Capabilities

Overview

  • Support for a wide array of types of optimisation problems (continuous, integer, single and multi-objective, constrained and unconstrained, with or without derivatives, stochastic, etc.).

  • A comprehensive library of algorithms, including global and local solvers, meta-heuristics, single and multi-objective algorithms, wrappers for third-party solvers (e.g., NLopt, Ipopt, etc.).

  • Comprehensive support for coarse-grained parallelisation via the generalised island model. In the island model, multiple optimisation instances run in parallel (possibly on different machines) and exchange information as the optimisation proceeds, improving the overall time-to-solution and allowing to harness the computational power of modern computer architectures (including massively-parallel high-performance clusters).

  • Support for fine-grained parallelisation (i.e., at the level of single objective function evaluations) in selected algorithms via the batch fitness evaluation framework. This allows to speed-up single optimisations via parallel processing (e.g., multithreading, high-performance clusters, GPUs, SIMD vectorization, etc.).

  • A library of ready-to-use optimisation problems for algorithmic testing and performance evaluation (Rosenbrock, Rastrigin, Lennard-Jones, etc.).

  • A library of optimisation-oriented utilities (e.g., hypervolume computation, non-dominated sorting, plotting, etc.).

List of algorithms

This is the list of user defined algorithms (UDAs) currently provided with pagmo. These are classes that can be used to construct a pagmo::algorithm, which will then provide a unified interface to access the algorithm’s functionalities.

Generally speaking, algorithms can solve only specific problem classes. In the tables below, we use the following flags to signal which problem types an algorithm can solve:

  • S = Single-objective

  • M = Multi-objective

  • C = Constrained

  • U = Unconstrained

  • I = Integer programming

  • sto = Stochastic

Note that algorithms that do not directly support integer programming will still work on integer problems (i.e., they will optimise the relaxed problem). Note also that it is possible to use meta-problems to turn constrained problems into unconstrained ones, and multi-objective problems into single-objective ones.

Heuristic Global Optimization

Common Name

Docs of the C++ class

Capabilities

Extended Ant Colony Optimization (GACO)

pagmo::gaco

S-CU-I

Differential Evolution (DE)

pagmo::de

S-U

Self-adaptive DE (jDE and iDE)

pagmo::sade

S-U

Self-adaptive DE (de_1220 aka pDE)

pagmo::de1220

S-U

Grey wolf optimizer (GWO)

pagmo::gwo

S-U

Improved Harmony Search

pagmo::ihs

SM-CU-I

Particle Swarm Optimization (PSO)

pagmo::pso

S-U

Particle Swarm Optimization Generational (GPSO)

pagmo::pso_gen

S-U-sto

(N+1)-ES Simple Evolutionary Algorithm

pagmo::sea

S-U-sto

Simple Genetic Algorithm

pagmo::sga

S-U-I-sto

Corana’s Simulated Annealing (SA)

pagmo::simulated_annealing

S-U

Artificial Bee Colony (ABC)

pagmo::bee_colony

S-U

Covariance Matrix Adaptation Evo. Strategy (CMA-ES)

pagmo::cmaes

S-U-sto

Exponential Evolution Strategies (xNES)

pagmo::xnes

S-U-sto

Non-dominated Sorting GA (NSGA2)

pagmo::nsga2

M-U-I

Multi-objective EA vith Decomposition (MOEA/D)

pagmo::moead

M-U

Multi-objective Hypervolume-based ACO (MHACO)

pagmo::maco

M-U-I

Non-dominated Sorting PSO (NSPSO)

pagmo::nspso

M-U

Local optimization

Common Name

Docs of the C++ class

Capabilities

Compass Search (CS)

pagmo::compass_search

S-CU

COBYLA (from NLopt)

pagmo::nlopt

S-CU

BOBYQA (from NLopt)

pagmo::nlopt

S-U

NEWUOA + bound constraints (from NLopt)

pagmo::nlopt

S-U

PRAXIS (from NLopt)

pagmo::nlopt

S-U

Nelder-Mead simplex (from NLopt)

pagmo::nlopt

S-U

Subplex (from NLopt)

pagmo::nlopt

S-U

MMA (Method of Moving Asymptotes) (from NLopt)

pagmo::nlopt

S-CU

CCSA (from NLopt)

pagmo::nlopt

S-CU

SLSQP (from NLopt)

pagmo::nlopt

S-CU

Low-storage BFGS (from NLopt)

pagmo::nlopt

S-U

Preconditioned truncated Newton (from NLopt)

pagmo::nlopt

S-U

Shifted limited-memory variable-metric (from NLopt)

pagmo::nlopt

S-U

Ipopt

pagmo::ipopt

S-CU

SNOPT (in pagmo_plugins_non_free affiliated package)

pagmo::snopt7

S-CU

WORHP (in pagmo_plugins_non_free affiliated package)

pagmo::wohrp

S-CU

Meta-algorithms

Common Name

Docs of the C++ class

Capabilities 1

Monotonic Basin Hopping (MBH)

pagmo::mbh

S-CU

Cstrs Self-Adaptive

pagmo::cstrs_self_adaptive

S-C

Augmented Lagrangian algorithm (from NLopt) 2

pagmo::nlopt

S-CU

Footnotes

1

The capabilities of the meta-algorithms depend also on the capabilities of the algorithms they wrap. If, for instance, a meta-algorithm supporting constrained problems is constructed from an algorithm which does not support constrained problems, the resulting meta-algorithms will not be able to solve constrained problems.

2

The Augmented Lagrangian algorithm can be used only in conjunction with other NLopt algorithms.

List of problems

This is the list of user defined problems (UDPs) currently provided with pagmo. These are classes that can be used to construct a pagmo::problem, which will then provide a unified interface to access the problem’s functionalities.

In the tables below, we classify optimisation problems according to the following flags:

  • S = Single-objective

  • M = Multi-objective

  • C = Constrained

  • U = Unconstrained

  • I = Integer programming

  • sto = Stochastic

Scalable problems

Common Name

Docs of the C++ class

Type

Ackley

pagmo::ackley

S-U

Golomb Ruler

pagmo::golomb_ruler

S-C-I

Griewank

pagmo::griewank

S-U

Hock Schittkowsky 71

pagmo::hock_schittkowsky_71

S-C

Inventory

pagmo::inventory

S-U-sto

Lennard Jones

pagmo::lennard_jones

S-U

Luksan Vlcek 1

pagmo::luksan_vlcek1

S-C

Rastrigin

pagmo::rastrigin

S-U

MINLP Rastrigin

pagmo::minlp_rastrigin

S-U-I

Rosenbrock

pagmo::rosenbrock

S-U

Schwefel

pagmo::schwefel

S-U

Problem suites

Common Name

Docs of the C++ class

Type

CEC2006

pagmo::cec2006

S-C

CEC2009

pagmo::cec2009

S-C

CEC2013

pagmo::cec2013

S-U

CEC2014

pagmo::cec2014

S-U

ZDT

pagmo::zdt

M-U

DTLZ

pagmo::dtlz

M-U

WFG

pagmo::wfg

M-U

Meta-problems

Meta-problems are UDPs that take another UDP as input, yielding a new UDP which modifies the behaviour and/or the properties of the original problem in a variety of ways.

Common Name

Docs of the C++ class

Decompose

pagmo::decompose

Translate

pagmo::translate

Unconstrain

pagmo::unconstrain

List of islands

This is the list of user defined islands (UDIs) currently provided with pagmo. These are classes that can be used to construct a pagmo::island, which will then provide a unified interface to access the island’s functionalities.

In the pagmo jargon, an island is an entity tasked with managing the asynchronous evolution of a population via an algorithm in the generalised island model. Different UDIs enable different parallelisation strategies (e.g., multithreading, multiprocessing, cluster architectures, etc.).

Common Name

Docs of the C++ class

Thread island

pagmo::thread_island

Fork island

pagmo::fork_island

List of batch fitness evaluators

This is the list of user defined batch fitness evaluators (UDBFEs) currently provided with pagmo. These are classes that can be used to construct a pagmo::bfe, which will then provide a unified interface to access the evaluator’s functionalities.

In the pagmo jargon, a batch fitness evaluator implements the capability of evaluating a group of decision vectors in a parallel and/or vectorised fashion. Batch fitness evaluators are used to implement fine-grained parallelisation in pagmo (e.g., parallel initialisation of populations, or parallel fitness evaluations within the inner loop of an algorithm).

Common Name

Docs of the C++ class

Default BFE

pagmo::default_bfe

Thread BFE

pagmo::thread_bfe