Many-objective problems are becoming common in several real-world application domains and there is a growing interest to develop evolutionary many-objective optimizers that can solve them effectively. Studies on selection for many-objective optimization and most recently studies on the characteristics of many-objective landscapes, the effectiveness of operators of variation, and the effects of large populations have proved successful to advance our understanding of evolutionary many-objective optimization. This work proposes an evolutionary many-objective optimization algorithm that uses adaptive epsilon-dominance principles to select survivors and also to create neighborhoods to bias mating, so that solutions will recombine with other solutions located close by in objective space. We investigate the performance of the proposed algorithm on DTLZ continuous problems, using a short number of generations to evolve the population, varying population size from 100 to 20000 individuals. Results show that the application of adaptive epsilon-dominance principles for survival selection as well as for mating selection improves considerably the performance of the optimizer.