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This note discusses properties of parametric discrete-time Mixed-Integer Optimal Control Problems (MIOCPs) as they often arise in mixed-integer NMPC. We argue that in want for a handle on similarity properties of parametric MIOCPs the classical turnpike notion from optimal control is helpful. We provide sufficient turnpike conditions based on a dissipativity notion of MIOCPs, and we show that the turnpike property allows specific and accurate guesses for the integer-valued controls. Moreover, we show how the turnpike property can be used to derive efficient node-weighted branch-and-bound schemes tailored to parametric MIOCPs. We draw upon numerical examples to illustrate our findings.

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We have written computer programs to determine exactly the coefficients in Wright's formula for f(n, n + k ) . the number of connected sparsely edged labeled graphs (see preceding paper), and used them up to k=24. We give the results up to k = 7 .