Hybrid evolutionary algorithms have been successfully applied to solve numerous multiobjective optimization problems (MOP). In this paper, a new hybrid evolutionary approach based on search strategy adaptation (HESSA) is presented. In HESSA, the search process is carried out through adopting a pool of different search strategies, each of which has a specified success ratio. A new offspring is generated using a randomly selected strategy. Then, according to the success of the generated offspring to update the population or the archive, the success ratio of the selected strategy is adapted. This provides the ability for HESSA to adopt the appropriate search strategy according to the problem on hand. Furthermore, the cooperation among different strategies leads to improve the exploration and the exploitation of the search space. The proposed pool is combined to a suitable evolutionary framework for supporting the integration and cooperation. Moreover, the efficient solutions explored over the search are collected in an external repository to be used as global guides. The proposed HESSA is verified against some of the state of the art MOEAs using a set of test problems commonly used in the literature. The experimental results indicate that HESSA is highly competitive and can be considered as a viable alternative.