Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:33:39

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 pharmaceutical company wants to optimize the selection of medicines for a clinical trial based on their interactions with enzymes, aiming to maximize the overall effectiveness while minimizing adverse interactions.",
  "optimization_problem": "The goal is to select a combination of medicines that maximizes the total effectiveness score while ensuring that the total adverse interaction score does not exceed a specified limit. The effectiveness and adverse interaction scores are derived from the medicine-enzyme interactions.",
  "objective": "maximize \u2211(effectiveness_score[medicine_id] \u00d7 x[medicine_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for effectiveness and adverse interaction scores, modifying the medicine table to include FDA approval status, and adding configuration logic for maximum adverse interaction score and maximum number of medicines."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map effectiveness and adverse interaction scores for medicines",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for effectiveness and adverse interaction scores, modifying the medicine table to include FDA approval status, and adding configuration logic for maximum adverse interaction score and maximum number of medicines.

CREATE TABLE medicine_effectiveness (
  medicine_id INTEGER,
  effectiveness_score FLOAT
);

CREATE TABLE medicine_adverse_interaction (
  medicine_id INTEGER,
  adverse_interaction_score FLOAT
);

CREATE TABLE medicine (
  medicine_id INTEGER,
  FDA_approved BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "medicine_effectiveness": {
      "business_purpose": "Effectiveness scores of medicines based on enzyme interactions",
      "optimization_role": "objective_coefficients",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "effectiveness_score": {
          "data_type": "FLOAT",
          "business_meaning": "Effectiveness score of the medicine",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            0.8,
            0.9,
            0.7
          ]
        }
      }
    },
    "medicine_adverse_interaction": {
      "business_purpose": "Adverse interaction scores of medicines based on enzyme interactions",
      "optimization_role": "constraint_bounds",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "adverse_interaction_score": {
          "data_type": "FLOAT",
          "business_meaning": "Adverse interaction score of the medicine",
          "optimization_purpose": "Coefficient in the constraint",
          "sample_values": [
            0.2,
            0.3,
            0.1
          ]
        }
      }
    },
    "medicine": {
      "business_purpose": "List of medicines with FDA approval status",
      "optimization_role": "constraint_bounds",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "FDA_approved": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the medicine is FDA approved",
          "optimization_purpose": "Constraint on decision variable x[medicine_id]",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_adverse_interaction_score": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum allowed total adverse interaction score",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "max_number_of_medicines": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of medicines that can be selected",
    "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": "medicine_enzyme_interaction",
  "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": "medicine_enzyme_interaction",
  "iteration": 1,
  "business_context": "A pharmaceutical company aims to optimize the selection of medicines for a clinical trial by maximizing the overall effectiveness score while ensuring the total adverse interaction score does not exceed a specified limit and the number of selected medicines does not exceed a predefined maximum.",
  "optimization_problem_description": "Select a combination of medicines that maximizes the total effectiveness score while ensuring the total adverse interaction score is within the allowed limit and the number of selected medicines does not exceed the maximum allowed.",
  "optimization_formulation": {
    "objective": "maximize \u2211(effectiveness_score[medicine_id] \u00d7 x[medicine_id])",
    "decision_variables": "x[medicine_id] \u2208 {0, 1} (binary variable indicating whether medicine_id is selected)",
    "constraints": [
      "\u2211(adverse_interaction_score[medicine_id] \u00d7 x[medicine_id]) \u2264 max_adverse_interaction_score",
      "\u2211(x[medicine_id]) \u2264 max_number_of_medicines",
      "x[medicine_id] \u2264 FDA_approved[medicine_id] (only FDA approved medicines can be selected)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "effectiveness_score[medicine_id]": {
        "currently_mapped_to": "medicine_effectiveness.effectiveness_score",
        "mapping_adequacy": "good",
        "description": "Effectiveness score of each medicine"
      }
    },
    "constraint_bounds": {
      "max_adverse_interaction_score": {
        "currently_mapped_to": "business_configuration_logic.max_adverse_interaction_score",
        "mapping_adequacy": "good",
        "description": "Maximum allowed total adverse interaction score"
      },
      "max_number_of_medicines": {
        "currently_mapped_to": "business_configuration_logic.max_number_of_medicines",
        "mapping_adequacy": "good",
        "description": "Maximum number of medicines that can be selected"
      },
      "FDA_approved[medicine_id]": {
        "currently_mapped_to": "medicine.FDA_approved",
        "mapping_adequacy": "good",
        "description": "Indicates if the medicine is FDA approved"
      }
    },
    "decision_variables": {
      "x[medicine_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether medicine_id is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Decision variable x[medicine_id] needs to be mapped to a table or configuration logic"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Map the decision variable x[medicine_id] to a table or configuration logic"
  }
}
