What does the purple curve in the OBJ_1-OBJ_2 graph represent?
The purple curve represents the trade-off curve in the objective space. It is formed by mapping the optimal solutions obtained as the weight changes, showing how improving one objective comes at the expense of the other.
Conditions
- At least two objectives are plotted against each other.
- Solutions are generated for multiple weight values.
Reasoning, step by step
- Vary the weight across a range of values.
- Compute the optimal solution for each weight.
- Plot the resulting pairs in the objective space.
- Connect the plotted points to form the trade-off curve.
Example
A purple curve connects several marked points in the OBJ_1-OBJ_2 plane. The lecturer says mapping solutions for different weights yields “this sort of trade-off curve.”
Common misconceptions
- Thinking the curve represents the feasible region in decision-variable space.
- Assuming the curve shows a single universal optimum rather than a family of trade-offs.
Watch the explanation
1:54 – 2:30Watch this moment ↗
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