hillclimb / problemsesc goes back

Example problems

Construction problems in one shape: the submission is a small CSV of numbers, the verifier checks the constraints and computes the score exactly, and there is no dataset, no hidden split and no noise. Each ships with the best known value as a reference line on the chart. hillclimb problem list prints this catalog; hillclimb problem get <id> copies one in. Every picture is a good construction, not the floor the search starts from.

Circle packing

circle-packing

26 circles in the unit square; maximize the sum of their radii.

sum-radii, maximize
best known 2.63598 AlphaEvolve

circle-packing-32

32 circles in the unit square; maximize the sum of their radii.

sum-radii, maximize
best known 2.93957 Georgiev et al. 2025

Heilbronn triangles

heilbronn-11

11 points in the unit square; make the smallest triangle they span as large as possible.

min-triangle-area, maximize
best known 0.037037 Goldberg 1972

heilbronn-14

14 points in the unit square; make the smallest triangle they span as large as possible.

min-triangle-area, maximize
best known 0.0243 Beyleveld 2006

heilbronn-17

17 points in the unit square; make the smallest triangle they span as large as possible.

min-triangle-area, maximize
best known 0.016481 Stead 2026

heilbronn-convex-13

13 points in convex position; smallest triangle relative to the hull area.

normalized-min-triangle-area, maximize
best known 0.0309369 AlphaEvolve

Low-autocorrelation binary sequences

labs-40

A ±1 sequence of length 40 with the least autocorrelation sidelobe energy.

autocorrelation-energy, minimize
best known 108 optimal (Packebusch & Mertens 2016)

labs-60

A ±1 sequence of length 60 with the least autocorrelation sidelobe energy.

autocorrelation-energy, minimize
best known 218 optimal (Packebusch & Mertens 2016)

Tammes

tammes-30

30 points on the sphere; maximize the smallest angle between any two.

min-angle-deg, maximize
best known 38.5971 Hardin, Sloane & Smith 1994

tammes-50

50 points on the sphere; maximize the smallest angle between any two.

min-angle-deg, maximize
best known 29.753 Hardin, Sloane & Smith 1994

Thomson

thomson-50

50 charges on the sphere; minimize their Coulomb energy.

coulomb-energy, minimize
best known 1055.18 Wikipedia Thomson table

thomson-100

100 charges on the sphere; minimize their Coulomb energy.

coulomb-energy, minimize
best known 4448.35 Wikipedia Thomson table

Autocorrelation inequalities

autocorr-1

A non-negative step function whose autocorrelation peak is small next to its mass.

c1-ratio, minimize
best known 1.5053 AlphaEvolve 2025

autocorr-3

A signed step function whose autocorrelation is flat next to its mass.

c3-ratio, minimize
best known 1.4557 AlphaEvolve 2025

erdos-overlap

A density on [0, 2] with mass 1 whose overlap with its own complement stays small under every shift.

overlap-bound, minimize
best known 0.380924 AlphaEvolve 2025

Kissing configuration

kissing-11

Integer points in 11 dimensions, pairwise at least as far apart as the longest of them.

points, maximize
best known 593 AlphaEvolve 2025

Golomb rulers

golomb-20

20 marks on a ruler, every pairwise distance distinct; make the ruler short.

length, minimize
best known 283 optimal (Garry, Vanderschel et al. 1997)

golomb-27

27 marks on a ruler, every pairwise distance distinct; make the ruler short.

length, minimize
best known 553 optimal (distributed.net 2014)

Travelling salesman

tsp-20

A tour through the first 20 of the 200 cities; small enough to untangle by hand.

tour-length, minimize
playground only

tsp-70

A tour through the first 70 of the 200 cities; a few minutes by hand.

tour-length, minimize
playground only

tsp-200

A tour through 200 fixed cities; make it short.

tour-length, minimize
no reference line yet

Multidimensional knapsack

mknap-100-5

100 items, each with a value and 5 weights; take the most value that fits all 5 capacities.

total-value, maximize
best known 24381 Chu & Beasley 1998

mknap-250-10

250 items, each with a value and 10 weights; take the most value that fits all 10 capacities.

total-value, maximize
best known 59187 Chu & Beasley 1998