pymoo

Multi-objective optimization finds trade-off solutions across competing objectives. Pymoo solves these problems using algorithms like NSGA-II and NSGA-III, producing Pareto fronts where no solution improves one objective without worsening another. It handles continuous, discrete, and mixed-variable domains with constraint support.

Yes. Pymoo applies constraint handling across single-, multi-, and many-objective scenarios for engineering and design tasks. You define problem variables, objectives, and constraints through a unified minimize interface, then pymoo executes your chosen algorithm and returns feasible, constraint-satisfied Pareto solutions.

Pymoo includes NSGA-II, NSGA-III, MOEA/D, SRES, CMA-ES, PSO, and GA. Each algorithm suits different problem structures—NSGA-II and NSGA-III excel at many-objective problems, MOEA/D decomposes objectives, and evolutionary strategies handle continuous domains. Benchmark problems like ZDT and DTLZ let you compare performance.

Pymoo provides scatter plots, parallel coordinate plots (PCP), and heatmaps to visualize Pareto fronts and trade-offs across objectives. After optimization, you can also apply MCDM methods like Pseudo-Weights and Compromise Programming to select preferred solutions from the front.

Pymoo is self-contained. It requires only numpy and matplotlib as dependencies. All algorithms, constraint handling, termination criteria, and benchmark problems are built in. You define objectives and variables in Python; pymoo executes the solve within your script.

Yes. Pymoo's unified minimize interface supports continuous, discrete, and mixed-variable domains. You specify variable types during problem definition, and algorithms automatically manage the search space—no separate discrete solver needed.