Antioptimisation of Trusses Using Two-Level Population-Based Incremental Learning

Algorithm 2

Population-based incremental learning for antioptimisation.

Initialisation 𝑃_𝑥,𝑖=0.5,  𝑃_𝑦,𝑖=0.5, and find 𝐛=𝐛_𝑥𝐛_𝑦 and 𝐰=𝐰_𝑥𝐰_𝑦 from an initial population.

Main procedure

(1) For 𝑘=1 to 𝑁_𝑂 (outer loop)

(2) Generate a binary population 𝐁_𝑥 according to 𝑃_𝑥,𝑖 and assign 𝐰_𝑦 as the second part of every solution in 𝐁_𝑥. The population is

𝐁=𝐁𝐰_𝑦.

(3) Perform function evaluations 𝑓(𝐁).

(4) Find the new best solution b from 𝐁∪𝐛 based on the objective function in (1).

(5) Update 𝑃_𝑥,𝑖 with 𝐛_𝑥 using (5).

(6) Set 𝑃_𝑥,𝑖 to [0.1,0.9] in cases that it is out of the interval.

(7) For 𝑗=1 to 𝑁_𝐼 (inner loop)

  (8) Generate a binary population 𝐖_𝑦 according to 𝑃_𝑦,𝑖 and assign 𝐰_𝑥 as the first part of every solution in 𝐖_𝑦. The population

  is 𝐖=𝐰_𝑥𝐖_𝑦.

  (9) Perform function evaluations 𝑓(𝐖)

  (10) Find the new worst solution w from 𝐖∪𝐰 based on the objective function in (3).

  (11) Update 𝑃_𝑦,𝑖 with 𝐰_𝑦 using (5).

  (12) Set 𝑃_𝑦,𝑖 to [0.1,0.9] in cases that it is out of the interval.

(13) Next 𝑗

(14) Next 𝑘