In ports, a variety of tasks are carried out, and scheduling these tasks is crucial due to its significant impact on productivity, making the generation of precise plans essential. This study proposes a method to solve the Quay Crane Scheduling Problem (QCSP), a representative task scheduling problem in ports known to be NP-Hard, more quickly and accurately. First, the study suggests a method to create more accurate work plans for Quay Cranes (QCs) by learning from actual port data to accurately predict the working speed of QCs. Next, a Surrogate Model is proposed by combining a Machine Learning (ML) model with a Genetic Algorithm (GA), which is widely used to solve complex optimization problems, enabling faster and more precise exploration of solutions. Unlike methods that use fixed-dimensional chromosome encoding, the proposed methodology can provide solutions for encodings of various dimensions. To validate the performance of the newly proposed methodology, comparative experiments were conducted, demonstrating faster search speeds and improved fitness scores. The method proposed in this study can be applied not only to QCSP but also to various NP-Hard problems, and it opens up possibilities for the further development of advanced search algorithms by combining heuristic algorithms with ML models.