He's mostly smoking funny stuff: He's talking applications of optimization. Okay. Optimization contributes problems, e.g., integer linear programming, in set NP-complete only if one insists on exact optimality down to the last tiny fraction of a penny of cost in the worst problems that can occur, even in principle, in execution time that grows no faster than a polynomial in the size of the problem. That's a LOT of very special and quite unrealistic context.

E.g., it's not the least bit clear that finance needs to attack the worst case problems. Even if so, finance, anywhere close to reality, doesn't need to get solutions that save all of the last tiny fraction of a penny.

If relax worst case problems and saving the last tiny fraction of a penny, then the situation is MUCH different. E.g., once I got a feasible solution to an ILP with 40,000 constraints and 600,000 variables within 0.025% of optimality on a 90 MHz Intel processor in 905 seconds. More generally, here's an easy approach to the ILP problems: Just drop the integer constraints, solve with LP, and then round to integer values. For the LP solution, if insist, then use a polynomial LP solver. Crude? Sometimes. Always crude? No.

He's making a common mistake: He's assuming that because in general ILP is in NP-complete that good work on all practical ILP problems has to be too challenging, and that's nonsense.