Are there strategies/rules/systematic approaches to derive alternative formulations for an optimization problem?

For a given optimization problem there are often many known math programming formulations. For example for the TSP here is a survey https://link.springer.com/chapter/10.1007/3-540-36626-1_5 of many different formulations, that all describe the same problem, sometimes in lifted spaces.

Often there is an "intuitive way" of modeling a problem. For example for the knapsack problem the single constraint formulation is the first things that comes to my mind. But there are alternative formulations in extended spaces, which do not come to my mind straightforward.

Are there strategies/rules/systematic approaches to derive "alternative formulation"? Is there literature on this?

• Mathematical modelling is more than science, it's an art. The more you do, the better you get. Deriving non-trivial models normally requires spending quite a lot of time. Of course, in theory we can have many alternative formulations by slight modifications. This is not what you want. – r.beigi Jan 16 at 23:15