Generative Engine Optimization (GEO) has emerged as a novel paradigm for transforming content to increase visibility in Large Language Model (LLM) responses. Traditional GEO methods, however, select rewriting strategies in isolation, ignoring a critical externality: as adoption of content optimization grows, optimal strategies for rewriting content change. We formalize GEO as a competitor-aware strategy selection problem and propose a two-phase pipeline to solve it: (1) We use Bayesian Optimization of Combinatorial Structures (BOCS) to efficiently search the space of rewriting strategies, (2) We generate preference pairs and grounded reasoning traces from the BOCS black-box observations to fine-tune a language model to analyze a document corpus and propose optimal rewriting strategy combinations. We achieve state-of-the-art performance across several impression metrics over existing agentic and single-heuristic methods on both geo-bench and our synthetically augmented competitive dataset geo-bench_comp. Our method also transfers to multiple out-of-distribution datasets, proving effective across domains, queries, and document types.

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