SIPSO_Optimization

sphere function is tested

Self-Interest Particle Swarm Optimization (SIPSO)

Self-Interest Particle Swarm Optimization (SIPSO) is a variation of the traditional Particle Swarm Optimization (PSO) that incorporates the concept of self-interest. Unlike standard PSO, where particles are influenced by the global best (gbestg_{\text{best}}gbest​) and local best (pbestp_{\text{best}}pbest​), SIPSO focuses more on individual particle behavior driven by self-interest to improve exploration and prevent premature convergence.

Key Features of SIPSO:

1. Self-Interest Mechanism:Each particle prioritizes its performance and chooses to either follow its personal best or deviate significantly for exploratory purposes.
2. Adaptive Weights:The influence of self-interest, local best, and global best is adjusted dynamically based on the iteration or swarm's diversity.
3. Exploration vs Exploitation:Balances exploration and exploitation by assigning greater self-interest in early iterations (to explore) and gradually reducing it in later iterations (to exploit).

SIPSO Algorithm Steps:

1. Initialization:

• Initialize particles with random positions and velocities in the search space.
• Evaluate the fitness of each particle and assign pbestp_{\text{best}}pbest​ and gbestg_{\text{best}}gbest​.

1. Velocity Update:

• Modify the velocity update rule to include a self-interest term: vi(t+1)=ωvi(t)+c1r1⋅(pbest,i−xi)+c2r2⋅(gbest−xi)+c3r3⋅SelfTermv_{i}(t+1) = \omega v_{i}(t) + c_1 r_1 \cdot (p_{\text{best},i} - x_i) + c_2 r_2 \cdot (g_{\text{best}} - x_i) + c_3 r_3 \cdot \text{SelfTerm}vi​(t+1)=ωvi​(t)+c1​r1​⋅(pbest,i​−xi​)+c2​r2​⋅(gbest​−xi​)+c3​r3​⋅SelfTerm
• SelfTerm: A self-interest-driven direction based on the particle’s random exploration or attraction to specific regions.

1. Position Update:

• Update the particle position based on its new velocity: xi(t+1)=xi(t)+vi(t+1)x_i(t+1) = x_i(t) + v_i(t+1)xi​(t+1)=xi​(t)+vi​(t+1)

1. Fitness Evaluation:

• Evaluate the fitness of the updated particle positions.

1. Update pbestp_{\text{best}}pbest​ and gbestg_{\text{best}}gbest​:

• If the particle's current position is better than its pbestp_{\text{best}}pbest​, update pbestp_{\text{best}}pbest​.
• If any particle's current position is better than gbestg_{\text{best}}gbest​, update gbestg_{\text{best}}gbest​.

1. Termination:

• Repeat until the maximum number of iterations or a convergence criterion is met.