I have some good news for you: For your goals, likely you do not have to wait for P = NP, even if it is true. Or, for your goals, you do not need the extreme

I have some good news for you: For your goals, likely you do not have to wait for P = NP, even if it is true. Or, for your goals, you do not need the extreme guarantees of P = NP, that is, guaranteed polynomial solutions for ALL your problems in NP, even the worst case that can exist. Instead, likely you can make nearly all the progress you have in mind with some techniques that just happen to work well for your class of problems. This is what the history shows. That is, people have been doing well solving NP-complete problems well enough for decades without worrying about P versus NP. So, learn some of what has been done, as I outlined and more, and then add to that material in ways important for your problems. Just MUST realize that the question of P versus NP has been formulated in a way that makes it often shockingly far from getting valuable results in practice. How can this be? Heavily because the P versus NP question concentrates on the worst cases that can exist, and the average cases in practice can be much, MUCH easier. For more, pay close attention to the Department of Combinatorics and Optimization at Waterloo and Nemhauser's department at Georgia Tech. Generally it will be tough for me to believe that the field of DNA biology has much knowledge of that material if only because very few people do. Indeed, your desire for P = NP does indicate that your field lets the P versus NP question keep it from going after the field's holy grail, likely for no good reason. Each protein you can correctly fold, each valuable molecule you can create, can be a big step ahead, even without P = NP. Net, f'get about P versus NP. Next, as I outlined, even if tomorrow someone shows an algorithm that shows P = NP, there is no guarantee that that algorithm will be 'fast'. Instead, something with integer linear programming, touched up with various techniques, might solve nearly all your problems plenty well and be much faster. Indeed, as in the classic Klee and Minty paper, the simplex algorithm is not polynomial but in practice it totally knocks the socks off the polynomial interior point algorithms. To be more clear, classic simplex runs in 3m where m is the number of constraints and we get to ignore the number of columns. So, classic simplex runs, in practice, faster than a polynomial of degree 1 in the size of the input data. Still, it's 'exponential' in worst case. There are more details on why in a classic paper by K. Borgward. The polynomial algorithms for linear programming are way too slow for practice. So, I'm not just blowing smoke here: DO work on your problems but F'GET about P versus NP.