An Enhanced NSGA-II for Solving Berth Allocation and Quay Crane Assignment Problem With Stochastic Arrival Times

The berth allocation and quay crane assignment problem (BACAP) is an important port operation planning problem. To obtain an effective and reliable schedule of berth and quay crane (QC), this study addresses the BACAP with stochastic arrival times of vessels. An efficient method combining scenario generation is presented to simulate the stochastic arrival times. After then, a mixed integer linear programming (MILP) model is established, aiming to minimize the expectation of the vessels’ total stay time in port. A multi-objective constraint-handling (MOCH) strategy is adopted to reformulate the developed model, which converts constraint violations into an objective, thus transforming the single-objective optimization model with complex constraints into a dual-objective optimization model with only easy-handling constraints. Then an enhanced non-dominated sorting genetic algorithm II (ENSGA-II) is proposed to solve the dual-objective model, in which a neighborhood search algorithm and a search bias mechanism are incorporated to strengthen the local exploitation capability. Furthermore, a repair method (RM), penalty function (PF) and the superiority of feasible solutions (SF) strategy for constraint handling are designed respectively and incorporated with genetic algorithm to solve the original single-objective optimization model. Finally, numerical experiments on instances in the literature are conducted to validate the effectiveness of the MOCH and the proposed ENSGA-II. The results show that the average total stay time of vessels is reduced when stochastic arrival times are considered. Comparison results with another two multi-objective methods and three single-objective methods combined with different constraint-handling strategies corroborate the superiority of the proposed ENSGA-II and MOCH.