A modified adaptive large neighborhood search algorithm for solving the multi-port continuous berth allocation problem with vessel speed optimization

Abstract

Despite its fast-growing popularity in maritime transportation, container shipping is still fraught with risks and uncertainties with its complex operating environments. This paper studies the multi-port continuous berth allocation problem with speed optimization (MCBAP). In the MCBAP, vessels visit multiple ports sequentially, and the problem aims at minimizing the sum of vessel sailing cost, waiting cost, delay cost and port handling cost, while satisfying various constraints related to vessel sailing and berthing. A mixed integer linear programming (MILP) model for MCBAP is formulated, and a modified adaptive large neighborhood search (MALNS) algorithm is proposed for solving large-scale MCBAPs. In the MALNS, an efficient initial solution generation strategy is developed, and a series of neighborhood solution generation operators are proposed. Finally, the proposed MILP model and MALNS algorithm are tested on a range of MCBAP instances. The numerical results demonstrate that the MILP model can be solved to optimality with CPLEX, and the MALNS can efficiently solve instances at various scales. In addition, sensitivity analyses on fuel prices and vessel design speeds (the planned maximum speeds) are performed, and management insights have been provided.