A PSO algorithm for continuous berth allocation problem

Abstract

Berth allocation problem (BAP) is defined as how to allocate the incoming ships to the berths along the entire quay, so that the total elapsed time of the ships is minimised. The problem is categorised into two types, namely discrete BAP and continuous BAP. In the first type, the ships should be allocated within any of the predefined berths; while in the second, all points of the quay are available as berthing locations. The continuous BAP (BAPC) is formulated as a mixed integer programming model, in which the variables of berthing locations and start times of handling the ships, among others, are integers. The model is difficult to solve on account of its combinatorial nature. This paper considers a relaxed version of the BAPC by treating the variables of berthing locations and start times as real numbers. Recently, a genetic algorithm (GA) was devised for the original BAPC and tested on some test examples. The goal of this paper is applying the particle swarm optimisation (PSO) meta-heuristic to the relaxed problem. An algorithm is implemented and tested by numerical examples, investigating the properties of the model and evaluating the PSO against the GA. The results show that the PSO works better in terms of accuracy and computational time.