Large language models (LLM) are increasingly integrated into pervasive applications spanning heterogeneous cloud-edge resources. These heterogeneous resources differ in computational capacity, energy efficiency, network conditions, and deployed model quality, creating trade-offs among response quality, monetary cost, energy consumption, and batch completion time when routing inference requests. Existing LLM routers typically make per-query routing decisions based primarily on model quality and token cost, whereas cloud-edge schedulers often overlook quality differences among deployed models. Consequently, these objectives remain insufficiently coordinated. We present CEMA-Router, an infrastructure-aware batch router for LLM inference in pervasive cloud-edge systems. CEMA-Router formulates batch routing as a multi-objective search problem that jointly minimizes model-quality loss, monetary cost, energy consumption, and straggler-dominated batch completion time. To efficiently explore the search space, it employs a routing-specific memetic algorithm, combining largest-request-first, load-aware seeding with probabilistic, evaluator-guided Lamarckian repair. Routing decisions are informed by deployment-specific node profiles, dynamic backlog estimates, and model-quality signals. We further implement CEMA-Router as an end-to-end system comprising a request manager, routing service, and profiler, supporting both real cloud-edge deployment and trace-driven simulation. We evaluate the system using RouterBench traces and GSM8K and MMLU workloads on a heterogeneous cloud-edge testbed. Compared with state-of-the-art methods, CEMA-Router reduces the weighted objective by up to 86% for GSM8K and 80% for MMLU, while reducing energy consumption by up to 33% and 19% and batch completion time by up to 27% and 30%, respectively.

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