In Particle Swarm Optimisation (PSO), acceleration coefficients c1 and c2 play crucial roles in influencing the cognitive and social components, respectively. These components represent the individual and collective learning aspects of PSO, contributing to the balance between local and global search.
The cognitive component (c1) represents each particle’s individual learning, emphasising the importance of personal best (pbest) information in guiding its movement within the search space. On the other hand, the social component (c2) reflects the collective learning aspect of PSO, emphasising the influence of the global best-known position (gbest) on particle movement.
When c1 is high, particles give greater weight to their own best-known positions, prioritizing exploitation of local solutions. Conversely, a lower �1c1 value encourages exploration by allowing particles to be more influenced by their current positions, promoting a broader search of the solution space.
A higher value of c2 places greater emphasis on the swarm’s collective knowledge, encouraging particles to explore promising regions identified by other particles. This promotes global exploration and helps the swarm converge towards the overall best-known solution. Conversely, a lower �2c2 value reduces the influence of gbest, allowing particles to focus more on exploiting their own best-known solutions, which can lead to faster convergence towards local optima.
Varying Values of Acceleration Coefficients (c1 and c2)
High Cognitive Component (c1):
Focus more on own best-known positions
- Advantages:
- Prioritise exploitation of local solutions, better optimisation
- Challenges:
- Easily neglecting swarm best positions
- Limiting exploration potential, trapped in local optima
High Cognitive Component (c2):
Focus more on social best-known positions
- Advantages:
- Prioritise exploration, expanding search space easily
- Aids in escaping local optima
- Challenges:
- May lead to oscillatory behaviour, excessively prioritising exploration
- Cause overshoot and exhibit erratic convergence behaviour, slowing down optimisation.
The optimal values of c1 and c2 may vary depending on the characteristics of the optimisation problem.
Different problems may require different settings of c1 and c2 to achieve optimal performance, making parameter tuning a problem-dependent task.
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Experimental Results
Varying c1 and c2 influences the algorithm’s convergence speed and solution quality. Higher values of c1 tend to prioritise exploitation, leading to faster convergence towards local optima, while higher values of c2 favour exploration, potentially discovering better solutions but with slower convergence.