This paper presents a biased random key genetic algorithm, or BRKGA, for solving a multi-user observation scheduling problem. BRKGA is an efficient method in the area of combinatorial optimization. It is usually applied to single objective problem. It needs to be adapted for multi-objective optimization. This paper considers two adaptations. The first one presents how to select the elite set, i.e., good solutions in the population. We borrow the elite selection methods from efficient multi-objective evolutionary algorithms. For the second adaptation, since the multi-objective optimization needs a set of solutions on the Pareto front, we investigate the idea to obtain several solutions from a single chromosome. Experiments are conducted on realistic instances, which concern the multi-user observation scheduling of an agile Earth observing satellite.