Pareto-Grid Evolution of LLMs (MPaGE)

• The paper introduces MPaGE, a bi-objective outer-loop optimization framework that integrates Pareto-grid search with evolutionary strategies to enhance LLM prompt configurations.
• It constructs a discrete grid over parameters like prompt templates and retrieval modes, employing MAP-Elites and diversity measures to balance first-try success and step-efficiency.
• Empirical results demonstrate significant improvements in success rates, compositional generalization, and computational efficiency compared to traditional LLM optimization methods.

Pareto-Grid-guided Evolution of LLMs (MPaGE) is a bi-objective outer-loop optimization paradigm that integrates Pareto-grid-based multiobjective search with evolutionary mechanisms over LLM prompt or heuristic configurations. MPaGE constructs a discrete search space grid spanning axes such as prompt template, retrieval mode, rule stacking, and retry policy, and evolves candidate configurations using systematic variations. The framework jointly optimizes first-try success rate and step-efficiency, maintains solution diversity via Pareto grid partitioning and MAP-Elites strategies, and achieves robust trade-offs under constrained rollout budgets. MPaGE has been instantiated both for prompt evolution in adaptive LLM agents and for automated heuristic generation in multi-objective combinatorial optimization.

1. Formal Framework and Objective Formulation

MPaGE defines a finite set $P$ of candidate configurations, each parameterized as a $D$-dimensional discrete vector over axes such as template choice $T$, retrieval mode $M$, rule stacking flag $S$, retry strategy $R$, and rollout multiplier $L$ (Shahmansoori, 10 Mar 2026). Each candidate $p \in P$ is evaluated by two real-valued objectives:

• $f_1(p)$: First-try success rate (primary task completion without retries)
• $f_2(p)$: Step-efficiency, defined as $D$0, where $D$1 is the maximum allowed retries

The bi-objective maximization is: $D$2 A candidate $D$3 Pareto-dominates $D$4 iff $D$5 for all $D$6 and $D$7 for some $D$8. The Pareto frontier $D$9 contains all non-dominated configurations, from which a deployment candidate $T$0 is selected using a scalarization criterion, e.g., $T$1 (Shahmansoori, 10 Mar 2026).

2. Discrete Grid Representation and Diversity Promotion

The search space $T$2 is treated as a grid: $T$3, yielding hundreds of prompt or heuristic phenotypes. Each axis captures a distinct operational dimension (e.g., template $T$4, retrieval modes $T$5). Each grid cell encodes a unique configuration, allowing structured coverage and explicit diversity measurement.

In heuristic-design settings, MPaGE applies Pareto Front Grid (PFG) partitioning in objective space for multiobjective combinatorial optimization (MOCOP), with candidates allocated to grid cells indexed by

$T$6

across objective dimensions $T$7 (Ha et al., 28 Jul 2025). Each cell maintains at most $T$8 best solutions by Pareto rank or crowding distance.

Diversity is quantified by topological distinctness (e.g., Hamming distance) for prompt grids (Shahmansoori, 10 Mar 2026), or by semantic code similarity (e.g., Levenshtein, Jaccard, or AST-edit distance) in code-based heuristics (Ha et al., 28 Jul 2025). Diversity triggers further search resource allocation if below a threshold $T$9.

3. MPaGE Evolutionary Algorithm and Outer Loop

The core evolutionary procedure is event-driven and distinct from standard high-frequency inner loops. Upon trigger (such as learning new rules or encountering persistent failures), the algorithm proceeds through:

1. Selection: Parents are drawn from $M$0 (initial configuration), with uniform sampling.
2. Mutation/Crossover: Axes are randomly perturbed; crossover may combine axes from two parents.
3. Candidate Evaluation: Offspring are evaluated over $M$1 trials for both objectives.
4. Pareto-Grid Update: Child is added to archive; $M$2 and grid are re-computed considering dominance and diversity.
5. Diversity Maintenance: If diversity falls below $M$3, $M$4 rollouts are allocated to explore new configurations.
6. Deployment Selection: $M$5 is chosen via scalarization or hypervolume maximization for deployment.

Pseudocode skeleton [adapted from (Shahmansoori, 10 Mar 2026)]: $S$7

Hyperparameters include immediate acceptance threshold $M$6, diversity threshold $M$7, and early-stop criterion $M$8 based on predicted success.

4. Integration in LLM Agent Architectures and Optimization Studies

Within PRECEPT (Shahmansoori, 10 Mar 2026), MPaGE is realized in the COMPASS module, operating at the prompt-configuration level. The inner loop of PRECEPT comprises:

• Deterministic exact-match rule retrieval eliminating partial-match errors.
• Conflict-aware Bayesian memory for drift and adversarial knowledge detection.
• Epistemic probes to ensure trajectory sanity.

Each candidate prompt is scored under the same execution pathway as at deployment, providing end-to-end objective fidelity. MPaGE thus underlies robust test-time adaptation, with grid-guided diversity ensuring compositional generalization and drift resilience.

In combinatorial optimization (Ha et al., 28 Jul 2025), MPaGE orchestrates LLM-guided heuristic evolution, using configuration grids in objective space to focus LLM variation on high-performing, semantically diverse code operators.

5. Empirical Results and Performance Assessment

PRECEPT with COMPASS (i.e., MPaGE) achieves a +41.1pp first-try advantage over Full Reflexion (with effect size $M$9), +33.3pp compositional generalization ($S$0), and 100% $S$1 on 2-way logistics compositions ($S$2). Continuous learning and robustness under adversarial static knowledge are demonstrated, with up to +55pp drift recovery and a 61% reduction in steps, often at $S$3 significance (Shahmansoori, 10 Mar 2026).

In MOCOP, MPaGE demonstrates empirically superior results compared to prior LLM-based multiobjective frameworks, and competitive or superior performance relative to traditional MOEAs (e.g., NSGA-II, MOEA/D), with substantially reduced runtime. Metrics include hypervolume (HV) and inverted generational distance (IGD) (Ha et al., 28 Jul 2025). For example, MPaGE can achieve HV and IGD improvements over baselines at lower computational cost.

Table: Illustrative Empirical Results (values adapted from (Ha et al., 28 Jul 2025))

Method	VRP-TW HV↑	VRP-TW IGD↓
NSGA-II	0.312 ±0.010	0.120 ±0.005
MOEA/D	0.328 ±0.012	0.115 ±0.004
LLMEA	0.340 ±0.015	0.105 ±0.006
MPaGE	0.365 ±0.008	0.085 ±0.003

6. Dominance Relations, Trade-off Analysis, and Hyperparameter Sensitivity

Dominance is computed with strict adherence to Pareto frontier definitions. Scalarized thresholds (e.g., $S$4) dictate immediate configuration adoption. Diversity thresholds ($S$5) and supplemental rollouts foster requisite phenotype exploration in under-explored grid regions. Early-stopping applies when projected success exceeds $S$6.

Hypervolume contribution may be exploited to prioritize which Pareto front configurations to mutate or retain in MAP-Elites–style archive cells, balancing convergence and diversity. Ablation analyses examine grid resolution, cell capacity, diversity thresholds, and semantic code distance thresholds, showing optimal trade-off settings for convergence and population heterogeneity.

7. Significance, Use Cases, and Extensions

MPaGE provides a principled approach to multiobjective prompt or heuristic evolution in constrained, high-stakes, or adversarial LLM deployment settings. It affords robust rule composition and adaptation in knowledge-driven agents—mitigating retrieval degradation, ensuring resilience to knowledge drift, and accelerating continuous learning (Shahmansoori, 10 Mar 2026). In MOCOP, MPaGE enables rapid, diverse, and high-quality heuristic discovery, with demonstrated runtime and solution-quality advantages over both standard LLM and dedicated multiobjective evolutionary approaches (Ha et al., 28 Jul 2025). A plausible implication is that Pareto-grid-guided outer-loop search over discrete, modular LLM configurations is broadly applicable wherever system-level trade-offs between accuracy and efficiency, or diversity and robustness, are paramount.