A Near-Optimal Algorithm for Constraint Test Ordering in Automated Stowage Planning

The container stowage planning problem is known to be NP-hard and heuristic algorithms have been proposed. Conventionally, the efficiency of the stowage planning algorithms are improved by pruning or reducing the search space. We observe that constraint evaluation is the core of most algorithms. In addition, the order at which the constraints are evaluated can have significant impact on the efficiency of the constraint evaluation engine. We propose random sample model (RSM) and sequential sample model (SSM) for analysis of the problem. We present and evaluate seven strategies in optimizing the constraint evaluation engine. We show how to achieve the optimal constraint ordering with respect to RSM and SSM, respectively. However, the optimal ordering for SSM requires perfect information about the states of the constraint tests, which is impractical. We present an alternative strategy and show empirically that its efficiency is close to the optimal. Experiments show that, compared to a naïve ordering, an average of 2.74 times speed up in the evaluation engine can be achieved.
Note to Practitioners
—Automated stowage planning has become a trend as the number of mega-scale containerships being deployed has increased drastically over the past decade. Due to the nature of the problem, it is impractical to expect the best stowage plan within a limited amount of time, and hence, many heuristics have been devised to reduce the solution space. Many heuristics algorithms share a common core-repeatedly selecting a stowage slot and a container (selection mechanism) and evaluate whether all of the constraints are satisfied. To improve the efficiency, most studies aim to reduce the number of location-container pairs being considered. We consider an alternative approach that improves the efficiency of the constraint evaluation engine. Specifically, we show how to improve the efficiency by strategically reordering the sequence in which the constraints are evaluated. With the improvements on the efficiency, the stowage algorithm is one step closer to being able to generate solutions in real time. This may enable the shipping companies to take last-minute shipment order and react to changes in demands quickly.