Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:27:59

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 high school wants to maximize the overall happiness of its students by strategically pairing them as friends, considering their existing friendships and likes. The goal is to ensure that students are paired with those they like, while also maintaining a balanced number of friends per student.",
  "optimization_problem": "The objective is to maximize the total happiness score, which is calculated based on the number of likes between paired friends. Constraints include ensuring each student has a minimum and maximum number of friends, and that friendships are mutual.",
  "objective": "maximize \u2211(happiness_score[student_id, friend_id] * x[student_id, friend_id]) where happiness_score is 1 if student_id likes friend_id, else 0",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a HappinessScore table to map likes between students, and moving max_friends and min_friends to business_configuration_logic.json. The Friend table is modified to ensure mutual friendships."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define max_friends and min_friends parameters and complete happiness_score mapping",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a HappinessScore table to map likes between students, and moving max_friends and min_friends to business_configuration_logic.json. The Friend table is modified to ensure mutual friendships.

CREATE TABLE HappinessScore (
  student_id INTEGER,
  friend_id INTEGER,
  score INTEGER
);

CREATE TABLE Friend (
  student_id INTEGER,
  friend_id INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "HappinessScore": {
      "business_purpose": "Maps happiness scores between student pairs based on likes",
      "optimization_role": "objective_coefficients",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the student",
          "optimization_purpose": "Identifies the student in the happiness score pair",
          "sample_values": "1, 2, 3"
        },
        "friend_id": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the friend",
          "optimization_purpose": "Identifies the friend in the happiness score pair",
          "sample_values": "2, 3, 1"
        },
        "score": {
          "data_type": "INTEGER",
          "business_meaning": "Happiness score (1 if student likes friend, else 0)",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1, 0, 1"
        }
      }
    },
    "Friend": {
      "business_purpose": "Represents mutual friendships between students",
      "optimization_role": "decision_variables",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the student",
          "optimization_purpose": "Identifies the student in the friendship pair",
          "sample_values": "1, 2, 3"
        },
        "friend_id": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the friend",
          "optimization_purpose": "Identifies the friend in the friendship pair",
          "sample_values": "2, 3, 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_friends": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of friends a student can have",
    "optimization_role": "Upper bound constraint for friendship count",
    "configuration_type": "scalar_parameter"
  },
  "min_friends": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of friends a student must have",
    "optimization_role": "Lower bound constraint for friendship count",
    "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": "network_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": "network_1",
  "iteration": 1,
  "business_context": "A high school aims to maximize student happiness by pairing them as friends based on mutual likes, ensuring each student has a balanced number of friends within specified limits.",
  "optimization_problem_description": "Maximize the total happiness score by pairing students as friends, subject to constraints on the minimum and maximum number of friends per student and ensuring mutual friendships.",
  "optimization_formulation": {
    "objective": "maximize \u2211(happiness_score[student_id, friend_id] * x[student_id, friend_id])",
    "decision_variables": "x[student_id, friend_id] \u2208 {0, 1} (binary variable indicating if student_id is paired with friend_id)",
    "constraints": [
      "\u2211(x[student_id, friend_id]) \u2265 min_friends \u2200 student_id (minimum friends constraint)",
      "\u2211(x[student_id, friend_id]) \u2264 max_friends \u2200 student_id (maximum friends constraint)",
      "x[student_id, friend_id] = x[friend_id, student_id] \u2200 student_id, friend_id (mutual friendship constraint)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "happiness_score[student_id, friend_id]": {
        "currently_mapped_to": "HappinessScore.score",
        "mapping_adequacy": "good",
        "description": "Happiness score between student_id and friend_id"
      }
    },
    "constraint_bounds": {
      "min_friends": {
        "currently_mapped_to": "business_configuration_logic.min_friends",
        "mapping_adequacy": "good",
        "description": "Minimum number of friends a student must have"
      },
      "max_friends": {
        "currently_mapped_to": "business_configuration_logic.max_friends",
        "mapping_adequacy": "good",
        "description": "Maximum number of friends a student can have"
      }
    },
    "decision_variables": {
      "x[student_id, friend_id]": {
        "currently_mapped_to": "Friend.student_id, Friend.friend_id",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if student_id is paired with friend_id",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
