what would be the best solution for decreasing transaction fees to rational level? Rational being that it could be rational to use these transactions in every day payments.
One solution exists already (Segwit 4MB blocks), but it's not fully adopted yet. It will take time for Segwit to have it's full impact on fee reduction, as the majority of everyday payments on the Bitcoin Network must be using Segwit addresses for it to work most effectively. Every time the old addresses are used, they consume 2-4x the block weight that Segwit transactions do, limiting blocksize closer to the old 1MB max (which is still in place for old style transactions). So, start using Segwit wallet software and Segwit addresses ASAP to help accelerate the process, and encourage others to do the same.
Really though, 2nd layer networks are the ultimate solution to high fees and the transaction rate. The big mistake that all the on-chain scaling advocates make is that their position is fundamentally untenable, as on-chain scaling isn't actually possible any time soon (certainly not with today's internet, and some argue that it will never be feasible).
On-chain is also not suitable for regular everyday purchases, you can't buy a cup of coffee then wait between 1 and 60 minutes for the transaction to clear, coffee shops and stands could have huge queues of people waiting for their coffee for the next block to get mined so that their transactions confirm. Then the coffee shop has to serve all those annoyed, caffeine-starved people really quickly! (and they'll probably all be extra cranky, waiting probably made them late for something) So on-chain doesn't work well for buying things where you need a quick turn around. 2nd layer networks on top of Bitcoin can be designed to clear instantly, without having to wait for blocks to be found by miners.
And the capacity of 2nd layer Bitcoin networks can be many orders of magnitude higher than the on-chain Bitcoin network. This could take alot of strain off the on-chain, and a new price equilibrium between fees would emerge. Transaction fees for the Lightning Network, to give an example of a 2nd layer Bitcoin network, can be far lower than miners charge for on-chain, as the costs needed to run Lightning nodes is an insignificant fraction of what's needed to mine Bitcoin blocks with included transactions. There's no good reason why Lightning transactions can't have free fees (although some larger routing nodes might try to charge fees if they offered purchase insurance or some other additional service)