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. 2025 Jul 31;11:e3042. doi: 10.7717/peerj-cs.3042

Table 4. Classification of MOO algorithms.

Category Representative algorithms Fundamental principle Year
Bio-inspired algorithms Genetic algorithm (GA) Simulates natural selection and genetic recombination based on Darwinian evolution 1975
Particle swarm optimization (PSO) Inspired by bird flocking behavior, where particles update their velocity and position based on individual and group best solutions 1995
Ant colony optimization (ACO) Models pheromone-based communication in ant colonies for cooperative pathfinding 1992
Mathematical theory-driven algorithms Weighted sum method Uses linear programming techniques to transform MOO into a single-objective problem 1950s
MOEA/D Applies game theory and decomposition strategies to divide high-dimensional objectives into subproblems for cooperative solving 2007
Physics-inspired algorithms Simulated annealing (SA) Maps the annealing process in metallurgy, using a temperature-controlled probabilistic acceptance mechanism to avoid local optima 1983
Gravitational search algorithm (GSA) Based on Newton’s law of gravitation, simulating the attraction forces between solutions to guide convergence 2009
Machine learning-enhanced optimization Neural network-based surrogate models Uses deep learning to approximate objective functions, reducing computational costs for real-world optimization 2010s
Reinforcement learning-based optimization Integrates Markov decision processes (MDP) and vectorized reward functions for optimizing strategies in dynamic environments 1998