France has a fleet of nuclear reactors that makes up a significant proportion of the electricity generation mix. This over-representation of nuclear power compared with other energy sources leads reactors to operate in load following mode in order to balance supply and demand on the electricity grid. The increasing penetration of intermittent energies in the mix and the desire not to renew the entire current nuclear fleet bring active research into optimising the control of reactors operating in load following mode to allow them greater flexibility. In this study, we propose to solve a new bi-objective unit commitment problem using an MOEA/D algorithm equipped with an adaptive mutation operator based on a Walsh surrogate model of a black-box function with a high computation cost. The method consists of taking advantage of the linear effects associated with the problem variables thanks to the Walsh coefficients to regularly update the mutation rate of the variation operator and explore the problem's search space more judiciously. We show that this method enables to penalize some variables by decreasing their mutation probability without affecting the global performance of the search for Pareto-optimal solutions, which makes it similar to an adaptive in-line fitness landscape analysis.