So Regtest as it says here on official bitcoin Developer notes. https://bitcoin.org/en/developer-examples#regtest-mode
Bitcoin Core’s regression test mode (regtest mode) lets you instantly
create a brand-new private block chain with the same basic rules as
testnet—but one major difference: you choose when to create new
blocks, so you have complete control over the environment.
Start bitcoind in regtest mode to create a private block chain.
## Bitcoin Core 0.10.1 and earlier
bitcoin-cli -regtest setgenerate true 101
## Bitcoin Core master (as of commit 48265f3)
bitcoin-cli -regtest generate 101
So on Regtest mode you do NOT need to mine with an ASIC. It is like testnet but you decide when to and how many blocks to generate for your testing.
Hope this helps.
EDIT: Old Post below, as missed the regtest part of the config file
Yes u can solo mine, but you will need to run the bitcoin client so it knows what the latest work is. I should mention that u should not be solo mining btc without at least 250TH or so hashing power from last calculation I saw with current difficulty, so u would need many ASICs for this.
Otherwise your conf file and connection string look ok.