An Enhanced Differential Evolution Based Algorithm with Simulated Annealing for Solving Multiobjective Optimization Problems

Algorithm 1

The proposed simulate annealing algorithm.

input: 𝑥_𝑖, 𝑤_𝑖, 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, 𝑇_min, 𝑇_max, 𝑃_𝑡, 𝑃_temp, 𝑚𝑎𝑥_𝑙𝑖𝑓𝑒_𝑐𝑖𝑐𝑙𝑒

If (𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒>𝑇_min) {

   Compute the value of Δdom_avg by (9).

   Calculate the acceptance probability prob:

       prob=exp(−Δdom_avg/𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒)

   With a probability prob Do

      Put the current individual 𝑥_𝑖 to the temporary population: 𝑃_temp=𝑃_temp∪𝑥_𝑖.

      Replace the current individual 𝑥_𝑖 by the trial individual 𝑤_𝑖: 𝑥_𝑖=𝑤_𝑖.

      Assign the life value 𝑚𝑎𝑥_𝑙𝑖𝑓𝑒_𝑐𝑦𝑐𝑙𝑒 to the new individual 𝑥_𝑖: 𝑙𝑖𝑓𝑒_𝑖=𝑚𝑎𝑥_𝑙𝑖𝑓𝑒_𝑐𝑦𝑐𝑙𝑒,

where 𝑙𝑖𝑓𝑒_𝑖 represents the life cycle value of solution 𝑥_𝑖.

   otherwise

      Put the current individual 𝑥_𝑖 to the temporary population: 𝑃_temp=𝑃_temp∪𝑥_𝑖.

}// End If