The local projectThe orienteering problem, starting from Benfleet station
A distance budget, 108 bus stops, and a walk that must end where it began.
From OpenStreetMap the learner downloads the roads in a box around Thundersley and South Benfleet, 858 mapped roads making a network of 145.9 km, and the 108 bus stops inside the same box. The agent's walk starts and finishes at Benfleet railway station. To make the choice interesting, we set a scoring rule of our own: a stop less than 1 km from the station in a straight line is worth 10 points, a stop 1 to 2 km away is worth 20, and anything further is worth 30. That gives 14 stops at 10 points, 15 at 20 and 79 at 30, and 2,810 points on offer. All distances walked are measured along the roads. Stops on opposite sides of a road often attach to the same point on the network, so one visit can collect a pair.
The learner codes four planners. The first always walks to the closest unvisited stop. The second goes for the stop offering the most points per metre from where it stands. Both check that they can still get back to the station. The third builds the loop differently: it starts with an empty round trip and keeps inserting whichever stop adds the most points per extra metre, then untangles the route so it does not cross itself. The fourth takes that result and spends 300 rounds removing three stops at random, re-inserting what fits, and keeping the change whenever the score is no worse.
Points collected on a round trip from Benfleet station, by distance budget (our Python run on OpenStreetMap data; scores use our own rule)| Budget | Closest stop next | Most points per metre | Insert and tidy | Remove and repair |
|---|
| 4 km | 200 | 220 | 220 | 220 |
| 6 km | 330 | 330 | 340 | 390 |
| 8 km | 630 | 820 | 620 | 840 |
| 10 km | 780 | 980 | 1,010 | 1,020 |
No simple rule wins everywhere. With 8 km to spend, points per metre collected 820 points from 39 stops, well ahead of the closest-stop rule on 630. The insert and tidy planner, which sounds more sophisticated, managed only 620 at that budget, fewer than the simplest rule: it spent its distance on 12 ten-point and 13 twenty-point stops and reached only 8 of the thirty-point ones, where points per metre reached 15. At 10 km it came out ahead of both simple rules with 1,010. Remove and repair finished first or level first at every budget, reaching 840 at 8 km and 1,020 at 10 km. We do not know the true maximum for any row. For problems of this kind no quick method is known that guarantees it, which is exactly why the comparison is worth running.
Ages 8 to 11
Plan a paper treasure hunt with a string of fixed length and see who can collect the most points.
Ages 11 to 15
Code the two simple rules in Python and find a budget at which they disagree.
Ages 15 and up
Add insertion, route tidying and remove and repair, then explain why 620 lost to 630.
Credits and caveats
Road and bus stop data (C) OpenStreetMap contributors, Open Database Licence, read 30 September 2026. The points rule, the four planners and all scores are ours; the scores say nothing about the bus services themselves. Roads are cut at the edge of the box, and the station is close to its southern edge.
