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A novel design methodology for filter and multiplexer design is presented. For the first time, finite-element electromagnetic (EM)-based simulators and space-mapping optimization are combined to produce an accurate design for manifold-coupled output multiplexers with dielectric resonator (DR) loaded raters. Finite-element EM-based simulators are used as a fine model of each multiplexer channel, and a coupling matrix representation is used as a coarse model. Fine details such as tuning screws are included in the fine model. The DR filter and multiplexer design parameters are kept bounded during optimization. The sparsity of the mapping between the design parameters and the coupling elements has been exploited. Our approach has been used to design large-scale output multiplexers and it has significantly reduced the overall tuning time compared to traditional techniques. The technique is illustrated through design of a five-pole DR filter and a ten-channel output multiplexer.