Does anyone know a formula that can be used to calculate the optimal box volume and tuning frequency for a particular subwoofer using the T/S parameters given by the manufacturer?

Optimal is given by the manufacturer!

Optimal is given by the manufacturer!

Not necessarily.

Anyways..."optimal" is a matter of opinion. There are advantages, disadvantages and trade-offs involved with all of the various alignments and a single formula is not going to be comprehensive enough to encompass all of these various factors. What's optimal for one driver or one goal may not be optimal for a different driver or a different goal. This is one of the main reasons you hear things like "you can't model a Fi BTL". You can, the physics are the same. The problem is that when you run the driver's parameters through the formulas for "optimal" enclosures meeting certain target curves such as flat frequency response, the results are nonsensical simply because the driver's parameters don't allow it to meet those target curves. Or if the formula you are using is the formula for optimally flat frequency response, you may be trading off low end extension or end up with too much low end extension for the environment, in which case that "optimally flat frequency response" won't be optimally flat in the actual environment.

If you really want to know formulas, DIY Subwoofers has a lot of various formulas to sift through. Being a big proponent of empirical analysis, I find formulas extremely useful. However, when dealing with things like ported enclosures it's best to not focus or limit yourself by the formulas themselves but instead use an accurate analysis tool, such as an enclosure modeling program, to design boxes based on the given set of goals you are trying to achieve.

Thank You, any ides on what type of alignment these formulas would be optimal for(flat frequency response..etc.)?

The one I linked to was for flat response. There are several others on that website.