For almost 20 years, quality indicators (QIs) have promoted the design of new selection mechanisms of multiobjective evolutionary algorithms (MOEAs). Each indicatorbased MOEA (IB-MOEA) has specific search preferences related to its baseline QI, producing Pareto front approximations with different properties. In consequence, an IB-MOEA based on a single QI has a limited scope of multi-objective optimization problems (MOPs) in which it is expected to have a good performance. This issue is emphasized when the associated Pareto front geometries are highly irregular. In order to overcome these issues, we propose here an island-based multi-indicator algorithm (IMIA) that takes advantage of the search biases of multiple IB-MOEAs through a cooperative scheme. Our experimental results show that the cooperation of multiple IB-MOEAs allows IMIA to perform more robustly (considering several QIs) than the panmictic versions of its baseline IB-MOEAs as well as several stateof-the-art MOEAs. Additionally, IMIA shows a Pareto-frontshape invariance property which makes it a remarkable optimizer when tackling MOPs with complex Pareto front geometries.