Design the cheapest welded cantilever beam that survives a 6 000-lb tip load under seven physical constraints (shear, bending, deflection, buckling, geometry). HumpDay's optimisers tune four variables โ weld thickness h, weld length l, beam thickness t, beam width b โ over a narrow feasible region. The world-class minimum cost is โ $1.725.
Try a manual design โ slide, load, compete against the algorithms. Sliders use the same physical bounds the optimisers search over.
Each design is drawn and load-tested at ~2ร the final-replay speed. At 50 designs that's about a minute of watchable search.
Each row is the cheapest feasible design a given algorithm found (lower cost = better; infeasible best-attempts shown in red and pushed to the bottom). The published world-class minimum is $1.725 โ anything under $2.00 is a very good design.
| Algorithm | Score | Cost ($) | Evals | h / l / t / b (in) |
|---|---|---|---|---|
| โ no runs yet โ | ||||
A classical structural engineering benchmark (Ragsdell & Phillips,
1976). A steel cantilever beam of fixed length L = 14 in
carries a downward tip load of P = 6 000 lb. The beam is
attached to a rigid wall by two fillet welds of leg size h
and length l. The beam itself has rectangular cross-section
t ร b. Cost โ material plus labour plus welding โ is
1.10471ยทhยฒยทl + 0.04811ยทtยทbยท(14 + l).
Seven constraints must hold simultaneously: shear stress in the weld โค 13 600 psi, bending stress in the beam โค 30 000 psi, tip deflection โค 0.25 in, buckling load Pc โฅ P, plus three geometric constraints (h โฅ 0.125, h โค b, combined-cost bound). Infeasible designs are penalised quadratically โ so the cost landscape has steep penalty cliffs around a narrow feasible corridor. The score shown is 100 at the published optimum and drops linearly to 0 at $6.725; infeasible designs score zero regardless of cost.
A smoke-test of 2 000 random unit-cube samples (seed 0) gave a feasibility rate of 2.6 % and a best random cost of $2.68. So unguided search burns most of its budget in the infeasible interior. Run a few optimisers and see how they each handle the penalty cliffs.
Mechanical formulation from
Ragsdell & Phillips (1976)
โ see example_applications/welded_beam/problem.py for the exact equations.
If your hyper-parameter searches are heating the Earth, drop this in Cursor or Claude:
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