Optimization

This page lists the available algorithms for solving optimization problems. The other feature catalogs are listed on this page.

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All the packagesgemseogemseo-bilevel-outer-approximationgemseo-egoboxgemseo-hexalygemseo-ipoptgemseo-mlearninggemseo-mmagemseo-pdfogemseo-pymoogemseo-pyoptsparsegemseo-smt

The algorithm...

requires the gradients YesNoEither

supports integer variables YesNoEither

supports several objectives YesNoEither

supports equality constraints YesNoEither

supports inequality constraints YesNoEither

requires a linear problem YesNoEither

• Augmented_Lagrangian_order_0=≤

  Augmented Lagrangian algorithm for gradient-less functions.

  gemseo 6.3.3

• Augmented_Lagrangian_order_1=≤grad

  Augmented Lagrangian algorithm using gradient information

  gemseo 6.3.3

• BILEVEL_MASTER_OUTER_APPROXIMATION=≤int

  BILEVEL_MASTER_OUTER_APPROXIMATION

  BiLevelMasterOuterApproximation · gemseo-bilevel-outer-approximation 0.1.1

• DIFFERENTIAL_EVOLUTION=≤int

  Differential Evolution algorithm

  SciPy Global Optimization · gemseo 6.3.3

• DUAL_ANNEALINGint

  Dual annealing

  SciPy Global Optimization · gemseo 6.3.3

• DUAL_SIMPLEX=≤linear

  Linear programming using the HiGHS dual simplex solver.

  SciPy Linear Programming · gemseo 6.3.3

• EGObox_Egor≤int

  Efficient Global Optimization (EGO)

  EGObox · gemseo-egobox unreleased

• HEXALY=≤int

  Commercial black-box Hexaly library. It relies on a global mixed-integer solver.

  Hexaly · gemseo-hexaly 1.1.1

• INTERIOR_POINT=≤linear

  Linear programming using the HiGHS interior point solver.

  SciPy Linear Programming · gemseo 6.3.3

• IPOPT=≤

  Interior Point Optimizer

  IPOPT · gemseo-ipopt 1.0.0

• L-BFGS-Bgrad

  Limited-memory BFGS algorithm implemented in the SciPy library

  SciPy Local · gemseo 6.3.3

• MMA≤grad

  The Method of Moving Asymptotes

  MMA · gemseo-mma 4.0.0

• MNBI=≤intmulti

  Modified Normal Boundary Intersection (mNBI) method

  MNBI · gemseo 6.3.3

• MultiStart=≤intmulti

  The optimization algorithm `multistart generates starting points using a DOE algorithmand run a sub-optimization algorithm from each starting point.Depending on the sub-optimization algorithm,multistart` can handle integer design variables,equality and inequality constraintsas well as multi-objective functions.

  gemseo 6.3.3

• NELDER-MEAD

  Nelder-Mead algorithm implemented in the SciPy library

  SciPy Local · gemseo 6.3.3

• NLOPT_BFGSgrad

  Broyden-Fletcher-Goldfarb-Shanno method (BFGS) implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• NLOPT_BOBYQA

  Bound Optimization BY Quadratic Approximation (BOBYQA) implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• NLOPT_COBYLA=≤

  Constrained Optimization BY Linear Approximations (COBYLA) implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• NLOPT_MMA≤grad

  Method of Moving Asymptotes (MMA)implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• NLOPT_NEWUOA

  NEWUOA + bound constraints implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• NLOPT_SLSQP=≤grad

  Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the NLOPT library

  NLopt · gemseo 6.3.3

• ORTOOLS_MILP=≤intlinear

  Mixed-integer linear programming

  Ortools · gemseo-bilevel-outer-approximation 0.1.1

• OUTER_APPROXIMATION=≤int

  OUTER_APPROXIMATION · gemseo-bilevel-outer-approximation 0.1.1

• PDFO_BOBYQA

  Bound Optimization By Quadratic Approximation

  PDFO · gemseo-pdfo 2.0.3

• PDFO_COBYLA=≤

  Constrained Optimization By Linear Approximations

  PDFO · gemseo-pdfo 2.0.3

• PDFO_NEWUOA

  NEWUOA

  PDFO · gemseo-pdfo 2.0.3

• PYMOO_GA≤int

  Genetic Algorithm (GA) implemented in the Pymoo library

  pymoo · gemseo-pymoo 5.0.1

• PYMOO_NSGA2≤intmulti

  Non-Dominated Sorting Genetic Algorithm II (NSGA2) implemented in the Pymoo library

  pymoo · gemseo-pymoo 5.0.1

• PYMOO_NSGA3≤intmulti

  Non-Dominated Sorting Genetic Algorithm III (NSGA3) implemented in the Pymoo library

  pymoo · gemseo-pymoo 5.0.1

• PYMOO_RNSGA3≤intmulti

  Reference Point Based NSGA III implemented in the Pymoo library

  pymoo · gemseo-pymoo 5.0.1

• PYMOO_UNSGA3≤intmulti

  Unified NSGA III implemented in the Pymoo library

  pymoo · gemseo-pymoo 5.0.1

• PYOPTSPARSE_SLSQP=≤grad

  Sequential Least-Squares Quadratic Programming (SLSQP) implemented in pyOptSparse library

  pyOptSparse · gemseo-pyoptsparse 1.1.1

• PYOPTSPARSE_SNOPT=≤grad

  SNOPT implemented in PyOptSparse library

  pyOptSparse · gemseo-pyoptsparse 1.1.1

• SBOint

  GEMSEO in-house surrogate-based optimizer.

  gemseo-mlearning · gemseo-mlearning 3.1.0

• Scipy_MILP=≤int

  Mixed-integer linear programming

  SciPy Mixed-Integer Linear Programming · gemseo 6.3.3

• Scipy_MILP=≤int

  Mixed-integer linear programming

  SciPy Mixed-Integer Linear Programming · gemseo-bilevel-outer-approximation 0.1.1

• SHGO=≤int

  Simplicial homology global optimization

  SciPy Global Optimization · gemseo 6.3.3

• SLSQP=≤grad

  Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the SciPy library

  SciPy Local · gemseo 6.3.3

• SMT_EGO

  Efficient Global Optimization

  SMT · gemseo-mlearning 3.1.0

• SMT_EGO

  Efficient Global Optimization (EGO)

  SMT · gemseo-smt unreleased

• TNCgrad

  Truncated Newton (TNC) algorithm implemented in SciPy library

  SciPy Local · gemseo 6.3.3

The data of this page were collected on 2026-09-17 from the latest version of each package.