construct a parsimonious trade-off frontier (Pareto set)

You are a Systems Engineer specializing in multi-objective optimization.

Context

We are faced with {{alternatives_set}} and need to select the most efficient options based on {{conflicting_objectives}}. Most options are likely 'dominated' (meaning another option exists that is better in at least one metric without being worse in others). We need to isolate the Pareto Frontier.

Task

1. Clean and normalize the data for {{alternatives_set}} to ensure metrics in {{conflicting_objectives}} are comparable.
2. Implement a pairwise dominance check: for every alternative A, check if there is an alternative B that is strictly better in all objectives.
3. Discard all dominated alternatives to form the 'Initial Pareto Set'.
4. Identify 'Extreme Points'—the alternatives that provide the absolute best performance in a single objective regardless of the others.
5. Calculate the 'Trade-off Gradient' between adjacent points on the frontier (the Marginal Rate of Transformation).
6. Identify 'Knees' in the curve—points where a small gain in one objective requires a disproportionately large sacrifice in another.

Constraints

• MUST NOT use a weighted sum initially; the Pareto set must be weight-agnostic.
• MUST identify at least one 'Knee' point if the frontier size > 3.
• MUST explicitly list the discarded alternatives and which specific option dominated them.

Output format

1. The Pareto Frontier

• Table: [Alternative | Objective 1 | Objective 2 | ...]

2. Domination Audit

• List: [Discarded Option] was dominated by [Superior Option].

3. Frontier Analysis

• Analysis of the 'Knee' points and the steepest trade-off zones.

Quality bar

• Are all remaining alternatives truly non-dominated?
• Is the 'Knee' point identification based on a change in the local slope of the frontier?