Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:48:45

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 photography company wants to optimize the selection of photos for a new mountain photography book. The goal is to maximize the visual diversity of the book by selecting photos with different colors and mountains, while considering the constraints on the number of photos that can be included from each mountain and the total number of photos.",
  "optimization_problem": "The company needs to maximize the diversity of selected photos by choosing a set of photos that includes a variety of colors and mountains. The objective is to maximize the sum of selected photos' diversity scores, subject to constraints on the maximum number of photos per mountain and the total number of photos.",
  "objective": "maximize sum(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for diversity scores and updating business configuration logic for constraints. These changes address the OR expert's mapping gaps and missing requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define diversity scores and set appropriate limits for constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for diversity scores and updating business configuration logic for constraints. These changes address the OR expert's mapping gaps and missing requirements.

CREATE TABLE photos (
  id INTEGER,
  diversity_score FLOAT
);

CREATE TABLE photo_diversity_scores (
  photo_id INTEGER,
  diversity_score FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "photos": {
      "business_purpose": "Stores information about each photo",
      "optimization_role": "decision_variables",
      "columns": {
        "id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each photo",
          "optimization_purpose": "Used as a decision variable in optimization",
          "sample_values": "1, 2, 3"
        },
        "diversity_score": {
          "data_type": "FLOAT",
          "business_meaning": "Diversity score of the photo based on color and mountain",
          "optimization_purpose": "Objective coefficient in optimization",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "photo_diversity_scores": {
      "business_purpose": "Stores diversity scores for each photo",
      "optimization_role": "objective_coefficients",
      "columns": {
        "photo_id": {
          "data_type": "INTEGER",
          "business_meaning": "Reference to the photo ID",
          "optimization_purpose": "Links diversity score to photo",
          "sample_values": "1, 2, 3"
        },
        "diversity_score": {
          "data_type": "FLOAT",
          "business_meaning": "Diversity score of the photo",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Photos_Limit": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of photos that can be selected for the book",
    "optimization_role": "Constraint on the total number of selected photos",
    "configuration_type": "scalar_parameter"
  },
  "Max_Photos_Per_Mountain": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of photos that can be selected from each mountain",
    "optimization_role": "Constraint on the number of selected photos per mountain",
    "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": "mountain_photos",
  "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": "mountain_photos",
  "iteration": 1,
  "business_context": "A photography company is optimizing the selection of photos for a new mountain photography book. The goal is to maximize the visual diversity of the book by selecting photos with different colors and mountains, while considering constraints on the number of photos that can be included from each mountain and the total number of photos.",
  "optimization_problem_description": "The company aims to maximize the diversity of selected photos by choosing a set of photos that includes a variety of colors and mountains. The objective is to maximize the sum of selected photos' diversity scores, subject to constraints on the maximum number of photos per mountain and the total number of photos.",
  "optimization_formulation": {
    "objective": "maximize sum(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected",
    "decision_variables": "x_i, a binary variable for each photo i indicating selection (0 or 1)",
    "constraints": [
      "sum(x_i) <= Total_Photos_Limit",
      "sum(x_i for photos from mountain j) <= Max_Photos_Per_Mountain for each mountain j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "d_i": {
        "currently_mapped_to": "photo_diversity_scores.diversity_score",
        "mapping_adequacy": "good",
        "description": "Diversity score of photo i used in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Photos_Limit": {
        "currently_mapped_to": "business_configuration_logic.Total_Photos_Limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of photos that can be selected for the book"
      },
      "Max_Photos_Per_Mountain": {
        "currently_mapped_to": "business_configuration_logic.Max_Photos_Per_Mountain",
        "mapping_adequacy": "good",
        "description": "Maximum number of photos that can be selected from each mountain"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "photos.id",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if photo i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
