C-Evolve: Consensus-Based Group Prompt Evolution

• Consensus-Evolve (C-Evolve) is an evolutionary algorithm that optimizes groups of prompts for black-box LLMs by focusing on collective consensus rather than individual prompt performance.
• It employs an island-based framework where prompts are evolved and scored using a voting mechanism with exponential moving average to guide group consensus.
• Empirical results show that C-Evolve outperforms single-prompt strategies, achieving notable improvements on tasks like HotpotQA, IFBench, and MATH.

Consensus-Evolve (C-Evolve) is an evolutionary algorithm for optimizing groups of prompts in black-box or closed-source large-language-model systems, rather than optimizing a single prompt in isolation. Its defining idea is that a compound AI system can exceed the capability of any one prompt configuration when multiple evolved prompts are executed in parallel and their outputs are aggregated into a consensus, using majority voting for closed-ended tasks or an LLM-based selector for open-ended tasks. C-Evolve therefore makes group consensus performance, not standalone prompt accuracy, the central evolutionary objective, and assigns fitness to each prompt through a voting score that measures its contribution inside sampled prompt groups (Li et al., 27 Sep 2025).

1. Formal problem and optimization target

C-Evolve is defined on a Compound AI System $\Phi = (M, L, \mathcal{X}, \mathcal{Y})$, where $M = \langle M_1,\dots,M_{|M|}\rangle$ denotes one or more language modules, $L$ denotes control flow, and $\mathcal{X}, \mathcal{Y}$ are global input and output schemas. Each module $M_i = (\theta_i,\mathcal{X}_i,\mathcal{Y}_i)$ is controlled by a system prompt $\pi_i$, and a full prompt configuration is an individual

$\Pi = \langle \pi_1,\dots,\pi_{|M|}\rangle.$

Given a task instance $(x,m)$, the system produces

$y = \Phi(x;\Pi),$

and an evaluation metric $\mu:\mathcal{Y}\times\mathcal{M}\to[0,1]$ scores the result.

The contrast with conventional prompt evolution is explicit. A single-prompt evolutionary method seeks

$M = \langle M_1,\dots,M_{|M|}\rangle$0

C-Evolve instead searches for a group of prompt configurations

$M = \langle M_1,\dots,M_{|M|}\rangle$1

whose outputs

$M = \langle M_1,\dots,M_{|M|}\rangle$2

are combined by a consensus operator $M = \langle M_1,\dots,M_{|M|}\rangle$3, yielding

$M = \langle M_1,\dots,M_{|M|}\rangle$4

The optimization target becomes

$M = \langle M_1,\dots,M_{|M|}\rangle$5

This shift is substantive rather than cosmetic. The method is motivated by the claim that different prompts tend to specialize in different aspects of complex tasks, so evolving them as committee members can produce complementarity that is inaccessible to isolated prompt search (Li et al., 27 Sep 2025).

2. Island-based evolutionary architecture

C-Evolve uses an island-model evolutionary algorithm with $M = \langle M_1,\dots,M_{|M|}\rangle$6 islands, each maintaining a population $M = \langle M_1,\dots,M_{|M|}\rangle$7 of prompt configurations. In the reported implementation, the number of islands is typically $M = \langle M_1,\dots,M_{|M|}\rangle$8, the population limit per island is $M = \langle M_1,\dots,M_{|M|}\rangle$9, the warm-up stage lasts 50 iterations, the voting stage lasts 50 iterations, the number of sampled groups per voting iteration is $L$0, the EMA parameter is $L$1, and inter-island migration occurs at a 10% rate (Li et al., 27 Sep 2025).

Two datasets are used during evolution. The metric set $L$2 is used for fitness evaluation. The feedback set $L$3 is used to build detailed traces for prompt mutation; each individual typically receives feedback compiled from 3 examples. Sampling of seed individuals is performance-based: if a population is

$L$4

then individual $L$5 is sampled with

$L$6

The evolutionary process has two stages.

The warm-up stage evolves prompts by individual performance. Each island starts from the same baseline prompt configuration $L$7. A sampled seed prompt is mutated by an evolver LLM, evaluated on $L$8, assigned an individual score $L$9, and inserted into the island population; if the population exceeds $\mathcal{X}, \mathcal{Y}$0, the lowest-scoring individual is removed. This stage is intended to produce viable prompts before group-level fitness becomes meaningful.

The voting stage changes the fitness signal. Each island again samples a seed according to current fitness, mutates it with the evolver LLM, and inserts the offspring. Then C-Evolve samples $\mathcal{X}, \mathcal{Y}$1 cross-island groups, one individual per island, evaluates each group under the consensus operator $\mathcal{X}, \mathcal{Y}$2, and updates individual fitness by the prompt’s average contribution across all groups in which it appeared. Populations are then truncated by this group-based score.

Mutation is implemented by an evolver LLM that receives the current prompt, task-specific traces, metric outcomes, and—in the voting stage—group-level feedback. It edits prompts using search/replace diff blocks of the form <<<<<<< SEARCH / ======= / >>>>>>> REPLACE, rather than token-level crossover or mutation (Li et al., 27 Sep 2025).

3. Voting score as cooperative fitness

The central formal innovation is the voting score. If an individual $\mathcal{X}, \mathcal{Y}$3 appears in sampled groups $\mathcal{X}, \mathcal{Y}$4, then its voting score is

$\mathcal{X}, \mathcal{Y}$5

This score is not an estimate of the prompt’s standalone quality. It is an estimate of how well the prompt participates in high-performing consensus groups.

Because the surrounding population changes over time, C-Evolve smooths this signal with an exponential moving average: $\mathcal{X}, \mathcal{Y}$6 During warm-up, $\mathcal{X}, \mathcal{Y}$7 is initialized from the individual score

$\mathcal{X}, \mathcal{Y}$8

This design encodes a cooperative notion of prompt fitness. Prompts that are merely strong in isolation can be discarded if they contribute little to group consensus, while prompts with moderate individual scores can be preserved if they systematically improve the committee outcome. The paper’s ablations support this interpretation: on IFBench with Qwen3-8B, replacing EMA voting by simple historical averaging yields 41.16%, replacing it by max-over-history yields 38.44%, while EMA with $\mathcal{X}, \mathcal{Y}$9 yields 42.85% (Li et al., 27 Sep 2025).

A common misconception is that C-Evolve is equivalent to evolving single prompts and only adding voting at inference time. The reported results contradict that reading: group-aware fitness changes which prompts survive evolution.

4. Consensus mechanisms and prompt diversity

C-Evolve uses task-dependent consensus operators. On closed-ended tasks such as MATH and GPQA, outputs are canonicalized and aggregated by majority voting. On MATH, answers are extracted from $M_i = (\theta_i,\mathcal{X}_i,\mathcal{Y}_i)$0; if no majority exists, one candidate is randomly selected. On GPQA, answer letters are extracted and majority voting is applied. On HoVer, supporting facts are retained only if they are produced by more than half of the islands, and the final fact set is their union (Li et al., 27 Sep 2025).

On open-ended tasks such as HotpotQA and IFBench, raw majority voting over strings is not meaningful, so C-Evolve uses an LLM-based aggregator. Two variants were tested: LLM-summary, which synthesizes a new answer, and LLM-selection, which selects the most representative answer among the candidate outputs. On IFBench with Qwen3-8B, LLM-selection achieved 42.85%, whereas LLM-summary achieved 38.66%, and LLM-selection became the default aggregator (Li et al., 27 Sep 2025).

The island model is used not only for search parallelism but for controlled diversity. Qualitative analysis on IFBench showed different islands specializing in different prompt styles: one emphasized core constraint prioritization and refined amendments, another precise constraint pre-declaration and hierarchical verification, and another task-priority stratification and critical failure-point verification. A t-SNE visualization of TF-IDF embeddings of top-EMA prompts showed islands diverging into distinct clusters over training. This suggests that the cooperative fitness signal rewards functional complementarity rather than convergence to a single prompt archetype (Li et al., 27 Sep 2025).

5. Empirical performance and ablation results

The reported evaluation covers HotpotQA, IFBench, HoVer, MATH, and GPQA, using Qwen3-8B and GPT-4.1-mini. The paper reports state-of-the-art performance across these tasks (Li et al., 27 Sep 2025).

Task	Qwen3-8B	GPT-4.1-mini
HotpotQA	70.67	70.64
IFBench	43.88	47.96
HoVer	50.33	51.66
MATH	85.33	95.33
GPQA	47.15	66.26

Against baselines, the paper reports the following averages. On Qwen3-8B, C-Evolve improves over the baseline by +13.85%, over GEPA by +5.83%, and over AlphaEvolve by +4.1%. On GPT-4.1-mini, it improves over the baseline by +16.09%, over GEPA by +6.89%, and over AlphaEvolve by +2.67% (Li et al., 27 Sep 2025).

The strongest direct evidence that C-Evolve is not just post hoc ensembling appears in the IFBench comparison with AlphaEvolve. For AlphaEvolve on Qwen3-8B, the best individuals per island scored 41.15%, 36.73%, and 37.07%; grouping these prompts and applying the same consensus mechanism still yielded 41.15%. For C-Evolve, the best EMA individuals per island scored 40.47%, 39.79%, and 38.77%, but their group consensus reached 43.88%. The group is therefore better than any constituent prompt and better than a naive group formed from single-prompt evolution (Li et al., 27 Sep 2025).

The MATH analysis shows where the gain arises. On easy subsets, individual prompts already exceed 90% accuracy and consensus helps only slightly. On Level-5 problems, individual accuracies fall to 62–67%, while group consensus rises to 68.33%. A finer partition shows that when exactly two prompts agree, the group reaches 49.33% accuracy whereas the single best prompt reaches 40%; when all three agree, both individual and group are 95.23%; when all three answers differ, the group slightly improves over the best individual, 17.54% versus 14.03% (Li et al., 27 Sep 2025).

The warm-up stage is also empirically justified: on IFBench with Qwen3-8B, removing warm-up reduced performance from 42.85% to 41.83% (Li et al., 27 Sep 2025).

6. Broader context, interpretation, and limitations

C-Evolve sits at the intersection of prompt evolution, ensemble aggregation, and consensus-driven search. A plausible intellectual backdrop is earlier work on evolutionary optimization of consensus objects, such as hierarchical clustering ensembles in which a genetic algorithm learns a weighted fusion of primitive fusion functions to maximize cophenetic correlation (Rashedi et al., 2018). A second nearby line is consensus-based optimization, where interacting particles contract toward a Laplace-weighted consensus point, and where consensus hopping has been linked to $M_i = (\theta_i,\mathcal{X}_i,\mathcal{Y}_i)$1-evolution strategies (Fornasier et al., 12 Feb 2026, Roith et al., 30 Jun 2025). More broadly, the literature on spontaneous consensus formation emphasizes that macroscopic coordination depends strongly on microscopic interaction rules, network structure, and reinforcement dynamics (Baronchelli, 2017). This suggests that C-Evolve can be read as an LLM-era instantiation of a wider pattern: consensus is not merely an output combiner, but a search principle.

Its limitations are practical and architectural rather than hidden. The paper identifies computational overhead, because group-based evaluation and multi-prompt inference are more expensive than single-prompt evolution. It identifies aggregator reliability, especially on open-ended tasks where the final answer depends on an LLM-based selector. It notes sensitivity to hyperparameters, including group size, number of islands, EMA factor, and group-sampling strategy. It also leaves open the method’s behavior on task families beyond those evaluated, such as code generation, dialogue, or more tool-intensive agents. A further practical issue is that evolved prompts may become long and intricate, which may raise inference cost or context-management concerns (Li et al., 27 Sep 2025).

Within those bounds, C-Evolve’s distinctive claim is precise: when deployment uses a prompt group and a consensus operator, fitness should be defined at the level of group consensus rather than prompt individuality. That principle, rather than majority voting alone, is what differentiates C-Evolve from earlier single-prompt evolutionary schemes (Li et al., 27 Sep 2025).