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Within the context of using shore side electricity (SSE) at container terminals, we propose a multi-objective optimization model to solve the problem of berth allocation and quay crane assignment (BACAP). The proposed optimization model integrates the interconnected decisions on each vessel's berthing position, berthing start and departure time, duration of using SSE, and duration of using auxiliary engines to minimize the costs of using SSE, departure delay and emissions. Several factors, including the availability of SSE at different berths and vessels and the time-of-use (TOU) electricity pricing, which have been frequently ignored by previous studies, are specifically considered in this paper. Due to the complexity of the proposed model, an integrative algorithm framework is developed, composed of Partial Optimization Metaheuristic Under Special Intensification Conditions (POPMUSIC), Strength Pareto Evolutionary Algorithm 2 (SPEA2), and k -means clustering. The numerical experiments for a real-world case illustrate the efficiency of the developed algorithm framework and the effectiveness of the proposed model. Compared to the best-known solutions with only one objective considered, the proposed model reduces the costs of using SSE, departure delay, and vessel emissions by 27.47%, 37.51%, and 51.44%. Besides, some managerial insights are outlined based on the experiments under a series of designed scenarios. In doing so, the proposed optimization model assists the promotion of using SSE and the development of green ports and green shipping. • Proposing a multi-objective optimization model for the quayside operation. • Considering the availability of shore side electricity at berths and vessels. • Considering the impact of time-of-use electricity pricing. • Developing an integrative algorithm framework. • Performing experiments on well-defined instances generated from real-word data. [ABSTRACT FROM AUTHOR]