive enzyme activities; color (CIELAB); and flavor (free amino acids, nucleotides, organic acids). A subsequent response-surface experiment varied inclusion ranges (β-carotene 200-500, canthaxanthin 100-300, astaxanthin 50-250 mg/kg) to model total astaxanthin, total carotenoids, total antioxidant capacity, and redness, followed by AHP-CRITIC-TOPSIS multi-criteria decision analysis to identify the global optimum.All carotenoid diets increased final weight and specific growth rate and reduced feed conversion ratio relative to the control, with the mixture outperforming any single carotenoid. Supplementation elevated digestive enzyme activities and enhanced antioxidant status (higher T-AOC, lower malondialdehyde), with astaxanthin the most efficient single additive and the mixture providing additional gains. Astaxanthin (> 80% of tissue carotenoids) accumulated mainly in the hepatopancreas; β-carotene promoted greater total carotenoid and astaxanthin deposition than direct astaxanthin, and the mixture produced the highest tissue levels. Carotenoids improved color (lower <i>L</i>*, higher <i>a</i>*) with a plateau in redness, and increased umami-related free amino acids, nucleotides, and succinic acid, thereby raising the equivalent umami concentration (EUC). Optimization identified a β-carotene: canthaxanthin: astaxanthin ratio of 368: 204.5: 219.2 mg/kg as the best composite solution.This work provides a rigorously benchmarked and optimization-based formulation strategy, yielding actionable inclusion ratios that reconcile biological performance with cost-effective feed design for intensive shrimp culture.