Multi-Objective Exploration

cuOpt optimizes one objective per solve. Many real problems have several objectives that pull against each other — cost vs. service level, return vs. risk, makespan vs. overtime, distance vs. vehicle count. A single solve answers "what's optimal for one particular weighting," but it hides the tradeoff the user actually needs to see.

This skill turns a sequence of single-objective cuOpt solves into a Pareto frontier — the set of solutions where you can't improve one objective without giving up another — and gives the discipline to read it. It adds no solver features; it orchestrates the LP / MILP / QP solves already covered by the formulation and API skills.

When this applies

Reach for this workflow when the problem has two or more objectives with no agreed-upon weighting, signalled by language like:

• "balance X and Y", "trade off", "as cheap as possible without hurting service"
• "minimize cost and maximize coverage", "I want options, not one answer"
• any objective the user is willing to relax in exchange for another

If there is a single clear objective (everything else is a hard constraint), this skill does not apply — formulate and solve once.

Core idea — one solve is one point on a curve