## 3 Related Work  
Most previous work on scheduling the stacking cranes has investigated plan (or schedule) search methods for determining the order of processing the container jobs requested within a fixed-length horizon. Since the search space becomes very large as the horizon becomes longer, some studies focus on finding a good plan within a rather short horizon [2; 3; 6], and some others try to cope with the search space by employing various techniques, such as branch-and-bound and its variants [2; 7] or local-search-based methods [1; 3; 4; 6]. Although a plan derived from a short horizon can be myopic, a plan from too long a horizon is not necessarily desirable. The plan obtained from a long horizon may not be well-optimized, due to the large search space. Even if the plan is well-optimized, it can become obsolete before long under an uncertain environment. Since the arrival times of ETs and AGVs (or yard tractors in conventional terminals) cannot be predicted accurately and the crane operations cannot be exactly deterministic, an execution of a plan can quickly deviate from the expected outcome. This leads to the studies on the online rolling horizon search method that replans for a horizon at regular intervals, in which the replanning interval is usually much shorter than the length of the planning horizon [1; 3; 4; 6; 18]. Important issues of scheduling the twin ASCs include how the workloads of the two ASCs can be balanced through cooperation and how the interferences between them can be minimized. [PERSON] et al. [1] achieve good load balancing by treating the preparatory jobs (i.e., rehandling and repositioning jobs) as independent jobs, so that the ASC with a lower workload can process more of them. [PERSON] et al. [19] reduced ASC interferences by defining the movement scheduling of the ASCs as a TSP problem, so that the minimum distance between the ASCs can be maintained. [PERSON] et al. [18] proposed a scheduling method that enabled ASC jobs to be performed in a pipelining manner, in order to improve the repositioning efficiency. However, all these (and previously mentioned works) ignore the issue of remarshaling. Early studies on remarshaling unrealistically assume that a long enough period of crane idle time is available, during which all the remarshaling jobs can be completed in a batch [20; 21]. A later work [22] deals with the problem of generating a selective remarshaling plan, under the constraint that the ASCs are idle for only a limited period of time. Nevertheless, this work assumes that the remarshaling works for a selected subset of containers that are performed in a batch. A more recent work [5] proposes a realistic ASC scheduling method, in which remarshaling jobs can be performed whenever the workloads of ASCs for the main jobs are light. Our work in this paper was an extension of the work in [5]. Instead of their plan to search under an online setting, however, we conducted an offline search for an optimal crane dispatching policy to be used for scheduling the ASCs online. Most works on noisy optimization use evolutionary algorithms, where the key issue is how to allocate samples efficiently in evaluating candidate solutions. A baseline approach to noisy optimization would be to take a number of fitness samples and average them to achieve the maximum noise-cancelling effect. However, such simple repeated resampling does not allow an efficient exploration of the search space as the computation for evaluating each individual candidate is too heavy. The adaptive resampling methods [8; 9; 23; 24] more effectively use the limited computational resources by dynamically adapting the number of samples during evolution. The duration-scheduling (DS) method [8] gradually increases the sample size at every generation but makes adjustments based on the estimated noise level of the current population, assuming a non-overlapping generation model. [PERSON] et al. [23] provided more samples to the candidates whose evaluation values showed larger standard deviations.