...problem.
The travelling salesman problem is to find the shortest route which starts at a certain point, visits a given set of destinations (customers), and returns to the starting point at the end.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...logic
technically called Horn clauses
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...weightings.
The intervals returned from ria are much narrower than this, but for this paper I have reduced the output to three significant figures.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...number.
Using the Simplex or Dual Simplex algorithms this cost goes up, in the worst case, exponentially with the number of constraints and variables.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...search.
Technically they are rarely facet-inducing cuts.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...goal.
The variable M denotes the module in which writeln is defined.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```
...library.
The fd library automatically loads the suspend library, so it is not actually necessary to load suspend explicitly.
```.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
```

Joachim Schimpf
Wed Sep 3 18:07:19 BST 1997