EngiAgent: Fully Connected Coordination of LLM Agents for Solving Open-ended Engineering Problems with Feasible Solutions

arxiv: 2605.02289 · v1 · submitted 2026-05-04 · 💻 cs.AI

EngiAgent: Fully Connected Coordination of LLM Agents for Solving Open-ended Engineering Problems with Feasible Solutions

Xiyuan Zhou , Ruixi Zou , Xinlei Wang , Yuheng Cheng , Yan Xu , Junhua Zhao , Jinjin Gu This is my paper

Pith reviewed 2026-05-09 16:29 UTC · model grok-4.3

classification 💻 cs.AI

keywords multi-agent systemsLLM coordinationengineering problem solvingfeasibility constraintsagent feedback routingopen-ended design

0 comments p. Extension

The pith

A fully connected coordinator among LLM agents produces feasible solutions for open-ended engineering problems by routing feedback between specialized stages.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces EngiAgent, a system of LLM agents each handling one part of an engineering task: analysis, modeling, verification, solving, and evaluation. A fully connected coordinator sits at the center and passes feedback in any direction needed instead of following a fixed sequence. This flexible routing is intended to catch problems such as inconsistent constraints or solver errors as soon as they appear. The authors argue that the result is higher rates of feasible solutions across different engineering domains. If the claim holds, LLMs would become more usable for real design and optimization work that must respect physical limits rather than just mathematical ones.

Core claim

We propose EngiAgent, a multi-agent system with a fully connected coordinator that simulates expert workflows through specialized agents for problem analysis, modeling, verification, solving, and solution evaluation. The fully connected coordinator enables flexible feedback routing, overcoming the rigidity of prior pipeline-based reflection methods and ensuring feasibility at every stage of the process. This design not only improves robustness to diverse failure cases such as data extraction errors, constraint inconsistencies, and solver failures, but also enhances the overall quality of problem solving.

What carries the argument

The fully connected coordinator that routes feedback in any direction among agents specialized in problem analysis, modeling, verification, solving, and solution evaluation.

If this is right

Higher feasibility rates across four representative engineering domains compared with earlier LLM approaches.
Better handling of specific failure modes including data extraction errors, constraint inconsistencies, and solver crashes.
Improved solution quality because feasibility is checked and enforced at every step instead of only at the end.
A shift toward feasibility-focused workflows when LLMs are applied to open-ended engineering tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same coordination pattern might transfer to other domains that require repeated constraint checking, such as scientific modeling or regulatory design.
Coordination overhead could become noticeable on very large problems, suggesting a need to test how the network scales with problem size.
Adding direct interfaces to external solvers or simulators inside the agents could reduce the number of internal iterations required.

Load-bearing premise

That the flexible feedback routing provided by the fully connected coordinator overcomes the rigidity of pipeline-based methods and keeps every stage feasible.

What would settle it

A head-to-head test on the same engineering benchmarks in which EngiAgent shows no gain in feasibility rate over a standard pipeline of LLM agents.

Figures

Figures reproduced from arXiv: 2605.02289 by Jinjin Gu, Junhua Zhao, Ruixi Zou, Xinlei Wang, Xiyuan Zhou, Yan Xu, Yuheng Cheng.

**Figure 1.** Figure 1: Comparison of fixed pipeline and fully connected coordinator. Fixed pipelines enforce rigid execution, whereas the fully connected coordinator enables dynamic routing and flexible error handling across agents. et al., 2023; Liang et al., 2024), and multi-agent coordination frameworks with fixed roles and protocols (Chen et al., 2023; Pan et al., 2025; Grötschla et al., 2025). These systems rely on stati… view at source ↗

**Figure 2.** Figure 2: Illustration of common error types in engineering problem solving with a community electricity and storage scheduling e: fancy but vague modeling, altering key data, violating physical laws, and over-constraining the model. (Zhou et al., 2024; Xia et al., 2024), and transportation (Yang et al., 2024; Qu et al., 2023), typically using fixed templates or tool-calling pipelines. While effective in predefined… view at source ↗

**Figure 3.** Figure 3: Overall Workflow of EngiAgent. The system consists of five functional agents (Analyzer, Modeler, Verifier, Solver, Evaluator) together with a Fully Connected Coordinator and shared Memory. The baseline pipeline (blue arrows) shows the predefined sequential cognitive architecture, while the coordinator layer (red arrows) enables flexible routing, error diagnosis, and adaptive scheduling across agents, ensur… view at source ↗

**Figure 4.** Figure 4: Distribution of evaluation scores across four dimensions for feasible and infeasible solutions. Scores above 10 are artifacts of kernel density estimation (KDE) smoothing. appear inflated. Many solutions that are infeasible under engineering constraints nevertheless receive relatively high ratings because they are well-written or logically coherent at the textual level. This creates a misleading distributi… view at source ↗

**Figure 5.** Figure 5: Ablation results over five metrics comparing degraded variants and the full EngiAgent. some dimensions but suffers from substantially higher inference overhead, with both runtime and token consumption at the highest level, resulting in poor overall cost-effectiveness. In contrast, EngiAgent (Coord.) demonstrates consistently strong cost efficiency across all three LLMs. While its runtime and token usage … view at source ↗

**Figure 6.** Figure 6: Distribution of task complexity in the EngiAgent benchmark. Left: density distribution of the number of constraints across all 53 tasks. Right: density distribution of the number of parameters. Both exhibit long-tailed behavior, indicating coverage from medium-scale to highly constrained engineering problems. Adjudication and Error Analysis. All three annotators agreed that the above six constraints are ma… view at source ↗

**Figure 7.** Figure 7: An example output generated by EngiAgent. The problem statement is extracted from a power system market allocation task with multiple supply and demand units and transformed into a modeling input. The system automatically produces the corresponding Pyomo code snippet and solves it under given parameters to obtain the optimal results. The outputs report key power flow allocations and local generation across… view at source ↗

read the original abstract

Engineering problem solving is central to real-world decision-making, requiring mathematical formulations that not only represent complex problems but also produce feasible solutions under data and physical constraints. Unlike mathematical problem solving, which operates on predefined formulations, engineering tasks demand open-ended analysis, feasibility-driven modeling, and iterative refinement. Although large language models (LLMs) have shown strong capabilities in reasoning and code generation, they often fail to ensure feasibility, which limits their applicability to engineering problem solving. To address this challenge, we propose EngiAgent, a multi-agent system with a fully connected coordinator that simulates expert workflows through specialized agents for problem analysis, modeling, verification, solving, and solution evaluation. The fully connected coordinator enables flexible feedback routing, overcoming the rigidity of prior pipeline-based reflection methods and ensuring feasibility at every stage of the process. This design not only improves robustness to diverse failure cases such as data extraction errors, constraint inconsistencies, and solver failures, but also enhances the overall quality of problem solving. Empirical results across four representative domains demonstrate that EngiAgent achieves substantial improvements in feasibility compared to prior approaches, establishing a new paradigm for feasibility-oriented engineering problem solving with LLMs. Our source code and data are available at https://github.com/AI4Engi/EngiAgent.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

EngiAgent wires a fully connected coordinator into a multi-agent LLM setup to push feasibility in open engineering problems, but the gains rest on LLM verification that may not catch real physical or data constraints.

read the letter

EngiAgent sets up five specialized agents—analysis, modeling, verification, solving, and evaluation—linked by a coordinator that routes feedback in any direction instead of a fixed pipeline. The claim is that this flexibility handles failure modes like bad data extraction or solver crashes better than rigid reflection loops, and the authors report better feasibility rates across four domains. The code and data are on GitHub, which is useful for anyone who wants to inspect or extend the implementation. That architecture detail is the clearest addition over prior multi-agent work for constrained tasks. The evaluation is the soft spot. The abstract states substantial feasibility gains without listing the actual percentages, the precise baselines, or the exact way feasibility was measured beyond the LLM verifier itself. If the full paper only shows LLM-to-LLM comparisons and no external solver checks or domain-expert validation, the numbers could be inflated exactly where the stress-test note worries—when an LLM accepts a solution that later fails a real physical or numerical test. The paper does not appear to reduce to fitted parameters or circular definitions, so the core idea is at least testable. This is for readers already working on LLM agents for applied optimization or design problems who need a concrete coordination pattern they can code up. Someone looking for new agent topologies might borrow the fully connected routing even if they swap out the verifier. It deserves peer review because the system is described in enough detail to reproduce and the public code lowers the barrier to checking the results, though referees will need to press for tighter metrics and independent feasibility oracles.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces EngiAgent, a multi-agent LLM framework for open-ended engineering problem solving. It deploys specialized agents for problem analysis, modeling, verification, solving, and solution evaluation, linked by a fully connected coordinator that routes feedback flexibly to enforce feasibility at each stage. The central claim is that this architecture yields substantial feasibility gains over prior pipeline-based methods across four representative domains, with code and data released at a GitHub repository.

Significance. If the empirical results hold under rigorous validation, the work could meaningfully advance feasibility-oriented multi-agent designs for LLM-based engineering tasks, where constraint satisfaction is load-bearing. The open release of code and data is a clear strength that aids reproducibility and follow-up work.

major comments (2)

[Abstract] Abstract: the claim that EngiAgent 'achieves substantial improvements in feasibility' and 'establishes a new paradigm' is presented without any quantitative metrics, baseline comparisons, domain descriptions, success rates, or error analysis. This absence prevents evaluation of the central empirical claim from the provided text.
[System Architecture] System description (verification and coordinator sections): the architecture assumes the LLM verification agent, combined with flexible feedback routing, reliably identifies and rejects infeasible outputs under physical, numerical, and data constraints. No evidence is supplied that this LLM-based check matches ground-truth solvers or domain-expert validation; known LLM limitations in constraint reasoning could inflate reported feasibility rates regardless of coordinator design.

minor comments (1)

[Abstract] The abstract would be clearer if it briefly named the four domains and the concrete feasibility metric (e.g., percentage of solutions passing exact solvers).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our empirical claims and the validation of key components. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that EngiAgent 'achieves substantial improvements in feasibility' and 'establishes a new paradigm' is presented without any quantitative metrics, baseline comparisons, domain descriptions, success rates, or error analysis. This absence prevents evaluation of the central empirical claim from the provided text.

Authors: We agree that the abstract would be more informative with concrete indicators of performance. In the revised version, we will incorporate specific feasibility rates (e.g., average improvement percentages across domains), brief domain descriptions, baseline names, and a high-level mention of error categories addressed. This change directly addresses the concern while preserving the abstract's brevity. revision: yes
Referee: [System Architecture] System description (verification and coordinator sections): the architecture assumes the LLM verification agent, combined with flexible feedback routing, reliably identifies and rejects infeasible outputs under physical, numerical, and data constraints. No evidence is supplied that this LLM-based check matches ground-truth solvers or domain-expert validation; known LLM limitations in constraint reasoning could inflate reported feasibility rates regardless of coordinator design.

Authors: We acknowledge this limitation in the current validation of the verification agent. The manuscript reports overall system feasibility gains via ablations on the coordinator, but does not include direct accuracy metrics for the LLM verifier against ground-truth solvers or expert labels. In revision, we will add a new subsection with manual verification on sampled cases, comparisons to available ground-truth solvers in two domains, and explicit discussion of LLM constraint-reasoning limitations together with how the fully connected routing mitigates cascading errors. This will provide the requested evidence without altering the core architecture. revision: yes

Circularity Check

0 steps flagged

No circularity: architecture proposal with empirical evaluation

full rationale

The paper describes a multi-agent LLM system (EngiAgent) with a fully-connected coordinator for engineering problem solving and reports empirical feasibility gains across four domains. No mathematical derivation chain, fitted parameters, or self-referential definitions exist. Claims rest on experimental comparisons to baselines rather than reducing to inputs by construction, self-citations, or ansatzes. The verification step is an explicit design choice whose reliability is an external empirical question, not a definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the background assumption that LLMs possess strong reasoning and code-generation capabilities that can be orchestrated through agent specialization and flexible routing. No free parameters or new invented entities are introduced in the abstract.

axioms (1)

domain assumption Large language models have strong capabilities in reasoning and code generation but often fail to ensure feasibility in engineering tasks.
Stated directly in the abstract as the motivation for the work.

pith-pipeline@v0.9.0 · 5546 in / 1220 out tokens · 29560 ms · 2026-05-09T16:29:36.753161+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

31 extracted references · 3 canonical work pages

[1]

Antunes, L

URL https://proceedings.mlr.press/ v235/ahmaditeshnizi24a.html. Antunes, L. M., Butler, K. T., and Grau-Crespo, R. Crystal structure generation with autoregressive large language modeling.Nature Communications, 15(1):10570, 2024. Astorga, N., Liu, T., Xiao, Y ., and van der Schaar, M. Auto- formulation of mathematical optimization models using LLMs. InFor...

2024
[2]

Anderson, B

Association for Computational Linguistics. ISBN 979-8-89176-189-6. doi: 10.18653/v1/2025.naacl-long

work page doi:10.18653/v1/2025.naacl-long 2025
[3]

The CoT collection: Improving zero-shot and few-shot learning of language models via chain-of- thought fine-tuning

URL https://aclanthology.org/2025. naacl-long.342/. Buehler, M. J. Mechgpt, a language-based strategy for mechanics and materials modeling that connects knowl- edge across scales, disciplines, and modalities.Applied Mechanics Reviews, 76(2):021001, 2024. Cemri, M., Pan, M. Z., Yang, S., Agrawal, L. A., Chopra, B., Tiwari, R., Keutzer, K., Parameswaran, A....

work page doi:10.18653/v1/2023.emnlp-main 2025
[4]

arXiv preprint arXiv:2504.18765 (2025)

URL https://aclanthology.org/2023. emnlp-main.574/. Jiang, X., Wang, W., Tian, S., Wang, H., Lookman, T., and Su, Y . Applications of natural language processing and large language models in materials discovery.npj Computational Materials, 11(1):79, 2025. Liang, Y ., Wu, C., Song, T., Wu, W., Xia, Y ., Liu, Y ., Ou, Y ., Lu, S., Ji, L., Mao, S., et al. Ta...

work page arXiv 2023
[5]

,8): Wt +G (1) t +G (2) t +H t =D t +C t

Hourly power balance (fort= 1, . . . ,8): Wt +G (1) t +G (2) t +H t =D t +C t
[6]

Conventional generator block limits: G(1) t =G (1) t,1 +G (1) t,2 ,0≤G (1) t,1 ≤120,0≤G (1) t,2 ≤120, G(2) t =G (2) t,1 +G (2) t,2 ,0≤G (2) t,1 ≤80,0≤G (2) t,2 ≤80
[7]

,8): G(1) t −G (1) t−1 ≤200, G (1) t−1 −G (1) t ≤180, G(2) t −G (2) t−1 ≤150, G (2) t−1 −G (2) t ≤130

Conventional generator ramping limits (fort= 2, . . . ,8): G(1) t −G (1) t−1 ≤200, G (1) t−1 −G (1) t ≤180, G(2) t −G (2) t−1 ≤150, G (2) t−1 −G (2) t ≤130
[8]

Wind availability bound: 0≤W t ≤ W t
[9]

Storage SOC dynamics, bounds, and initial condition: SOC t =SOC t−1 +η cCt − 1 ηd Ht,0≤SOC t ≤200, SOC 0 = 100
[10]

system architect

Storage power limits and charge/discharge exclusivity: 0≤C t ≤200u t,0≤H t ≤200v t, u t +v t ≤1, u t, vt ∈ {0,1}. 15 EngiAgent: Fully Connected Coordination of LLM Agents for Solving Open-ended Engineering Problems with Feasible Solutions 0 10 20 30 40 50 60 70 Constraints 0.00 0.02 0.04 0.06 0.08 0.10Density Constraints 0 20 40 60 80 100 Parameters 0.00 ...
[11]

This is the foundation of modeling

**Information Extraction (Information Extraction) **: Your goal is to identify all " atomic" information needed for modeling - entities, numerical values, relationships, and goals. This is the foundation of modeling
[12]

dress" these

**Domain-specific Reasoning (Domain-specific Reasoning) **: You need to "dress" these " atomic" pieces of information with "domain clothing". Using professional engineering knowledge, transform raw data into meaningful parameters, convert relationships into physical or logical constraints, and select the most appropriate modeling paradigm
[13]

A **core optimization goal ** must be clearly defined, while other goals are recognized as secondary or trade-off items

**Multi-objective Decision-making (Multi-objective Decision-making) **: You need to prioritize all goals. A **core optimization goal ** must be clearly defined, while other goals are recognized as secondary or trade-off items. This is the "compass" guiding your decisions
[14]

cracks" in the information - missing, fuzzy, or variable parts. Your task is to

**Uncertainty Handling (Uncertainty Handling) **: You need to identify all "cracks" in the information - missing, fuzzy, or variable parts. Your task is to "fill" these cracks through reasonable assumptions, ensuring the integrity and certainty of the core model. 31 32### Strict Output Format: Hierarchical JSON Modeling Blueprint ### 17 EngiAgent: Fully C...
[15]

**Absolute Data Integrity **: Every valid numerical value in the original problem ** must** be present in the ‘parameters‘ list with a unique entry, and its origin must be traceable through the ‘source_reference‘ field
[16]

**Mandatory Internal References **: Cross-references within JSON are mandatory. For example, ‘sensitivity_factors‘ must reference ‘param_id‘ of ‘parameters‘; ‘ key_assumptions‘’s ‘impact_on_model‘ must explicitly point to a specific element in ‘ core_model_elements‘. This ensures traceability and consistency of the model
[17]

It must be a model that can be independently solved and clearly defined

**Core Model Priority **: ‘core_model_elements‘ is the cornerstone. It must be a model that can be independently solved and clearly defined. All supplementary, trade-off, and uncertainty analyses are based on it in ‘extended_analysis_and_robustness‘
[18]

Do not mix in assumptions or uncertain elements in the core model

**Clear Roles and Responsibilities **: Strictly differentiate between ‘ core_model_elements‘ (what they do) and ‘extended_analysis_and_robustness‘ (how to do it better/more robustly). Do not mix in assumptions or uncertain elements in the core model
[19]

[...]" or

**Designed for Code Generation **: All mathematical expressions (‘expression‘) must use standard, unambiguous mathematical notation so that downstream agents can easily parse and convert them into code. """ C.2. Modeler The Modeler prompt focuses on translating structured problem formulations into executable Pyomo optimization code. It employs domain-spec...
[20]

Complete imports: ‘from pyomo.environ import *‘
[21]

All parameter data with realistic values (no [...] placeholders)
[22]

Complete ConcreteModel() definition with ALL variables from JSON
[23]

Complete Objective function (maximize/minimize something meaningful)
[24]

ALL constraint definitions from the JSON properly implemented
[25]

Complete solver setup and solve() call
[26]

" 3if self.consecutive_verification_failures > 8: 4tolerance_adjustment =

Result extraction and printing 107 108 **VERIFICATION CHECKLIST - Your code must pass ALL these checks: ** 109Does it import pyomo.environ? 110Does it create a ConcreteModel()? 111Does it define ALL variables mentioned in the JSON? 112Does it implement ALL constraints from the JSON? 113Does it define a meaningful objective function? 114Does it call a solv...
[27]

**[Problem Specification] Original Engineering Problem (The Problem Specification) **: 27‘‘‘ 28{safe_original_problem} 29‘‘‘
[28]

Catastrophic

**[Solution Implementation] Engineering Model Code (The Implemented Solution) **: 31‘‘‘python 32{safe_pyomo_code} 33‘‘‘ 34 35### Core Verification Instructions: Judgment Hierarchy Based on Historical Context ### 36Please strictly follow this judgment logic to ensure your verification is context-aware. 37 38 **Step 1: Check for "Catastrophic" Errors (Deal-...
[29]

**Objective Direction Reversed **: Minimization problems implemented as maximization, or vice versa
[30]

supply-demand balance

**Core Physical/Economic Law Violations **: Complete omission of constraints that define the problem foundation, such as "supply-demand balance", "energy conservation", etc
[31]

Pragmatic Deviations

**Key Decision-Making Entities Missing **: In an obvious multi-agent game problem, the code completely fails to reflect interactions or decisions between different entities (even in simplified form). 43 44 * If any of the above is found, immediately judge as ‘FAIL‘ and stop subsequent checks. 45 * If none are found, **proceed directly to Step 2 and finall...

[1] [1]

Antunes, L

URL https://proceedings.mlr.press/ v235/ahmaditeshnizi24a.html. Antunes, L. M., Butler, K. T., and Grau-Crespo, R. Crystal structure generation with autoregressive large language modeling.Nature Communications, 15(1):10570, 2024. Astorga, N., Liu, T., Xiao, Y ., and van der Schaar, M. Auto- formulation of mathematical optimization models using LLMs. InFor...

2024

[2] [2]

Anderson, B

Association for Computational Linguistics. ISBN 979-8-89176-189-6. doi: 10.18653/v1/2025.naacl-long

work page doi:10.18653/v1/2025.naacl-long 2025

[3] [3]

The CoT collection: Improving zero-shot and few-shot learning of language models via chain-of- thought fine-tuning

URL https://aclanthology.org/2025. naacl-long.342/. Buehler, M. J. Mechgpt, a language-based strategy for mechanics and materials modeling that connects knowl- edge across scales, disciplines, and modalities.Applied Mechanics Reviews, 76(2):021001, 2024. Cemri, M., Pan, M. Z., Yang, S., Agrawal, L. A., Chopra, B., Tiwari, R., Keutzer, K., Parameswaran, A....

work page doi:10.18653/v1/2023.emnlp-main 2025

[4] [4]

arXiv preprint arXiv:2504.18765 (2025)

URL https://aclanthology.org/2023. emnlp-main.574/. Jiang, X., Wang, W., Tian, S., Wang, H., Lookman, T., and Su, Y . Applications of natural language processing and large language models in materials discovery.npj Computational Materials, 11(1):79, 2025. Liang, Y ., Wu, C., Song, T., Wu, W., Xia, Y ., Liu, Y ., Ou, Y ., Lu, S., Ji, L., Mao, S., et al. Ta...

work page arXiv 2023

[5] [5]

,8): Wt +G (1) t +G (2) t +H t =D t +C t

Hourly power balance (fort= 1, . . . ,8): Wt +G (1) t +G (2) t +H t =D t +C t

[6] [6]

Conventional generator block limits: G(1) t =G (1) t,1 +G (1) t,2 ,0≤G (1) t,1 ≤120,0≤G (1) t,2 ≤120, G(2) t =G (2) t,1 +G (2) t,2 ,0≤G (2) t,1 ≤80,0≤G (2) t,2 ≤80

[7] [7]

,8): G(1) t −G (1) t−1 ≤200, G (1) t−1 −G (1) t ≤180, G(2) t −G (2) t−1 ≤150, G (2) t−1 −G (2) t ≤130

Conventional generator ramping limits (fort= 2, . . . ,8): G(1) t −G (1) t−1 ≤200, G (1) t−1 −G (1) t ≤180, G(2) t −G (2) t−1 ≤150, G (2) t−1 −G (2) t ≤130

[8] [8]

Wind availability bound: 0≤W t ≤ W t

[9] [9]

Storage SOC dynamics, bounds, and initial condition: SOC t =SOC t−1 +η cCt − 1 ηd Ht,0≤SOC t ≤200, SOC 0 = 100

[10] [10]

system architect

Storage power limits and charge/discharge exclusivity: 0≤C t ≤200u t,0≤H t ≤200v t, u t +v t ≤1, u t, vt ∈ {0,1}. 15 EngiAgent: Fully Connected Coordination of LLM Agents for Solving Open-ended Engineering Problems with Feasible Solutions 0 10 20 30 40 50 60 70 Constraints 0.00 0.02 0.04 0.06 0.08 0.10Density Constraints 0 20 40 60 80 100 Parameters 0.00 ...

[11] [11]

This is the foundation of modeling

**Information Extraction (Information Extraction) **: Your goal is to identify all " atomic" information needed for modeling - entities, numerical values, relationships, and goals. This is the foundation of modeling

[12] [12]

dress" these

**Domain-specific Reasoning (Domain-specific Reasoning) **: You need to "dress" these " atomic" pieces of information with "domain clothing". Using professional engineering knowledge, transform raw data into meaningful parameters, convert relationships into physical or logical constraints, and select the most appropriate modeling paradigm

[13] [13]

A **core optimization goal ** must be clearly defined, while other goals are recognized as secondary or trade-off items

**Multi-objective Decision-making (Multi-objective Decision-making) **: You need to prioritize all goals. A **core optimization goal ** must be clearly defined, while other goals are recognized as secondary or trade-off items. This is the "compass" guiding your decisions

[14] [14]

cracks" in the information - missing, fuzzy, or variable parts. Your task is to

**Uncertainty Handling (Uncertainty Handling) **: You need to identify all "cracks" in the information - missing, fuzzy, or variable parts. Your task is to "fill" these cracks through reasonable assumptions, ensuring the integrity and certainty of the core model. 31 32### Strict Output Format: Hierarchical JSON Modeling Blueprint ### 17 EngiAgent: Fully C...

[15] [15]

**Absolute Data Integrity **: Every valid numerical value in the original problem ** must** be present in the ‘parameters‘ list with a unique entry, and its origin must be traceable through the ‘source_reference‘ field

[16] [16]

**Mandatory Internal References **: Cross-references within JSON are mandatory. For example, ‘sensitivity_factors‘ must reference ‘param_id‘ of ‘parameters‘; ‘ key_assumptions‘’s ‘impact_on_model‘ must explicitly point to a specific element in ‘ core_model_elements‘. This ensures traceability and consistency of the model

[17] [17]

It must be a model that can be independently solved and clearly defined

**Core Model Priority **: ‘core_model_elements‘ is the cornerstone. It must be a model that can be independently solved and clearly defined. All supplementary, trade-off, and uncertainty analyses are based on it in ‘extended_analysis_and_robustness‘

[18] [18]

Do not mix in assumptions or uncertain elements in the core model

**Clear Roles and Responsibilities **: Strictly differentiate between ‘ core_model_elements‘ (what they do) and ‘extended_analysis_and_robustness‘ (how to do it better/more robustly). Do not mix in assumptions or uncertain elements in the core model

[19] [19]

[...]" or

**Designed for Code Generation **: All mathematical expressions (‘expression‘) must use standard, unambiguous mathematical notation so that downstream agents can easily parse and convert them into code. """ C.2. Modeler The Modeler prompt focuses on translating structured problem formulations into executable Pyomo optimization code. It employs domain-spec...

[20] [20]

Complete imports: ‘from pyomo.environ import *‘

[21] [21]

All parameter data with realistic values (no [...] placeholders)

[22] [22]

Complete ConcreteModel() definition with ALL variables from JSON

[23] [23]

Complete Objective function (maximize/minimize something meaningful)

[24] [24]

ALL constraint definitions from the JSON properly implemented

[25] [25]

Complete solver setup and solve() call

[26] [26]

" 3if self.consecutive_verification_failures > 8: 4tolerance_adjustment =

Result extraction and printing 107 108 **VERIFICATION CHECKLIST - Your code must pass ALL these checks: ** 109Does it import pyomo.environ? 110Does it create a ConcreteModel()? 111Does it define ALL variables mentioned in the JSON? 112Does it implement ALL constraints from the JSON? 113Does it define a meaningful objective function? 114Does it call a solv...

[27] [27]

**[Problem Specification] Original Engineering Problem (The Problem Specification) **: 27‘‘‘ 28{safe_original_problem} 29‘‘‘

[28] [28]

Catastrophic

**[Solution Implementation] Engineering Model Code (The Implemented Solution) **: 31‘‘‘python 32{safe_pyomo_code} 33‘‘‘ 34 35### Core Verification Instructions: Judgment Hierarchy Based on Historical Context ### 36Please strictly follow this judgment logic to ensure your verification is context-aware. 37 38 **Step 1: Check for "Catastrophic" Errors (Deal-...

[29] [29]

**Objective Direction Reversed **: Minimization problems implemented as maximization, or vice versa

[30] [30]

supply-demand balance

**Core Physical/Economic Law Violations **: Complete omission of constraints that define the problem foundation, such as "supply-demand balance", "energy conservation", etc

[31] [31]

Pragmatic Deviations

**Key Decision-Making Entities Missing **: In an obvious multi-agent game problem, the code completely fails to reflect interactions or decisions between different entities (even in simplified form). 43 44 * If any of the above is found, immediately judge as ‘FAIL‘ and stop subsequent checks. 45 * If none are found, **proceed directly to Step 2 and finall...