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```python
# AI Dev Tool: FastAPI PostgreSQL Vector Search Extension Boilerplate
# ================================================================
# This is a production-ready developer code asset for building fast and scalable vector search APIs.
# It leverages the power of FastAPI, PostgreSQL, and the PostgreSQL Vector Search Extension.

from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.encoders import jsonable_encoder
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
import psycopg2.extras
import json

# Define the FastAPI application
app = FastAPI()

# Define the PostgreSQL connection settings
POSTGRES_HOST = "localhost"
POSTGRES_DB = "vector_search"
POSTGRES_USER = "postgres"
POSTGRES_PASSWORD = "postgres"

# Define the VectorSearch model
class VectorSearch(BaseModel):
    id: int
    vector: List[float]
    metadata: Optional[dict]

# Define the PostgreSQL connection function
def get_postgres_connection():
    try:
        return psycopg2.connect(
            host=POSTGRES_HOST,
            database=POSTGRES_DB,
            user=POSTGRES_USER,
            password=POSTGRES_PASSWORD
        )
    except psycopg2.OperationalError as e:
        raise

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