A new parameterisation approach for mixed-integer optimisation

Mixed-integer problems represent a wide class of industrial optimization applications. We speak about "mixed-integer" optimization problem when the design variables are of type discrete and continuous together. In particular, we are interested in a class of problems for which the (integer) number of design variables is an optimization variable itself. For all the optimization problems, the selection of the number of design variables represents a basic assumption, and the final solution of the problem is largely influenced by this choice. Indeed, different solutions may be obtained with different parametrisation schemes of the same problem. In this paper, a strategy for tackling and solve a problem with an unprescribed number of design variables is presented. The number of the design variables and their values will be defined implicitly, by adopting a rearrangement of the data structure, eliminating the direct definition of the number of design variables and their values: the number of design variables is simply limited in between two extreme values, and it will represents a part of the outcome of the optimization problem.