This paper extends an elitist multi-objective evolutionary algorithm, named GAME, based on several Pareto fronts corresponding to various fitness definitions. An additional operator is defined to create an adaptive version of this algorithm, called aGAME. This new operator alternates different modes of exploration of the search place all through aGAME execution. Mode switching is controlled according to the values of two performance indicators, in order to maintain a good compromise between the quality and diversity of the returned solutions. aGAME is compared with the previous version (GAME) and with the three best-ranking algorithms of the CEC 2009 competition, using five bi-objective benchmarks and the rules of this competition. This experimental comparison shows that aGAME outperforms these four algorithms, which validates both the efficiency of the proposed dynamic adaptive operator and the algorithm performance.