cuopt-multi-objective-exploration

# 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 A single optimum encodes **one implicit weighting** of the objectives. Change the weighting and the optimum moves. The frontier is the curve traced by all the non-dominated optima. A solution **A dominates** B when A is at l...