Lab teaching track · used across the design, material and process work
Optimisation
Every project on this page ends in the same question: of all the settings you could choose, which one do you actually run? This is how that gets answered.
The industrial problem
An engineer can usually describe what "good" means — the least warpage, the lowest drag, the longest life. What they cannot do is try every combination. A press has four settings with a realistic range each; sweeping them at ten values apiece is ten thousand physical runs, and each run costs machine time and material. The search space is always vastly larger than the budget for exploring it.
So the real question is not "what is the best setting" but "where should I spend my next expensive trial". Answer it badly and you spend the whole budget refining a mediocre answer while a much better one sits untried a few degrees away. That trap — a search that settles for the first decent thing it finds — is the single most common failure in engineering optimisation, and it is what both demos below are built to make visible: one searching a single dial, one searching an entire shape.
The system
The problem
One press, one dial, one honest answer
Two strategies, two shapes of problem. The first searches a single dial — the press temperature that produces the least warpage — where two settings look good and only one actually is. The second searches a whole geometry, where the thing being optimised is the design itself. Neither is told where the answer is; both have to spend trials to find out, exactly as you would on a real line.
Strategy 1
Model your own ignorance, then aim at it
Fit a cheap stand-in to the trials run so far, and have it report not just a prediction but how confident it is. Then press next wherever the combination of “might be good” and “barely understood” is strongest. It is the strategy to reach for when every single trial is expensive. Which named method does this is a question for week three — the point here is the reasoning, not the acronym.
- Trial
- 2
- Best warpage
- 2.73 mm
- At
- 50°C
- Next try
- 120°C
- ━ what the model currently believes, with the shaded band as its uncertainty
- ┄ the real answer — the optimiser never sees this
- ┆ where it will press next: the point that is either promising or badly understood
Strategy 2
Evolve the shape, don’t guess it
Here the candidate is not a number, it is a design. Sixteen random profiles are scored, the better half survives, and pairs of survivors produce children that inherit a blend of both parents plus a random mutation. Twice in the run a calamity wipes out the weakest designs and drops fresh random ones in, which makes the average temporarily worse and the search permanently better. No single design has to be right, so an unlucky start cannot trap the process — it buys that robustness by evaluating far more candidates. Step through the generations and watch blobs become a teardrop.
Generation 0 — sixteen random designs. None of them is any good, and that is the point: nobody had to guess where the answer was.
Best design · generation 0
The population — who survives
15.51random
19.20random
15.20random
9.15random
11.09random
35.80random
40.06random
28.26random
11.33random
22.03random
27.03random
25.97random
21.50random
18.43random
13.65random
26.55random
- Generation
- 0 / 7
- Best drag index
- 9.15
- Population average
- 21.30
- Survived
- 8 of 16
- ▰ survived selection — these breed the next generation
- ▰ new blood — a random design introduced after a calamity
- ▰ eliminated — did not make the top half
- ▭ best design in this generation
- Drag index is an illustrative objective — wetted length × form factor, plus base drag and a separation penalty — not measured project data.
So which one?
Count the evaluations. The first strategy reaches its answer in roughly nine presses because it reasons about where to look next; the second spends a population of sixteen across eight generations — well over a hundred evaluations — and never needed a model of the problem to do it. When a trial costs a day of machine time you pay for the thinking. When evaluations are cheap because a surrogate stands in for the solver, and the thing you are searching is a whole geometry rather than one dial, you pay for the crowd. Knowing which situation you are in is the actual skill.
How it was built
- 01
Build a cheap stand-in for the expensive thing
The physical trial, or the solver run, is the expensive step. So the first move is always to fit something fast that approximates it — a surrogate — and then do the searching against the surrogate instead. This is why the graph networks elsewhere on this site matter: a model that predicts a quality field in milliseconds turns an impossible search into a routine one.
- 02
Decide where to look next, deliberately
Every strategy is a different answer to one question: exploit what already looks good, or explore what you do not yet understand? The first demo answers it by tracking its own uncertainty and going wherever the payoff or the ignorance is greatest. The second answers it by keeping a whole population of candidate designs alive — breeding the survivors, mutating the children, and periodically wiping out the weakest — so no single early guess can trap the search.
- 03
Keep the trade-off visible
Real objectives conflict — lighter parts warp more, faster cycles cost quality. The output an engineer can actually sign off is not one number but the trade-off curve behind it, together with the record of every trial that produced it. An optimiser that hands over a setting without that history is asking to be trusted rather than checked.
What this builds on
- Teaching demonstrations
- The two interactive demos on this page run deliberately shaped illustrative objectives, not measured project data — a two-basin warpage curve for the first, and a textbook drag decomposition over an evolving profile for the second. Both are shaped so the behaviour of the strategy is visible in a handful of steps. The strategies are deliberately not named here: the point of the exercise is to reason about what each one is doing, which is harder once you can look the method up.
Lab teaching track — the method shared by the design, material and process work