GPU clusters serve as a cornerstone of high-performance computing and support a wide range of batch jobs with complex resource demands. However, the diverse requirements of batch jobs and resource heterogeneity present significant challenges to efficient scheduling. Existing approaches either rely on static rules or overlook the interdependencies among virtual machines introduced by resource heterogeneity, making it difficult to address the diverse resource demands and dynamic load balancing. In this paper, we propose a novel scheduling model based on Graph Neural Networks (GNNs) and Double Deep Q-Networks (DDQNs), termed GNN-DDQN, for batch job load balancing and scheduling of multi-dimensional resources (e.g. GPU, CPU and memory) in heterogeneous clusters. We propose a system model that integrates batch job resource requests, multi-dimensional resource configurations, and a multi-objective optimization framework. The scheduling problem is formulated as a Markov Decision Process based on this model. A GNN is employed to effectively capture the interdependencies among virtual machines, while a DDQN optimizes scheduling decisions using a dynamic target network update mechanism. Extensive experiments are conducted using two real-world Alibaba cluster traces. Results demonstrate the effectiveness and generalization capabilities of the proposed scheduling model. Compared to baseline methods, the results confirm its superiority in load balancing, job latency, fairness, and time efficiency.