<![CDATA[Optimization methods play a crucial role in problem-solving processes, particularly for addressing complex problems. Among the most effective approaches for achieving optimal solutions is Particle Swarm Optimization (PSO), an algorithm inspired by the social behavior of animals. In PSO, particles—analogous to individual animals—are initialized and subsequently move through continuous position updates guided by two combined factors: attraction toward the individual's best-known position (pBest) and attraction toward the global best position (gBest), until an optimal position is reached. Particle movement is governed by three main control parameters: the cognitive coefficient (c1), the social coefficient (c2), and the inertial weight (ω), which together enable the algorithm to produce optimal values while avoiding entrapment in local solutions. Compared to other optimization methods such as the Firefly Algorithm (FA) and Gray Wolf Optimizer (GWO), PSO offers notable advantages in convergence speed and its ability to handle non-linear problems involving noise. These strengths make PSO well suited for complex applications, including solving non-linear mathematical models, optimizing fuzzy controllers, and optimizing exhaust gas emission parameters and engine performance on ships.]]>
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