We present a matheuristic, an integer programming based heuristic, for the Liner Shipping Network Design Problem. The heuristic applies a greedy construction heuristic based on an interpretation of the liner shipping network design problem as a multiple quadratic knapsack problem. The construction heuristic is combined with an improvement heuristic with a neighborhood defined by the solution space of a mixed integer program. The mixed integer program optimizes the removal and insertion of several port calls on a liner shipping service. The objective function is based on evaluation functions for revenue and transshipment of cargo along with in/decrease of vessel- and operational cost for the current solution. The evaluation functions may be used by heuristics in general to evaluate changes to a network design without solving a large scale multicommodity flow problem.