Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:26:33

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A platform wants to maximize the overall trust-weighted ratings of reviews by assigning optimal weights to reviews based on the trust levels between users.",
  "optimization_problem": "The platform aims to maximize the sum of trust-weighted ratings of reviews, where the weight of each review is determined by the trust level between the reviewer and the user. The decision variables are the weights assigned to each review, and constraints ensure that the weights are non-negative and do not exceed the trust levels.",
  "objective": "maximize \u2211(trust_weight[u_id, a_id] \u00d7 rating[a_id, i_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding a trust_weight table for decision variables, updating the review table to include optimization-relevant data, and moving scalar parameters to business_configuration_logic.json."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the constraints and ensure all necessary data is available for the optimization model",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a trust_weight table for decision variables, updating the review table to include optimization-relevant data, and moving scalar parameters to business_configuration_logic.json.

CREATE TABLE trust_weight (
  weight FLOAT
);

CREATE TABLE review (
  rating FLOAT
);

CREATE TABLE trust (
  trust FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "trust_weight": {
      "business_purpose": "Stores the trust weights assigned to reviews",
      "optimization_role": "decision_variables",
      "columns": {
        "weight": {
          "data_type": "FLOAT",
          "business_meaning": "The weight assigned to a review based on trust",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "review": {
      "business_purpose": "Stores review data including ratings",
      "optimization_role": "objective_coefficients",
      "columns": {
        "rating": {
          "data_type": "FLOAT",
          "business_meaning": "The rating of the review by the author",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "4.5, 3.8, 5.0"
        }
      }
    },
    "trust": {
      "business_purpose": "Stores trust levels between users",
      "optimization_role": "constraint_bounds",
      "columns": {
        "trust": {
          "data_type": "FLOAT",
          "business_meaning": "The trust level between the source and target user",
          "optimization_purpose": "Bound in the constraints",
          "sample_values": "0.6, 0.8, 1.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "trust_weight_upper_bound": {
    "sample_value": 1.0,
    "data_type": "FLOAT",
    "business_meaning": "The maximum allowable trust weight for a review",
    "optimization_role": "Upper bound constraint for trust weights",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "epinions_1",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "epinions_1",
  "iteration": 1,
  "business_context": "A platform aims to maximize the overall trust-weighted ratings of reviews by assigning optimal weights to reviews based on the trust levels between users, ensuring the weights are non-negative and do not exceed the trust levels.",
  "optimization_problem_description": "Maximize the sum of trust-weighted ratings of reviews, where the weight of each review is determined by the trust level between the reviewer and the user. The decision variables are the weights assigned to each review, and constraints ensure that the weights are non-negative and do not exceed the trust levels.",
  "optimization_formulation": {
    "objective": "maximize \u2211(weight[u_id, a_id] \u00d7 rating[a_id, i_id])",
    "decision_variables": "weight[u_id, a_id] (continuous)",
    "constraints": [
      "weight[u_id, a_id] \u2265 0 for all u_id, a_id",
      "weight[u_id, a_id] \u2264 trust[u_id, a_id] for all u_id, a_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "rating[a_id, i_id]": {
        "currently_mapped_to": "review.rating",
        "mapping_adequacy": "good",
        "description": "The rating of the review by the author"
      }
    },
    "constraint_bounds": {
      "trust[u_id, a_id]": {
        "currently_mapped_to": "trust.trust",
        "mapping_adequacy": "good",
        "description": "The trust level between the source and target user"
      }
    },
    "decision_variables": {
      "weight[u_id, a_id]": {
        "currently_mapped_to": "trust_weight.weight",
        "mapping_adequacy": "good",
        "description": "The weight assigned to a review based on trust",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
