Assuming you have the MQTT server on the PI then put the IP address of the PI as the broker address in HA and the same address as the server IP in the Ardruino, so in your case that would be 192.168.1.111 for both :), since both talk to the broker/server.
2017-07-20 15:27:28 ERROR (MainThread) [homeassistant.setup] Error during setup of component mqtt
Traceback (most recent call last):
File “/srv/homeassistant/lib/python3.4/site-packages/homeassistant/setup.py”, line 187, in _async_setup_component
result = yield from component.async_setup(hass, processed_config)
File “/srv/homeassistant/lib/python3.4/site-packages/homeassistant/components/mqtt/init.py”, line 377, in async_setup
success = yield from hass.data[DATA_MQTT].async_connect()
File “/srv/homeassistant/lib/python3.4/site-packages/homeassistant/components/mqtt/init.py”, line 487, in async_connect
self._mqttc.connect, self.broker, self.port, self.keepalive)
File “/usr/lib/python3.4/asyncio/futures.py”, line 388, in iter
yield self # This tells Task to wait for completion.
File “/usr/lib/python3.4/asyncio/tasks.py”, line 286, in _wakeup
value = future.result()
File “/usr/lib/python3.4/asyncio/futures.py”, line 277, in result
raise self._exception
File “/usr/lib/python3.4/concurrent/futures/thread.py”, line 54, in run
result = self.fn(*self.args, **self.kwargs)
File “/home/homeassistant/.homeassistant/deps/paho/mqtt/client.py”, line 700, in connect
return self.reconnect()
File “/home/homeassistant/.homeassistant/deps/paho/mqtt/client.py”, line 822, in reconnect
sock = socket.create_connection((self._host, self._port), source_address=(self._bind_address, 0))
File “/usr/lib/python3.4/socket.py”, line 509, in create_connection
raise err
File “/usr/lib/python3.4/socket.py”, line 500, in create_connection
sock.connect(sa)
ConnectionRefusedError: [Errno 111] Connection refused
Since you have followed BRUHs video, you should also follow his video on setting up Mosquitto as that’s what he uses as the broker/server. It looks to me like you are trying to use the internal MQTT broker but you can’t do that with the settings you have put in HA.