pymoo

Use pymoo's minimize function with a problem definition and an algorithm like NSGA-II. The result object contains the Pareto-optimal decision variables in result.X and objective values in result.F, which you can visualize with a scatter plot.

Use NSGA-II for problems with 2-3 objectives, as it is fast and well-tested. Use NSGA-III for 4 or more objectives, since its reference-direction mechanism maintains uniform Pareto front coverage in high-dimensional objective spaces.

Extend the ElementwiseProblem class, set n_var, n_obj, n_ieq_constr, and bounds in __init__, then implement _evaluate to return objectives in out["F"] and constraints in out["G"]. Inequality constraints must be formulated as g(x) <= 0.

Yes, pymoo handles constraints through feasibility-first selection by default, penalty methods, constraint-as-objective conversion, and specialized algorithms like SRES and ISRES for heavily constrained problems. Custom repair operators are also supported.

Poor distribution often results from insufficient population size, too few generations, or missing duplicate elimination. For NSGA-III, verify that reference directions match the objective count and consider increasing partitions for denser coverage.

Normalize the objective values to [0, 1], then apply a multi-criteria decision making method such as PseudoWeights with your preference weights, compromise programming toward an ideal point, or knee-point detection for balanced trade-offs.