Well of course, it's a big company - people are coming in such companies to be safe and in a mass. They are not keen to make something disrupting.
Of course, some employees would be happy to achieve a success with their innovation, but it's not easy at all - because it's a big company...
Big companies have rules and the hierachy (birocracy), so it's not easy that the right idea would be heard from right people.
Right way is surely building of innovation climate in every department and assuring the continues presence of innovation news to employees.
Next issue is, that's not easy to spot an innovator in large firms - because they would be in a mass where most of people aren't innovative.
Essential thing is that in big companies, not everyone will be closely connected with the customer. Thatswhy this part of manpower will have less opportunity for ideas, or to even know for which kind of ideas are his/her company looking for? Here the solution is to link customer-connected employees with at least innovation manager, who can propagate the customer wishes to innovative power of every company - it's employees.