Heterogeneous multiprocessor platforms are the foundation of systems that require high computational power combined with low energy consumption, like the IoT and mobile robotics. In this paper, we present five new algorithms for the design space exploration of platforms with elements grouped in clusters with very few connections in between, while these platforms have favorable electric properties and lower production costs, the limited interconnectivity and inability of heterogeneous platform elements to execute all types of tasks, significantly decrease the chance of finding a feasible mapping of application to the platform. We base the new algorithms on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) meta-heuristic and the previously published SDSE mapping algorithm designed for fully interconnected multiprocessor platforms. With the aim to improve the chance of finding feasible solutions for sparsely connected platforms, we have modified the parts of the search process concerning the penalization of infeasible solutions, chromosome decoding, and mapping strategy. Due to the lack of adequate existing benchmarks, we propose our own synthetic benchmark with multiple application and platform models, which we believe can be easily extended and reused by other researchers for further studying this type of platform. The experiments show that four proposed algorithms can find feasible solutions in 100% of test cases for platforms with dedicated clusters. In the case of tile-like platforms, the same four algorithms show an average success rate of 60%, with one algorithm going up to 84%.