Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems

Algorithm 2

Algorithm for PSO_CLUS.

Begin 𝐏𝐒𝐎_{𝐂𝐋𝐔𝐒} Algorithm

 Step  1. Definition Phase

      (1.1) function to optimize as  𝑓

      (1.2) Parameter

     (1.2.1) swarm size

     (1.2.2) problem dimension

     (1.2.3) solution search space

     (1.2.4) particle velocity range

 Step  2. Initialized phase

     For all particles randomly initialized in search space

     (2.1) position 𝑥_𝑖←(𝑥_𝑖1,…,𝑥_𝑖𝑑)

     (2.2) velocity 𝑣_𝑖←(𝑣_𝑖1,…,𝑣_𝑖𝑑),

     (2.3) 𝑝best_𝑖←(𝑥_𝑖1,…,𝑥_𝑖𝑑)

     (2.4) 𝑔best ← best of  𝑝best_𝑖

     (2.5) evaluate 𝑓(𝑥_𝑖) using objective function of problem

 Step  3. Operation Phase

     Repeat until a stopping criterion is satisfied

     (3.1). Compute inertia weight using any inertia weight formula

     (3.2). For each particle 𝑖

     (3.2.1). update 𝑣_𝑖 for particle using (1)

     (3.2.2). validate for velocity boundaries

     (3.2.3). update 𝑥_𝑖 for particle using (2)

     (3.2.4). validate for position boundaries

     (3.2.5). If 𝑓(𝑥_𝑖)<𝑓(𝑝best_𝑖) then 𝑝best_𝑖←𝑥_𝑖

     (3.3). 𝑔best ← best of 𝑝best𝑖

     (3.4). Implement local search using CLUS in  Algorithm 1

 Step  4. Solution Phase

     (4.1). 𝑥^∗←𝑔best

     (4.2). 𝑓^∗←𝑓(𝑔best)

     (4.3). Return 𝑥^∗ and  𝑓^∗

End   𝐏𝐒𝐎_{𝐂𝐋𝐔𝐒}   Algorithm