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In this paper, we study the time allocation optimization problem to maximize the sum throughput in a dual-hop heterogeneous visible light communication (VLC)/radio frequency (RF) communication system. Two scenarios are investigated in this paper. For the first scenario, we consider an optical wireless powered communication network (WPCN) in which all users harvest energy from the received lightwave over downlink (DL), and then they use the harvested energy to transmit information signals in the uplink (UL) channels based on the time division multiple access (TDMA) scheme. The optimal time allocation in the UL is obtained to maximize the sum throughput of all users. For the second scenario, the time switching simultaneous lightwave information and power transfer (TS-SLIPT) based on the dual-hop VLC/RF is assumed that the LED transmits information and power simultaneously in the first hop DL (i.e., VLC link). The harvested energy at the relay is used to transmit information signals over the UL in the second hop (i.e., RF link). We propose a multi-objective optimization problem (MOOP) to study the trade-off between UL and DL sum-rate maximization. The non-convex MOOP framework is then transformed into an equivalent form, which yields a set of Pareto optimal resource allocation policies. We also illustrate the effectiveness of the proposed approaches through numerical results.