pymoo

# Pymoo - Multi-Objective Optimization in Python ## Overview Pymoo is a comprehensive Python framework for optimization with emphasis on multi-objective problems. Solve single and multi-objective optimization using state-of-the-art algorithms (NSGA-II/III, MOEA/D, SPEA2), benchmark problems (ZDT, DTLZ), customizable genetic operators, and multi-criteria decision making methods. Excels at finding trade-off solutions (Pareto fronts) for problems with conflicting objectives. Current stable release: **pymoo 0.6.1.6** (November 2025). ## Installation ```bash uv pip install pymoo ``` For reproducible environments, pin a version: `uv pip install "pymoo==0.6.1.6"`. **Dependencies:** NumPy (2.x compatible since 0.6.1.3), SciPy, matplotlib (visualization). Autograd is optional for gradient-based features (since 0.6.1.3). **Documentation:** https://pymoo.org/ — LLM-friendly index: https://pymoo.org/llms.txt ## When to Use This Skill This skill should be used when: - Solving optimization problems with one or multiple objectives - Finding Pareto-optimal solutions and analyzing trade-offs - Implementing evolutionary algorithms (GA, DE, PSO, NSGA-II/III) - Working with constrained optimization problems - Benchmarking algorithms on standard test problems (ZDT, DTLZ, WFG) - Customizing genetic operators (crossover, mutation, selection) - Visualizing high-dimensional optimization results - Making decisions from multiple competing solutions - Handling binary, discrete, continuous, or mixed-variable problems ## Core Concepts ### The Unified Interface Pymoo uses a consistent `minimize()` function for all optimization tasks: ```python from pymoo.optimize import minimize result = minimize( problem, # What to optimize algorithm, # How to optimize termination, # When to stop seed=1, verbose=True ) ``` **Result object contains:** - `result.X`: Decision variables of optimal solution(s) - `result.F`: Objective values of optimal solution(s) - `result.G`: Constraint violations (if constrained) - `result.algorithm`: Algorithm object with history ### Problem Definition Styles Pymoo supports three problem definition styles: - **`Problem`**: Vectorized — `_evaluate` receives a batch of solutions (matrix) - **`ElementwiseProblem`**: One solution per call — recommended for custom problems and parallel evaluation - **`FunctionalProblem`**: Define objectives and constraints as separate functions without subclassing ### Problem Types **Single-objective:** One objective to minimize/maximize **Multi-objective:** 2-3 conflicting objectives → Pareto front **Many-objective:** 4+ objectives → High-dimensional Pareto front **Constrained:** Objectives + inequality/equality constraints **Mixed-variable:** Continuous, integer, binary, and categorical variables in one problem **Dynamic:** Time-varying objectives or constraints ## Quick Start Workflows Nine runnable workflows are in [references/quick_start_workflows.md](references/quick_start_workflows.md): | # | Workflow | Use when | | --- | --- | --- | | 1 | Single-objective optimization | one objective, GA or DE | | 2 | Multi-objective (2-3 objectives) | NSGA-II and a Pareto front | | 3 | Many-objective (4+ objectives) | NSGA-III or reference-direction methods | | 4 | Custom problem definition | subclassing `Problem` / `ElementwiseProblem` | | 5 | Constraint handling | inequality and equality constraints | | 6 | Decision making from a Pareto front | scalarization and MCDM selection | | 7 | Visualization | scatter, PCP, radviz, and heatmap views | | 8 | Parallel evaluation | threads, processes, or Dask for expensive objectives | | 9 | Mixed-variable optimization | integer, binary, and categorical variables | ## Algorithm Selection Guide ### Single-Objective Problems | Algorithm | Best For | Key Features | |-----------|----------|--------------| | **GA** | General-purpose | Flexible, customizable operators | | **DE** | Continuous optimization | Good global search | | **PSO** | Smooth landscapes | Fast convergence | | **CMA-ES** | Difficult/noisy problems | Self-adapting | ### Multi-Objective Problems (2-3 objectives) | Algorithm | Best For | Key Features | |-----------|----------|--------------| | **NSGA-II** | Standard benchmark | Fast, reliable, well-tested | | **SPEA2** | Archive-based MOO | Strength-based fitness, external archive | | **R-NSGA-II** | Preference regions | Reference point guidance | | **MOEA/D** | Decomposable problems | Scalarization approach | ### Many-Objective Problems (4+ objectives) | Algorithm | Best For | Key Features | |-----------|----------|--------------| | **NSGA-III** | 4-15 objectives | Reference direction-based | | **RVEA** | Adaptive search | Reference vector evolution | | **AGE-MOEA** | Complex landscapes | Adaptive geometry | ### Constrained Problems | Approach | Algorithm | When to Use | |----------|-----------|-------------| | Feasibility-first | Any algorithm | Large feasible region | | Specialized | SRES, ISRES | Heavy constraints | | Penalty | GA + penalty | Algorithm compatibility | **See:** `references/algorithms.md` for comprehensive algorithm reference ## Benchmark Problems ### Quick problem access: ```python from pymoo.problems import get_problem # Single-objective problem = get_problem("rastrigin", n_var=10) problem = get_problem("rosenbrock", n_var=10) # Multi-objective problem = get_problem("zdt1") # Convex front problem = get_problem("zdt2") # Non-convex front problem = get_problem("zdt3") # Disconnected front # Many-objective problem = get_problem("dtlz2", n_obj=5, n_var=12) problem = get_problem("dtlz7", n_obj=4) ``` **See:** `references/problems.md` for complete test problem reference ## Genetic Operator Customization ### Standard operator configuration: ```python from pymoo.algorithms.soo.nonconvex.ga import GA from pymoo.operators.crossover.sbx import SBX from pymoo.operators.mutation.pm import PM algorithm = GA( pop_size=100, crossover=SBX(prob=0.9, eta=15), mutation=PM(eta=20), eliminate_duplicates=True ) ``` ### Operator selection by variable type: **Continuous variables:** - Crossover: SBX (Simulated Binary Crossover) - Mutation: PM (Polynomial Mutation) **Binary variables:** - Crossover: TwoPointCrossover, UniformCrossover - Mutation: BitflipMutation **Permutations (TSP, scheduling):** - Crossover: OrderCrossover (OX) - Mutation: InversionMutation **See:** `references/operators.md` for comprehensive operator reference ## Performance and Troubleshooting ### Common issues and solutions: **Problem: Algorithm not converging** - Increase population size - Increase number of generations - Check if problem is multimodal (try different algorithms) - Verify constraints are correctly formulated **Problem: Poor Pareto front distribution** - For NSGA-III: Adjust reference directions - Increase population size - Check for duplicate elimination - Verify problem scaling **Problem: Few feasible solutions** - Use constraint-as-objective approach - Apply repair operators - Try SRES/ISRES for constrained problems - Check constraint formulation (should be g <= 0) **Problem: High computational cost** - Reduce population size - Decrease number of generations - Use simpler operators - Enable parallel evaluation via `elementwise_runner` (see Workflow 8) ### Best practices: 1. **Normalize objectives** when scales differ significantly 2. **Set random seed** for reproducibility 3. **Save history** to analyze convergence: `save_history=True` 4. **Visualize results** to understand solution quality 5. **Compare with true Pareto front** when available 6. **Use appropriate termination criteria** (generations, evaluations, tolerance) 7. **Tune operator parameters** for problem characteristics ## Resources This skill includes comprehensive reference documentation and executable examples: ### references/ Detailed documentation for in-depth understanding: - **algorithms.md**: Complete algorithm reference with parameters, usage, and selection guidelines - **problems.md**: Benchmark test problems (ZDT, DTLZ, WFG) with characteristics - **operators.md**: Genetic operators (sampling, selection, crossover, mutation) with configuration - **visualization.md**: All visualization types with examples and selection guide - **constraints_mcdm.md**: Constraint handling techniques and multi-criteria decision making methods - **parallelization.md**: Parallel evaluation with StarmapParallelization and JoblibParallelization **Search patterns for references:** - Algorithm details: `grep -r "NSGA-II\|NSGA-III\|MOEA/D" references/` - Constraint methods: `grep -r "Feasibility First\|Penalty\|Repair" references/` - Visualization types: `grep -r "Scatter\|PCP\|Petal" references/` ### scripts/ Executable examples demonstrating common workflows: - **single_objective_example.py**: Basic single-objective optimization with GA - **multi_objective_example.py**: Multi-objective optimization with NSGA-II, visualization - **many_objective_example.py**: Many-objective optimization with NSGA-III, reference directions - **custom_problem_example.py**: Defining custom problems (constrained and unconstrained) - **decision_making_example.py**: Multi-criteria decision making with different preferences **Run examples:** ```bash python3 scripts/single_objective_example.py python3 scripts/multi_objective_example.py python3 scripts/many_objective_example.py python3 scripts/custom_problem_example.py python3 scripts/decision_making_example.py ``` ## Additional Notes **Common patterns:** - Use `ElementwiseProblem` for custom problems (or `FunctionalProblem` for function-based definitions) - Use `vars` dict with typed variables for mixed-variable problems - Constraints formulated as `g(x) <= 0` and `h(x) = 0` - Reference directions required for NSGA-III - Normalize objectives before MCDM - Use appropriate termination: `('n_gen', N)` or `get_termination("f_tol", tol=0.001)` ## Citing Scientific Agent Skills This skill is part of Scientific Agent Skills by K-Dense. 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