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Get Started Free →Build the Pareto frontier from multi-objective optimization, visualize trade-offs, and select a portfolio from non-dominated solutions.
.claude/skills/yogsoth-ai-pareto-frontier-construction/SKILL.md| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-03 | ✗→✓ | ▲ Improved | -30% | 0% |
| case-10 | ✗→✓ | ▲ Improved | 20% | 0% |
| case-14 | ✗→✓ | ▲ Improved | 46% | 0% |
| case-23 | ✓→✗ | ▼ Worse | 61% | 0% |
| case-01 | ✓→✓ | ＝ Same ✓ | -8% | 0% |
Systematically construct the set of non-dominated solutions across multiple objectives, visualize the trade-off surface, and guide selection of a final portfolio from the frontier.
| Stage | SOP | Purpose | |-------|-----|---------| | 1 | objective-definition | Define objectives, constraints, and trade-off preferences | | 2 | optimization-run | Run multi-objective optimization to generate Pareto front | | 3 | pareto-visualization | Visualize the frontier and trade-off relationships | | 4 | selection-from-frontier | Select final portfolio based on preferences |
<!-- BEGIN available-tables (generated) -->
Optional, no fixed order; the final leaf is always a sop.
| SOP | When to use | | --- | --- | | objective-definition | Define optimization objectives, constraints, and trade-off preferences from context and candidate information. | | optimization-run | Execute multi-objective optimization on candidates to produce a Pareto front of non-dominated solutions. | | pareto-visualization | Create visual representation of the Pareto frontier showing trade-offs between objectives with narrative explanation. | | selection-from-frontier | Select the final portfolio from the Pareto front by applying stakeholder preferences and decision criteria. |
<!-- END available-tables (generated) -->
| Case | Status | Duration (ms) | Turns | Tokens | Tool calls | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Without | With | Δ | Without | With | Δ | Without | With | Δ | Without | With | Δ | ||
case-01 | pass→pass | 40,968 | 38,091 | -7% | 1 | 1 | 0% | 8,261 | 7,617 | -8% | 0 | 0 | — |
case-02 | fail→fail | 29,938 | 42,080 | +41% | 1 | 1 | 0% | 6,218 | 8,744 | +41% | 0 | 0 | — |
case-03 | fail→pass | 39,313 | 52,295 | +33% | 1 | 1 | 0% | 8,250 | 5,785 | -30% | 0 | 0 | — |
case-04 | fail→fail | 13,795 | 27,923 | +102% | 1 | 1 | 0% | 1,582 | 3,953 | +150% | 0 | 0 | — |
case-05 | fail→fail | 6,080 | 28,725 | +372% | 1 | 1 | 0% | 1,133 | 4,230 | +273% | 0 | 0 | — |
case-06 | fail→fail | 16,103 | 9,537 | -41% | 1 | 1 | 0% | 2,129 | 2,096 | -2% | 0 | 0 | — |
case-07 | pass→pass | 23,604 | 64,752 | +174% | 1 | 1 | 0% | 4,846 | 8,291 | +71% | 0 | 0 | — |
case-08 | pass→pass | 19,248 | 23,298 | +21% | 1 | 1 | 0% | 3,290 | 4,969 | +51% | 0 | 0 | — |
case-09 | fail→fail | 11,051 | 6,109 | -45% | 1 | 1 | 0% | 1,896 | 1,416 | -25% | 0 | 0 | — |
case-10 | fail→pass | 17,075 | 18,964 | +11% | 1 | 1 | 0% | 3,374 | 4,045 | +20% | 0 | 0 | — |
case-11 | pass→pass | 37,321 | 35,474 | -5% | 1 | 1 | 0% | 7,833 | 7,879 | +1% | 0 | 0 | — |
case-12 | pass→pass | 27,144 | 25,636 | -6% | 1 | 1 | 0% | 3,170 | 5,836 | +84% | 0 | 0 | — |
case-13 | pass→pass | 10,824 | 16,893 | +56% | 1 | 1 | 0% | 2,353 | 3,925 | +67% | 0 | 0 | — |
case-14 | fail→pass | 30,261 | 39,786 | +31% | 1 | 1 | 0% | 5,819 | 8,518 | +46% | 0 | 0 | — |
case-15 | pass→pass | 22,805 | 39,935 | +75% | 1 | 1 | 0% | 4,357 | 7,140 | +64% | 0 | 0 | — |
case-16 | pass→pass | 17,153 | 25,512 | +49% | 1 | 1 | 0% | 3,241 | 5,622 | +73% | 0 | 0 | — |
case-17 | pass→pass | 74,730 | 21,940 | -71% | 1 | 1 | 0% | 4,376 | 4,608 | +5% | 0 | 0 | — |
case-18 | pass→pass | 19,474 | 27,832 | +43% | 1 | 1 | 0% | 2,612 | 3,652 | +40% | 0 | 0 | — |
case-19 | pass→pass | 21,247 | 31,810 | +50% | 1 | 1 | 0% | 3,940 | 6,507 | +65% | 0 | 0 | — |
case-20 | fail→fail | 37,096 | 37,449 | +1% | 1 | 1 | 0% | 8,060 | 8,726 | +8% | 0 | 0 | — |
case-21 | pass→pass | 22,352 | 24,565 | +10% | 1 | 1 | 0% | 4,617 | 5,642 | +22% | 0 | 0 | — |
case-22 | pass→pass | 44,702 | 22,893 | -49% | 1 | 1 | 0% | 4,354 | 4,897 | +12% | 0 | 0 | — |
case-23 | pass→fail | 18,082 | 25,084 | +39% | 1 | 1 | 0% | 3,314 | 5,322 | +61% | 0 | 0 | — |
DecimalAI ran this skill against gemini-3.6-flash twice over the same eval suite — once with the skill loaded and once without — and compared the two runs case by case. 23 cases were attempted. The headline lift of +9 percentage points is the difference between those two pass rates over the 23 comparable cases. 1 case got worse with the skill loaded, and it is included in that figure.
Without the skill loaded, the model failed this case. With it loaded, the same prompt on the same model passed. This is one improved case from the latest verified run; every case, including any that regressed, is in the table above.
Other measured skills in the registry, with their headline benchmark lift.