Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:32:41

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 camera lenses for photographing mountains based on their height and prominence, while minimizing the total cost of lenses used.",
  "optimization_problem": "The company aims to minimize the total cost of camera lenses used for photographing mountains, considering constraints on the focal length and aperture of the lenses, as well as the height and prominence of the mountains.",
  "objective": "minimize \u2211(cost_of_lens \u00d7 lens_selection_variable)",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for lenses and mountains, and updating business configuration logic to handle scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define the missing parameters and refine the constraints based on business requirements",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for lenses and mountains, and updating business configuration logic to handle scalar parameters and formulas.

CREATE TABLE lenses (
  lens_id INTEGER,
  cost FLOAT,
  focal_length_mm INTEGER,
  max_aperture FLOAT,
  selected BOOLEAN
);

CREATE TABLE mountains (
  mountain_id INTEGER,
  minimum_focal_length INTEGER,
  minimum_aperture FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "lenses": {
      "business_purpose": "camera lenses available for photographing mountains",
      "optimization_role": "objective_coefficients",
      "columns": {
        "lens_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each lens",
          "optimization_purpose": "index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost of the lens",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": [
            500.0,
            750.0,
            1000.0
          ]
        },
        "focal_length_mm": {
          "data_type": "INTEGER",
          "business_meaning": "focal length of the lens in millimeters",
          "optimization_purpose": "used in constraints",
          "sample_values": [
            24,
            50,
            85
          ]
        },
        "max_aperture": {
          "data_type": "FLOAT",
          "business_meaning": "maximum aperture of the lens",
          "optimization_purpose": "used in constraints",
          "sample_values": [
            1.8,
            2.8,
            4.0
          ]
        },
        "selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "whether the lens is selected for use",
          "optimization_purpose": "decision variable",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "mountains": {
      "business_purpose": "mountains to be photographed with their specific requirements",
      "optimization_role": "constraint_bounds",
      "columns": {
        "mountain_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each mountain",
          "optimization_purpose": "index for constraints",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "minimum_focal_length": {
          "data_type": "INTEGER",
          "business_meaning": "minimum focal length required for photographing the mountain",
          "optimization_purpose": "constraint bound",
          "sample_values": [
            24,
            50,
            85
          ]
        },
        "minimum_aperture": {
          "data_type": "FLOAT",
          "business_meaning": "minimum aperture required for photographing the mountain",
          "optimization_purpose": "constraint bound",
          "sample_values": [
            1.8,
            2.8,
            4.0
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "maximum_lenses_per_mountain": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of lenses that can be used per mountain",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "minimum_lenses_per_mountain": {
    "sample_value": 1,
    "data_type": "INTEGER",
    "business_meaning": "minimum number of lenses that must be used per mountain",
    "optimization_role": "constraint bound",
    "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 aims to optimize the selection of camera lenses for photographing mountains based on their height and prominence, while minimizing the total cost of lenses used, ensuring that the lenses meet the minimum focal length and aperture requirements for each mountain.",
  "optimization_problem_description": "The company seeks to minimize the total cost of camera lenses used for photographing mountains, subject to constraints on the focal length and aperture of the lenses, as well as the minimum and maximum number of lenses that can be used per mountain.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_of_lens[lens_id] \u00d7 lens_selection_variable[lens_id, mountain_id])",
    "decision_variables": "lens_selection_variable[lens_id, mountain_id]: binary variable indicating whether lens l is selected for mountain m",
    "constraints": [
      "\u2211(lens_selection_variable[lens_id, mountain_id]) \u2265 minimum_lenses_per_mountain for each mountain_id",
      "\u2211(lens_selection_variable[lens_id, mountain_id]) \u2264 maximum_lenses_per_mountain for each mountain_id",
      "focal_length_mm[lens_id] \u2265 minimum_focal_length[mountain_id] for each lens_id and mountain_id",
      "max_aperture[lens_id] \u2265 minimum_aperture[mountain_id] for each lens_id and mountain_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_of_lens[lens_id]": {
        "currently_mapped_to": "lenses.cost",
        "mapping_adequacy": "good",
        "description": "cost of each lens"
      }
    },
    "constraint_bounds": {
      "minimum_focal_length[mountain_id]": {
        "currently_mapped_to": "mountains.minimum_focal_length",
        "mapping_adequacy": "good",
        "description": "minimum focal length required for each mountain"
      },
      "minimum_aperture[mountain_id]": {
        "currently_mapped_to": "mountains.minimum_aperture",
        "mapping_adequacy": "good",
        "description": "minimum aperture required for each mountain"
      },
      "maximum_lenses_per_mountain": {
        "currently_mapped_to": "business_configuration_logic.maximum_lenses_per_mountain",
        "mapping_adequacy": "good",
        "description": "maximum number of lenses that can be used per mountain"
      },
      "minimum_lenses_per_mountain": {
        "currently_mapped_to": "business_configuration_logic.minimum_lenses_per_mountain",
        "mapping_adequacy": "good",
        "description": "minimum number of lenses that must be used per mountain"
      }
    },
    "decision_variables": {
      "lens_selection_variable[lens_id, mountain_id]": {
        "currently_mapped_to": "lenses.selected",
        "mapping_adequacy": "partial",
        "description": "whether lens l is selected for mountain m",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Mapping for lens_selection_variable[lens_id, mountain_id] needs to be refined to include mountain_id"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping for lens_selection_variable to include mountain_id and ensure it is properly defined as a binary variable for each lens-mountain pair."
  }
}
