Goal programming

For now I'm going to stick with the linear programming model of the diet problem that I've been talking about

minimize carbohydrates
subject to constraints on
protein
calorie intake
calories from fat
sodium
etc, etc

But there is an alternative modeling technique (which I might try later) called goal programming.

In goal programming I'd want to minimize deviations from goals where the goals are various intake levels of
carbohydrates
protein
calories
calories from fat
sodium

I'm already doing that to some extent in my linear programming model by introducing slack variables to allow for exceeding or falling short of various levels of nutrients and mathematically treating these slack variables as "foods" with very high carb counts. That's just a mathematical modeling trick to allow the solution algorithm to work even in situations where the constraints are at odds with each other and a feasible solution that meets all the constraints can't be found.

So changing the model to a goal programming model rather than a linear programming model isn't going to be a big leap, but I'm not going to do it for a couple of weeks. I'll be thinking about it though.