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I know this was probably brought up before but I cannot find any good resources on some potential, at least theoretical way of achieving this.
So basically I have a lot of UTXOs whose value is between lets say 1k sats and 5k sats and I want to transfer them all into a single UTXO.
With current fee rates of 15sats/byte I would barely break even in the best case scenario.
Is there any strategy or algorithm that could help with this kind of issue?
There's no free lunch. You can spend all the UTXOs in one transaction to spread the output bytes across many inputs, but each input still needs a certain number of bytes. To my knowledge, there isn't any more efficient way of spending them than the standard transaction types. (If there were, it would be the standard.)
You can of course attach a fee below the current prevailing rate, and hope that the transaction gets picked up during some period of low transaction demand (when fees drop), or wait until such a time to broadcast your transaction. Certain times of day or days of the week may be somewhat better; you could look back at historical transaction fees to get a sense. But there's no guarantee that such a low-fee transaction will get confirmed.
Depending on your time-restraints, you either have to pay the market's current fee rate, or wait until the block space demand is low enough to include your transaction at a much lower fee rate. Nate did a good job at describing that.
I wanted to add that there is an on-going discussion to generally lower the minFeeRate, so if you can be very patient, your transaction may eventually relay and get mined even paying a fee rate below 1 satoshi per byte. See: https://github.com/bitcoin/bitcoin/pull/13922, https://github.com/bitcoin/bitcoin/pull/13990
