Convergence and diversity are two basic issues in evolutionary multiobjective optimization (EMO). However, it is far from trivial to address them simultaneously, especially when tackling problems with complicated Pareto-optimal sets. This paper presents a dual-population paradigm (DPP) that uses two separate and co-evolving populations to deal with convergence and diversity simultaneously. These two populations are respectively maintained by Pareto- and decomposition-based techniques, which arguably have complementary effects in selection. In particular, the so called Pareto-based archive is assumed to maintain a population with competitive selection pressure towards the Pareto-optimal front, while the so called decomposition-based archive is assumed to preserve a population with satisfied diversity in the objective space. In addition, we develop a restricted mating selection mechanism to coordinate the interaction between these two populations. DPP paves an avenue to integrate Pareto- and decomposition-based techniques in a single paradigm. A series of comprehensive experiments is conducted on seventeen benchmark problems with distinct characteristics and complicated Pareto-optimal sets. Empirical results fully demonstrate the effectiveness and competitiveness of the proposed algorithm.