Network discovery is a fundamental task in different scenarios of IEEE 802.15.4-based wireless personal area networks. Scenario examples are body sensor networks requiring health- and wellness-related patient monitoring or situations requiring opportunistic message propagation. In this paper, we investigate optimized discovery of IEEE 802.15.4 static and mobile networks operating in multiple frequency bands and with different beacon intervals. We present a linear programming model that allows finding two optimized strategies, named OPT and SWOPT, to deal with the asynchronous and multi-channel discovery problem. We also propose a simplified discovery solution, named SUBOPT, featuring a low-complexity algorithm requiring less memory usage. A cross validation between analytical, simulation, and experimental evaluation methods is performed. Finally, a more detailed simulation-based evaluation is presented, when considering varying sets of parameters (i.e., number of channels, network density, beacon intervals, etc) and using static and mobile scenarios. The performance studies confirm improvements achieved by our solutions in terms of first, average, and last discovery time as well as discovery ratio, when compared to IEEE 802.15.4 standard approach and the SWEEP approach known from the literature.