Abstract
The problems in this chapter are classical examples of integer programs (IP). A better name would be discrete linear programs because we described the past ones as continuous linear programs and the antonym of continuous is discrete. Alas, the tradition is firmly entrenched so we will refer to them as IPs. They are characterized by algebraically linear constraints and linear objectives with the additional requirement that variables must take on only integral values.
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- 1.
This might be a case, in the words of Wigner, of the unreasonable effectiveness of mathematics in the natural sciences; or more prosaically, because we mostly solve problems that we know how to solve.
- 2.
There are cases where a binary choice -1, 1 would make the model simpler. Alas, no popular integer solver offers that option.
- 3.
- 4.
The interested reader should search “branch and bound” to start reading about the solution techniques.
- 5.
No other fractions are possible in a pure set cover problem for fascinating reasons the reader is encouraged to research (keyword search: half-integrality).
- 6.
For the theoretically minded, this is a case of dual-degeneracy.
- 7.
The symmetry stems from visualizing the search tree and noticing that there are multiple branches with exactly the same structure and value.
- 8.
Whether the trace comes back to the origin is irrelevant from a complexity standpoint. We can assume a distance zero between Vcc and Vee if need be.
- 9.
See www.math.uwaterloo.ca/tsp/concorde.html for instance
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© 2018 Serge Kruk
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Kruk, S. (2018). Classic Discrete Models. In: Practical Python AI Projects. Apress, Berkeley, CA. https://doi.org/10.1007/978-1-4842-3423-5_5
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DOI: https://doi.org/10.1007/978-1-4842-3423-5_5
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