BIZNIQUE / CALCULUS / 48
Make a trade-off explicit
Make a trade-off explicit
Move along a curve where improving one objective can worsen another.
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THE IDEA
Read the example.
Read the example.
The example has two competing objectives on 0 ≤ x ≤ 1. Weight α expresses the emphasis given to the first. For this particular quadratic pair, the weighted optimum is x = 1−α. The plotted point reports both objectives separately.
F(x) = αx² + (1−α)(1−x)²
Use it well
Use it well
Weights carry meaning only alongside the objectives’ units and scaling. Weighted sums do not reveal every Pareto-optimal point in every non-convex problem.
TRY IT YOURSELF
A quick check.
A quick check.
For equal weights, where is the optimum and what are the two objective values?
Check your reasoning
Check your reasoning
x = 0.5, and both x² and (1−x)² are 0.25.
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