Abstract Inspired by migratory graying, Pan et al. proposed the fish migration optimization (FMO) algorithm. It integrates the models of migration and swim into the optimization process. This paper firstly proposes a binary version of FMO, called BFMO. In order to improve the search ability of BFMO, ABFMO is introduced to solve the problems of stagnation and falling into local traps. The transfer function is responsible for mapping the continuous search space to the binary space. It plays a critical factor in the binary meta-heuristics. This paper brings a new transfer function and compares it with the transfer functions used by BPSO, BGSA and BGWO. Experiments prove that the new transfer function has realized good results in the solving quality. Unit commitment (UC) is a NP-hard binary optimization problem. BFMO and ABFMO are tested with the IEEE benchmark systems consisting of various generating units with 24-h demand horizon. The effectivenesses of BFMO and ABFMO are compared with seven binary evolutionary algorithms. The simulation results and non-parametric tests verify that they achieve great performance.