Choosing, and recording why

The knee

The knee is the front member furthest from the straight line joining the two extremes: the point where the trade-off curve bends most sharply. Past it, further gain in one objective starts costing disproportionately in the other.

It is a good place to start a conversation and a bad place to end one, for three reasons:

It depends on the axes. Swap one objective for another and the knee moves.

It depends on the scaling. The measure normalises each objective to 0–1 across the front, so the knee's position depends on how wide that range happens to be — which depends on which designs you included.

It knows nothing about who is paying. A client who has committed publicly to a carbon target does not want the knee; they want the low-carbon end, and no geometric property of the curve says so.

Crowding distance

How isolated a front member is from its neighbours. The two extremes are infinitely isolated by convention, and interior members are scored by how much of the front they have to themselves.

It is a diversity measure, not a quality one. A design with a large crowding distance occupies a region of the trade-off that nothing else does — which is a reason to keep it in the conversation, and no reason at all to build it.

Its main use is inside a multi-objective search, to stop a population collapsing onto one part of the front. Presented to a human it answers 'which options are genuinely different from each other?', which is a useful question when a list of twelve schemes turns out to be three schemes and nine variations.

Change the axes and the front changes

This is the point that most needs demonstrating, because a front looks authoritative.

Take the same four schemes. On carbon against depth, three are on the front and the composite steel frame is dominated.

Now plot mass against carbon instead. The CLT hybrid has both the lowest mass and the lowest carbon, so it dominates all three others outright. The front collapses to a single design, and two schemes that were legitimate answers a moment ago are eliminated.

Neither front is wrong. They answer different questions, and the objectives you chose are the question. Choosing them is a design decision that happens before any of the arithmetic, and it gets far less scrutiny than the arithmetic does.

A Pareto front is a rigorous answer to whatever question you posed. It has no view on whether that was the right question.

The decision record

A record needs five things:

• What was chosen.
• Which objectives it was assessed on, and why those.
• What was rejected, and because of what. Not 'it scored lower' — the actual reason.
• The reason for the choice.
• Who decided, and when.

And one more that is not optional in practice: what influenced the decision that was not in the model. The contractor's familiarity, the programme, the planning position, the client's public commitments. Those things decide real projects and they are invisible in any front. Writing them down is what stops the record looking like the arithmetic made the choice.

Six months later the choice is a fact and the reason is gone. The record exists for the person who has to change something and needs to know what the original decision depended on.