Counterintuitively, numerical optimizations are easiest (though rarely actually easy) when all of the variables are continuous and can take any value. When integer variables enter the mix, optimization becomes much, much harder. This typically happens when the optimization is constrained by a limited selection of objects, for example packages in a weight-limited cargo shipment, or stocks in a portfolio constrained by sector weightings and transaction costs. For tasks like these, you often need an algorithm for a specialized type of optimization: Mixed Integer Programming.
For problems like these, Dirk Schumacher has created the ompr package for R. This package provides a convenient syntax for describing the variables and contraints in an optimization problem. For example, take the classic “knapsack” problem of maximizing the total value of objects in a container subject to its maximum weight limit.
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