The design of automated landscape-aware techniques requires low-cost features that characterize the structure of the target optimization problem. This paper approximates network-based landscape models of multi-objective optimization problems, which were constructed by full search space enumeration in previous studies. Specifically, we propose a sampling method using dominance-based local search for constructing an approximation of the Pareto local optimal solution network (PLOS-net) and its variant, the compressed PLOS-net. Both models are valuable to visualize and compute features on the distribution of Pareto local optima. We conduct experiments with multi-objective nk-landscapes and compare the features of full-enumerated PLOS-nets with that of approximate PLOS-nets. We analyze the correlation between landscape features and the performance of well-established multi-objective evolutionary and local search algorithms. Our results show that approximated networks can predict algorithm performance and provide recommendation for algorithm selection with the same level of accuracy, even though they are much more computationally affordable compared to full-enumerated networks. We finally illustrate how the approximate PLOS-net scale to large-size instances.