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Key message: Simulations highlight the potential of genomic selection to substantially increase genetic gain for complex traits in sugarcane. The success rate depends on the trait genetic architecture and the implementation strategy. Genomic selection (GS) has the potential to increase the rate of genetic gain in sugarcane beyond the levels achieved by conventional phenotypic selection (PS). To assess different implementation strategies, we simulated two different GS-based breeding strategies and compared genetic gain and genetic variance over five breeding cycles to standard PS. GS scheme 1 followed similar routines like conventional PS but included three rapid recurrent genomic selection (RRGS) steps. GS scheme 2 also included three RRGS steps but did not include a progeny assessment stage and therefore differed more fundamentally from PS. Under an additive trait model, both simulated GS schemes achieved annual genetic gains of 2.6–2.7% which were 1.9 times higher compared to standard phenotypic selection (1.4%). For a complex non-additive trait model, the expected annual rates of genetic gain were lower for all breeding schemes; however, the rates for the GS schemes (1.5–1.6%) were still greater than PS (1.1%). Investigating cost–benefit ratios with regard to numbers of genotyped clones showed that substantial benefits could be achieved when only 1500 clones were genotyped per 10-year breeding cycle for the additive genetic model. Our results show that under a complex non-additive genetic model, the success rate of GS depends on the implementation strategy, the number of genotyped clones and the stage of the breeding program, likely reflecting how changes in QTL allele frequencies change additive genetic variance and therefore the efficiency of selection. These results are encouraging and motivate further work to facilitate the adoption of GS in sugarcane breeding. [ABSTRACT FROM AUTHOR]