With the rise of large language models (LLMs), generative engines have become powerful alternatives to traditional search, creating the need for generative engine optimization (GEO)---improving content visibility and relevance for generative engines. Despite its growing importance, current GEO practices are largely ad hoc, and their impacts remain understudied. In e-commerce, for instance, conversational shopping agents now guide consumers to relevant products, yet it is unclear if GEO can affect how products surface to users. We address this gap by introducing E-GEO, which contains 13,746 realistic, multi-sentence consumer product queries, each paired with 10 retrieved Amazon listings, capturing rich intent, constraints, preferences, and shopping contexts that existing datasets miss. Using this dataset, we conduct a large-scale empirical study of e-commerce GEO across five representative generative engines, seven LLM rewriters, and fifteen rewriting heuristics. We further formulate GEO as an optimization problem and develop a prompt meta-optimization algorithm that significantly improves over heuristic baselines. Notably, prompts independently optimized from different heuristics converge to a stable pattern, suggesting a shared, transferable GEO strategy. Finally, we red-team the GEO system through both static and optimization-based attacks and show that, under a simple in-prompt defense in our setting, gains from GEO reflect genuine content improvement, anchoring GEO as a substantive optimization problem.

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