A hybrid generalized extremal optimization algorithm for the quay crane   scheduling problem with interference constraints
  The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulted GEO is termed as the modified GEO. A randomized searching method for neighboring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by \citet{KimPark2004}. Compared with other well known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in reasonable time, especially for large-sized problems. 
Peng Guo, Wenming Chen, Yi Wang
math.OC