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Waste sorting is an imperative and significant issue in China, of which sorted-waste collection and transportation are indispensable parts. Despite its vital yet practical significance, few studies research mathematical models or algorithms of waste collection and transportation from the perspective of waste sorting. To address this issue, we extend a novel transportation model for the waste management system, namely, capacitated location routing problem with queuing time (CLRPQT) and design a cross-entropy and simulated-annealing based hyper-heuristic algorithm (CE-SAHH) for it. The main idea of this paper is three-fold: (1) As a particular property of this problem, source nodes cannot but need to be served by more than one vehicle that causes queuing time between a heterogeneous fleet of vehicles, which is novel in terms of the proposed model; (2) For the methodological contribution, a character encoding scheme, new decoding procedure, and local search strategy are designed embedded in the proposed method; (3) An integration of simulated annealing strategy and the cross-entropy-based hyper-heuristic algorithm is developed to overcome the combinatorial optimization problem with a more complex solution of this study. Finally, the results and analysis of three numeric experiments on benchmark datasets, new instances of CLRPQT, and simulation data in Shanghai, China, verify the effectiveness and universality of the proposed model and method. • A novel model with interactional routes for sorted-waste transportation is proposed. • A cross-entropy-based hyper-heuristic algorithm is proposed and performs well. • The novel model and method based on sorted waste enrich the waste management system. • Real-life data is used to verify the method and some managerial insights are drawn. [ABSTRACT FROM AUTHOR]