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Beyond the Vacuum: Combinatorial Strategy Selection for Competitor-Aware Generative Engine Optimization

Vaibhav Sourirajan, Yao Zhang, Himanshu Kumar, Sahil Wadhwa, Mann Patel, Amirfarrokh Iranitalab

arXiv:2608.27631v1cs.IR

TL;DR

Existing GEO methods optimize rewriting strategies in isolation even though their effectiveness changes as competitor adoption grows. The paper addresses this with BOCS-based combinatorial search and preference tuning using grounded reasoning traces, achieving state-of-the-art results across competitive and standard benchmarks with out-of-distribution transfer.

  • Problem

    Existing GEO methods select rewriting strategies in isolation, although strategy effectiveness decreases as more competing documents adopt optimization.

  • Method

    The paper combines BOCS combinatorial search with hard-negative mining and teacher-generated reasoning traces to preference-tune a selector language model.

  • Results

    The selector achieves state-of-the-art performance on geo-bench and geo-benchcomp, with robust transferability to out-of-distribution datasets.

  • Takeaways & Limitations

    GEO strategy selection is treated as corpus-conditioned and adaptive, with the selector recommending strategies from the query and full document corpus without adoption-rate labels.

  • Takeaways & Limitations

    Evaluation uses LLM-generated responses and synthetic competitor-adoption distributions, while the strategy space is not exhaustive and retrieval, re-ranking, and faithfulness remain limited.

Abstract

from arXiv · show

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.

1 Introduction

GEO shifts content optimization toward visibility in LLM-generated responses, but existing approaches optimize documents without accounting for competitors. This paper formalizes competitor-aware strategy selection and combines combinatorial search with preference-tuned selection.

  • Generative Engine Optimization rewrites source content to increase its visibility and citation likelihood in LLM-generated responses.
  • Single heuristics and agentic methods optimize target documents in isolation, producing fixed rewrites without competitive-corpus awareness.
  • When multiple documents adopt the same strategies, overall gains decrease, making GEO a relative optimization problem.
  • The paper formalizes competitor-aware GEO as selecting strategy combinations that maximize target-document visibility given a query, target document, and surrounding corpus.
  • Its two-stage pipeline uses BOCS observations, statistically grounded hard-negative mining, teacher-generated reasoning traces, and DPO to train a reasoning-backed selector.
  • The selector achieves state-of-the-art performance on geo-bench and geo-benchcomp and transfers robustly to out-of-distribution datasets.

2 Related Work

Prior GEO research established rewriting-based visibility gains and increasingly realistic evaluation, while showing that strategy effectiveness declines as competitor adoption increases. These findings motivate competitor-aware optimization beyond isolated rewriting.

  • GEO was introduced with geo-bench, showing that targeted rewrites such as quotation addition can increase visibility in LLM-generated responses.
  • AutoGEO automated strategy discovery by extracting rules associated with the largest citation-rate changes and merging them into concrete rewrites.
  • Puerto et al. introduced adoption rate to quantify the fraction of documents using GEO strategies.
  • Strategy effectiveness degrades as more competitors optimize their content, indicating that isolated optimization is fundamentally flawed.
  • SAGEO Arena evaluates whether documents survive full retrieval and re-ranking before generation, exposing failures of strategies effective in isolation under retrieval conditions.

3 Problem Formulation

The paper formulates GEO as corpus-conditioned combinatorial optimization: select rewriting heuristics for a target document while competitors may also optimize. It constructs heterogeneous competitive corpora, evaluates visibility with PAWC, and uses BOCS observations with hard-negative mining to support preference learning.

  • 3 Problem Formulation: Competitor-aware GEO selects a rewriting strategy combination maximizing target-document visibility given a query, target document, and competitive corpus.
  • 3 Problem Formulation: The adoption rate α determines how many non-target documents are rewritten, with practical values discretized by corpus size.
  • 3 Problem Formulation: Each strategy combination x ∈ {0, 1}^r includes or excludes heuristics in the rewriting prompt and transforms the target document.
  • 3 Problem Formulation: The rewritten target replaces its original document in the competitive corpus, which the generative engine receives with the query to produce a cited response.
  • 3 Problem Formulation: PAWC measures target-source impression by weighting cited word count according to sentence position, giving earlier citations greater weight.
  • 3.1 Competitor Simulation: Competitor simulation uses three rewriting functions: uniformly sampled combinations, the strongest single strategy, and the full AutoGEO heuristic set.
  • 3.1 Competitor Simulation: Hard-negative mining uses BOCS observations, means, standard errors, and a significance threshold to produce preferred-versus-rejected strategy pairs or NONE.
  • 3.1 Competitor Simulation: For adoption rate α, the simulator samples competitor documents without replacement, assigns functions cyclically, and leaves non-selected documents unchanged.

4 Methodology

The methodology combines BOCS-based combinatorial search with preference optimization to train a selector language model for competitor-aware GEO. It evaluates candidate rewrites empirically, constructs grounded preference data, and trains the selector without exposing adoption rates or BOCS scores.

  • 4.2.1 BOCS Training: The pipeline uses BOCS to search a 15-strategy binary space containing 32,768 possible rewriting combinations.The strategies include established heuristics and five additional strategies introduced in this work.
  • 4.2.1 BOCS Training: BOCS models the black-box objective with a second-order polynomial, horseshoe priors, Gibbs sampling, and simulated annealing over binary strategy vectors.The search runs 50 function evaluations, including 10 random initializations and up to 40 surrogate-guided iterations.
  • 4.2.1 BOCS Training: Each BOCS evaluation rewrites the target document once, evaluates the resulting corpus five times, and records mean PAWC and standard error.The rewrite uses temperature 0, while generative-engine evaluations use temperature 0.7.
  • 4.3 Preference Optimization: Hard negative mining selects the highest-mean-PAWC combination when it significantly beats the zero-vector baseline under a one-tailed Welch’s t-test with threshold tthresh = 1.860.Training points without a statistically significant winning combination are discarded.
  • 4.3 Preference Optimization: Teacher-generated post-hoc reasoning traces enrich strategy preference pairs, after which the selector is trained through SFT and length-normalized DPO.The teacher is gemma-4-31b-it, while the student selector is gemma-4-E2B-it fine-tuned with LoRA.
  • 4.3 Preference Optimization: The selector receives queries, the full document corpus, the target index, and strategy descriptions, but no adoption rate or BOCS scores.It must infer competitive pressure from document content, supporting deployment when the true adoption rate is unknown.

5 Experimental Setup

The experiments construct competitive training and test data from geo-bench, rewrite documents with gpt-oss-120b, and evaluate under two generative engines. The evaluation reports repeated citation-based impression measurements after one deterministic target rewrite.

  • 5 Experimental Setup: The competitive dataset is generated from the geo-bench training split, with all competitor and target rewrites performed by gpt-oss-120b.Evaluation uses both gpt-oss-120b and Llama-3.3-70B-Instruct as generative engines.
  • 5 Experimental Setup: During evaluation, the selector generates a reasoning trace and strategy recommendation at temperature 0.1, and the target document is rewritten once at temperature 0.The recommendation is parsed from <final_answer> tags before generating five independent engine responses at temperature 0.7.
  • 5 Experimental Setup: Performance is summarized using mean and standard deviation across three citation-based impression metrics.The reported metrics include PAWC, position count, and word count.

6 Results

Competitor-Aware GEO outperforms existing baselines across datasets and evaluation models, while degrading most slowly as competitor optimization increases. Its strongest qualitative coverage comes with a faithfulness–enrichment trade-off, and it transfers zero-shot to distinct domains.

  • Main Results: 32.62 PAWC on gpt-oss-120b and 29.55 on Llama 3.3 70B exceed AgenticGEO by +4.67 and +2.75 PAWC, respectively.The gpt-oss-120b result recovers 84% of the Oracle BOCS ceiling of 39.00.
  • Main Results: 29.93 PAWC on geo-benchcomp outperforms agentic methods by > 18%, while the no-rewrite baseline falls to 17.99 when competitors rewrite.The margin over AgenticGEO grows 2.1% between geo-bench and geo-benchcomp.
  • Performance Scales with Adoption Rate: 11.4% degradation across α=0.0 to α=0.8 is the slowest among methods, with no statistically significant drop from α=0.0 to α=0.2.Single-strategy methods at α=0.8 fall below the unoptimized α=0 baseline.
  • Performance Scales with Adoption Rate: The selector shifts toward less saturated strategy alternatives as competitive optimization increases by inferring alpha from competitive context at inference time.This adaptation occurs without relying on adoption-rate labels in the cited results passage.
  • Competitor-Aware GEO Transfers to Out-of-Distribution Datasets: Competitor-Aware GEO achieves the highest PAWC on both E-Commerce and Researchy-GEO, improving upon the strongest existing method by > 8% zero-shot.The transfer datasets have distinct query and document distributions, and content-conditioned methods show stronger transferability.
  • PAWC Optimization Introduces a Faithfulness–Enrichment Trade-off: The method achieves the highest Key Point Coverage (7.48), alongside Faithfulness of 4.90 and Attribution Accuracy of 4.18.The paper characterizes these metrics as reflecting a faithfulness–enrichment trade-off because they measure divergence from the original source.

7 Conclusion

The paper frames GEO as competitor-aware combinatorial strategy selection and combines BOCS search with preference tuning using score-grounded reasoning traces. The resulting selector outperforms existing baselines, degrades slowly under adoption, and transfers across domains.

  • Conclusion: The paper formalizes GEO as a competitor-aware combinatorial strategy selection problem over the competitive document landscape.The target is to maximize document visibility in generative-engine responses using corpus context.
  • Conclusion: BOCS-driven strategy search followed by preference tuning with score-grounded reasoning traces produces a selector that recommends tailored rewriting strategies.The selector operates without adoption-rate labels or privileged information at inference time.
  • Conclusion: The method significantly outperforms single-strategy and agentic baselines on geo-bench and geo-benchcomp while degrading most slowly across adoption rates.The selector infers competitive pressure from the full document corpus.
  • Conclusion: Robust transferability to other datasets supports reasoning over document dynamics across domains and motivates corpus-conditioned, adaptive content optimization.The paper describes strategy selection in generative settings as inherently multi-agent, corpus-conditioned, and adaptive.

Limitations

The evaluation uses several proxies and a limited strategy space, and it does not fully simulate production retrieval or real-world adoption. The method also has an information advantage and observed faithfulness concerns.

  • The evaluation relies on LLM-generated responses and synthetic competitor-adoption distributions rather than production behavior and observed real-world patterns.
  • The 15-strategy space is not exhaustive, despite covering strategies identified in prior GEO work.
  • The evaluation primarily uses controlled generation instead of comprehensively simulating retrieval and re-ranking.
  • Observed faithfulness drops motivate future optimization with retrievability and faithfulness as explicit constraints.
  • At inference, the method uses the full competitive corpus, giving it an information advantage over approaches conditioned only on target content or fixed strategies.

Ethics Statement

The method targets visibility for high-quality, relevant material but could also be misused to degrade information quality. The authors prohibit fabricated citations and unsupported claims and identify faithfulness-constrained optimization as future work.

  • GEO is intended to improve the visibility of high-quality, relevant material in generative search.
  • The techniques could be misused by fabricating citations or inserting unsupported claims that degrade information quality.
  • Rewriting prompts forbid invented quotations, fabricated sources, and unverifiable numbers.
  • Faithfulness-constrained optimization and continued investigation of ethical concerns are identified as future directions.

A Additional Results

Additional analyses show that grounded reasoning traces strengthen preference optimization, pairwise BOCS interactions improve search, and teacher leakage is rare but auditable. The section also defines citation- and length-based evaluation metrics.

  • Reasoning Traces: Adding grounded reasoning traces to SFT and DPO produces the largest ablation improvement, with DPO adding +3.35 PAWC to 32.62±0.25.
  • Reasoning Traces: Preference optimization becomes effective when chosen and rejected responses differ in rich reasoning traces rather than strategy label lists alone.
  • BOCS Order Ablation: The order-2 BOCS surrogate reaches mean best PAWC 31.02 versus 30.63 for order-1, a +0.39 improvement from modeling pairwise interactions.
  • Teacher Reasoning Trace Audit: Teacher traces reference scorecard rankings or scores in approximately 1% of 12,124 audited traces, motivating post-hoc filtering.
  • B.1 Citation-Based Metrics: PAWC weights cited word count by sentence position, while Pos Count weights citation frequency and Word Count measures raw cited words.
  • B.2 Length-Based Metrics: Length Ratio compares rewritten and original word counts: LR = 1 is length-neutral, above 1 indicates expansion, and below 1 indicates compression.

B.3 Qualitative Metrics via LLM Evaluation

The evaluation framework uses an LLM judge to score rewritten documents on eight qualitative dimensions covering surface and structural value plus information-source integrity. These scores include readability, positioning, preservation, semantic integrity, attribution, faithfulness, key-point coverage, and answer dominance.

  • Evaluation framework: Eight metrics are scored on a 1–10 scale by an LLM judge under the DSV-CF framework.The framework combines SSV and ISI dimensions.
  • Information-Source Integrity: Response-level Faithfulness penalizes hallucinated facts, omitted critical information, or distortions of the original document’s meaning.The metric evaluates semantic preservation between the rewritten candidate and the source.
  • Surface & Structural Value: SSV measures word-level value, document-position awareness, content preservation, and semantic integrity.These dimensions assess fluency, visibility-oriented structure, retained meaning and facts, and logical coherence.
  • Information-Source Integrity: ISI measures attribution accuracy, response-level faithfulness, key-point coverage, and answer dominance.These dimensions assess source entailment, semantic preservation, transferred substance, and comparative recommendation strength.
  • Information-Source Integrity: Attribution Accuracy checks whether claims attributed to the target document are entailed by the original source.It functions as the main anti-hallucination safeguard.
  • Information-Source Integrity: Key-Point Coverage measures recall of source key points in the response, while Answer Dominance assesses whether the target is presented as the primary solution.Answer Dominance is designed for comparative or recommendation queries.

D Fine-Tuning Training Details

The training pipeline fine-tunes a language model with supervised reasoning traces and preference optimization, while representing each rewriting strategy as a reusable prompt template. Multiple active strategies are composed into one prompt, and recommendations vary with competitor adoption rates.

  • Fine-tuning: The system fine-tunes gemma-4-E2B-it using the TRL library for both supervised fine-tuning and direct preference optimization.LoRA adapters are merged after SFT and reinitialized for DPO; gradient checkpointing reduces peak DPO memory use.
  • Fine-tuning: SFT on chosen reasoning traces establishes format compliance, followed by DPO on contrastive preference pairs.Both stages use LoRA, with length-normalized loss during DPO.
  • Strategy prompts: Each of the 15 rewriting strategies is implemented as a standalone prompt template with shared GEO context and strategy-specific instructions.The source document fills the {text} placeholder at inference time.
  • Strategy prompts: The strategy library includes rewrites for fluency, citations, simplification, technical style, keywords, statistics, explanations, vocabulary, formatting, balance, concision, comparisons, summaries, authority, and quotations.The templates generally constrain rewrites to preserve core content and avoid fabricated additions.
  • Strategy composition: Active strategies are combined into one unified prompt by numbering their instruction fragments as simultaneous objectives.The composition template also supplies query context and constraints to preserve core information and meaning.
  • Adoption-rate analysis: At α=0.0, the selector reasons solely from target-document gaps because the competitor corpus contains no rewrites.Tables 12 and 13 show how recommendations shift as adoption rates and competitor strategies change.
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