hr-studioSearch · 06
A computational design primer · Multi-objective & Pareto

The geometry of trade-offs.

Real briefs never ask for one thing. They ask for area and elegance, light and economy, strength and lightness — and between honest rivals there is no single best, only trades. Plot every design by its scores and a frontier appears: the Pareto front, the set of designs you cannot improve without paying somewhere else. This is where the Search part ends — because the front is where the algorithm stops and the designer begins.

Scroll to begin
i.

Two scores, no single best

Give the tower two judges — floor area and slenderness — and every design becomes a point in objective space: not where its knobs are, but how well it scores. The two champions from earlier sit in different corners, and neither can call itself the winner, because each loses the other’s contest.

Drag on the design map; watch your scores travel.

Left: the knobs · right: the scores
ii.

Dominance, the only fair verdict

When is one design simply better? Only when it wins or ties on every score and wins at least one — then it dominates. Anything else is a matter of taste, not fact. Tap any design: its shadow — everything it dominates — falls down and to the left; anything sitting up and to the right has beaten it outright.

Tap designs and read their verdicts.

Down-left: dominated · up-right: dominators
iii.

The front is a menu

Remove everything dominated and what remains is the front: the complete menu of rational choices. And it’s not a list — it’s a path. Slide along it and the tower morphs continuously from full-height slab to tapered spire, every stop a design that trades a little area for a little elegance. Nothing off this curve deserves to be built.

Slide along the frontier; the building follows.

Every stop on the front is defensible
iv.

The weighted-sum trap

The tempting shortcut: blend the scores into one number — so much area plus so much slenderness — and optimize that. But a weighted sum can only ever pick points where a straight line first touches the front. Where the front dents inward, whole stretches of perfectly rational designs are invisible to every possible weighting. Slide the weight and watch the winner skip across the gaps.

No blend of judges can order from the dented part of the menu.

The rolling line skips the dents
v.

Breed the frontier

Last chapter evolution chased one number and its population collapsed onto a single champion. Give selection two judges and a taste for uncrowded company, and something better happens: the population lands on the front and spreads along it — evolving the entire menu at once. Below the chart, the current frontier stands as a parade of towers, slab to spire. Evolution doesn’t pick for you; it lays out every defensible option. Choosing is still yours.

The population becomes the menu · tap a tower to inspect
Search can carve the space, read the landscape, climb, anneal and breed — but faced with two honest judges it can only draw the frontier and hand you the pen. That is the right ending for a part about search: the algorithms find the menu; the values that pick from it are yours. The Search part is complete.