Part 3 – Optimisation algorithms

A non-exhaustive list of optimisation algorithms, classed by categories.

Capabilities:

  • S = Single-objective
  • M = Multi-objective
  • C = Constrained
  • U = Unconstrained
  • I = Integer programming
  • sto = Stochastic

1. Global optimisation

1.1. Evolutionary optimisation

1.1.1. Genetic algorithms

  • Simple Genetic Algorithm (GA) – S / U / I / Sto
  • Non-dominated Sorting Genetic Algorithm (NSGA-II) – M / U / I – 2000
  • Epsilon-Non-dominated Sorting Genetic Algorithm (ε-NSGA-II) – M / U / I – 2006
  • Reference point based Non-dominated Sorting Genetic Algorithm (R-NSGA-II) – 2006
  • Non-dominated Sorting Genetic Algorithm (NSGA-III) – 2014
  • Reference point based Non-dominated Sorting Genetic Algorithm (R-NSGA-II) – 2018
  • Unified Non-dominated Sorting Genetic Algorithm (U-NSGA-III) – 2016
  • Vector Evaluated Genetic Algorithms (VEGA) – 1985
  • Adapting Scatter Search to Multiobjective Optimization (AbYSS) – 2008
  • Fast Pareto Genetic Algorithm (FastPGA) – 2007
  • Multi-Objective Cellular Genetic Algorithm (MOCell) – 2006
  • Multi-Objective Cross generational elitist selection, Heterogeneous recombination, Cataclysmic mutation (MOCHC) – 2007
  • Biased Random Key Genetic Algorithm (BRKGA)

1.1.2. Differential Evolution

  • Differential Evolution (DE) – S / U
  • Self-adaptive Differential Evolution (jDE, iDE and pDE) – S / U
  • Generalized Differential Evolution 3 (GDE3) – 2005
  • Cellular Differential Evolution (CellDE)

1.1.3. Evolution Strategy

  • Evolution Strategy (ES) – S
  • Covariance Matrix Adaptation Evolution Strategy (CMA-ES) – M / S / U / Sto – 2007
  • Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES)
  • Bi-Population Covariance Matrix Adaptation Evolution Strategy (BI-POP CMA-ES)
  • Exponential Evolution Strategy (xNES) – S / U / Sto
  • Pareto Archived Evolutionary Strategy (PAES) – 1999

1.1.4. Indicator-based

  • Indicator Based Evolutionary Algorithm (IBEA) – 2004
  • Simple Indicator-Based Evolutionary Algorithm (SIBEA)
  • Sampling-Based Hypervolume-Oriented Algorithm (SHV)
  • Hypervolume Estimation Algorithm for Multiobjective Optimization (HypE)
  • S-Metric Selection Evolutionary Multiobjective Optimisation Algorithm (SMS-EMOA) – 2007
  • Set Preference Algorithm for Multiobjective Optimization (SPAM)

1.1.5. Decomposition algorithms

  • Multi-Objective Evolutionary Algorithm with Decomposition (MOEA/D) – M / U – 2009
  • Decomposition-Based Evolutionary Algorithm (DBEA) – 2015

1.1.4. Other evolutionary algorithms

  • (N+1)-ES Simple Evolutionary Algorithm (SEA) – S / U / Sto
  • Epsilon-Multi-Objective Evolutionary Algorithm (ε-MOEA) – 2003
  • Pareto Envelope-Based Selection Algorithm II (PESA-II) – 2001
  • Strength Pareto Evolutionary Algorithm (SPEA2) – 2002
  • Duplicate Elimination Non-domination Sorting Evolutionary Algorithm (DENSEA) – 2006
  • Epsilon-Constraint Evolutionary Algorithm (ECEA)
  • Fair Evolutionary Multiobjective Optimizer (FEMO)
  • Simple Evolutionary Multiobjective Optimizer (SEMO2)
  • Multiple Single Objective Pareto Sampling (MSOPS)
  • Borg Multi-Objective Evolutionary Algorithm (Borg MOEA) – 2013
  • Reference Vector Guided Evolutionary Algorithm (RVEA)
  • Estimation of Distribution Algorithm (EDA)
  • Strongly Typed Genetic Programming (STGP)
  • Constrained Two-Archive Evolutionary Algorithm (C-TAEA) – M – 2019

1.2. Bio-inspired algorithms

1.2.1. Particle Swarm

  • Particle Swarm Optimization (PSO) – S / U
  • Particle Swarm Optimization Generational (GPSO) – S / U / Sto
  • Non-dominated Sorting Particle Swarm Optimization (NSPSO) – M / U
  • Multi-Objective Particle Swarm Optimization (MOPSO or OMOPSO) – 2005
  • Speed-constrained Multi-objective Particle Swarm Optimization (SMPSO) – 2009
  • Multiswarm Particle Swarm Optimization (MPSO)

1.2.2. Ant Colony

  • Ant Colony Optimisation (ACO)
  • Extended Ant Colony Optimization (GACO) – S / C / U / I
  • Multi-objective Hypervolume-based Ant Colony Optimisation (MHACO) – M / U / I

1.2.3. Other bio-inspired algorithms

  • Grey Wolf Optimizer (GWO) – S / U
  • Simulated Annealing (SA) – S / U
  • Artificial Bee Colony (ABC) – S / U
  • Improved Harmony Search (IHS) – S / M / C / U / I

2. Local optimisation

  • Nelder-Mead simplex – S / U
  • Method of Moving Asymptotes (MMA) – S / C / U