# Deriving Situation-Adaptive Policy for Container Stacking in an Automated Container Terminal
## 1 Introduction  
One of the most important operational goals of a container terminal is to minimize the vessel turnaround time by maximizing the efficiency of _vessel operations_ with regard to loading or unloading containers onto or from the vessels. The _outbound_ containers brought in by the trucks from inland are stored in the yard until they are loaded onto the vessels. On the other hand, the _inbound_ containers unloaded from the vessels dwell in the storage yard until they are claimed by the external trucks for inland transportation. As buffer storage for both inbound and outbound containers, the operational efficiency in the storage yard critically affects the overall productivity of the terminal. A very important factor that affects the operational efficiency in the storage yard is the determination of the stacking locations of the containers that arrive at the yard. If, for example, a container just unloaded from a vessel is stacked on top of another to be loaded soon, the upper one has to be relocated to a different stack when retrieving the lower one. Such _rehandling_ of containers should be minimized in order to maximize the operational efficiency in the yard. When the containers are loaded onto a vessel, they follow a predetermined sequence. The loading sequence is determined at the planning stage, taking into account the vessel stability, ports of destination, and the efficiency of operation at the storage yard. Still, rehandling is the major cause of loading delay because the retrieval schedules are usually unknown at the time the containers arrive at the yard, and thus, they can be stacked at the wrong locations. In this paper, we deal with the problem of determining good locations for stacking notonly the containers that newly arrive at the yard but also those that are relocated within the yard. Perhaps the simplest approach to determining the stacking locations in the yard is using a heuristic rule based on a simple criterion such as preferring the nearest location or preferring the stack-top of containers of the same category [1; 2; 3]. More recent and advanced methods use multiple criteria to evaluate candidate stacking locations from various perspectives [4; 5; 6]. These methods use _scoring functions_ to calculate the score of a candidate location by a weighted sum of the results of evaluations based on various criteria. Since the scores and the resulting best stacking location depend on the weight combination, or _weight vector_, used in the scoring function, the weight vector can be regarded as a _stacking policy_. To find a good weight vector, i.e., a good stacking policy, References [4; 6] use genetic algorithms (GA) in which each candidate policy is evaluated through simulations of applying the policy to various scenarios of operations in the yard and measuring the resulting performance. However, the policy found in this way is the one whose _average_ performance in various scenarios is the best. In certain situations, there may be other policies that work better than the average policy. What we propose in this paper is a method for deriving a stacking policy, which can be adapted to changing situations by having its weight vectors adjusted. As an indicator of the situation, we use the workload of vessel operation because good stacking locations are very much dependent on it. Our method is based on the idea that a new policy may be synthesized if we are given two boundary policies: one for a very low workload and the other for a very high workload. We assume that a good policy for any intermediate situation can be derived by taking an interpolation of the weight vectors of the two boundary policies. We use a GA to search for not only the two boundary policies but also the two numeric values that quantify the two fuzzy terms'very low' and'very high'. Our GA can be seen as a reinforcement learning algorithm conducting a search in the policy space [7] instead of learning a value function based on rewards from the environment.