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```python
# AI Dev Tool: Tank Body Problem Solver with FastAPI and PostgreSQL Vector Search
# Description: A production-ready API to solve the Tank Body Problem using FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel
from typing import List
import psycopg2
from psycopg2 import Error
from psycopg2.extras import DictCursor
import numpy as np
from sentence_transformers import SentenceTransformer

# Initialize the FastAPI app
app = FastAPI()

# Define the Tank Body Problem request model
class TankBodyProblemRequest(BaseModel):
    """Request model for the Tank Body Problem"""
    tank_id: int
    body_type: str
    armor_thickness: float
    fuel_capacity: float

# Define the Tank Body Problem response model
class TankBodyProblemResponse(BaseModel):
    """Response model for the Tank Body Problem"""
    tank_id: int
    body_type: str
    armor_thickness: float
    fuel_capacity: float
    solution: str

# Initialize the PostgreSQL connection
def init_db_connection():
    """Initialize the PostgreSQL connection"""
    try:
        connection = psycopg2.connect(
            dbname="tank_body_problem

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