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Multiobjective optimization design of compact multiple-input and multiple-output (MIMO) antennas with canonical structures (viz., transformation or combination by regular shapes) for wideband radiation and fragment structures (viz., combination by discrete fragment patches) for high isolation is proposed and demonstrated. In the design, multiobjective evolutionary algorithm based on decomposition combined with differential evolution (MOEA/D-DE) for optimization of canonical structures and MOEA/D combined with genetic operator (MOEA/D-GO) for optimization of fragment structures are combined and iterated. The design is demonstrated with compact bow-tie MIMO antennas sharing a small common ground plane. The four orthogonally deployed bow-tie antennas are optimized by using MOEA/D-DE to acquire dual polarization and wideband radiation. Fragment-type structures on the common ground plane are …