A Hybrid Bat Algorithm with Path Relinking for Capacitated Vehicle Routing Problem

Algorithm 7

HBA-PR.

(1) Initialize the 𝑝𝑠,  bat population and other parameters;

(2) Evaluate fitness for each individual;

(3) 𝐸𝑆←𝐸𝑙𝑖𝑡𝑒_Set(𝑥);

(4) while  𝑡≤𝑡_max  do

(5)  Compute pulse emission rate by (7);

(6)  Determine frequency 𝑓𝑟 by (8);

(7)  for 𝑖=1:  ps do

(8)    𝑥←𝐺𝑟𝑒𝑒𝑑𝑦_Randomized_Construction(𝑓𝑟);

(9)    𝑥←𝐿𝑜𝑐𝑎𝑙_Search_Phase (𝑥);

(10)  end

(11)  Evaluate fitness for each individual 𝑥;

(12)   𝐸𝑆←𝐸𝑙𝑖𝑡𝑒_Set(𝑥);

(13)   𝐸𝑆_∗←𝑆𝑒𝑙𝑒𝑐𝑡_Best_Elite(𝐸𝑆); // select the best individual in elite set 𝐸𝑆

(14)  for 𝑖=1:   𝑝𝑠 do

(15)    𝑥←𝑃𝑎𝑡ℎ_Relinking(𝐸𝑆_∗,  𝑥);

(16)  end

(17)  Evaluate fitness for each individual 𝑥;

(18)   𝐸𝑆←𝐸𝑙𝑖𝑡𝑒_Set(𝑥);

(19)   𝐿𝑑_𝑖←𝐶𝑜𝑚𝑝𝑢𝑡𝑒_Loudness(𝑓(𝑥)); //Compute loudness of each individual by (9);

(20)   𝐸𝑆_∗←𝑆𝑒𝑙𝑒𝑐𝑡_Best_Elite(𝐸𝑆);

(21)   𝑥←𝑆𝑢𝑏-sequence_Local_Search (𝐸𝑆_∗)  //carry out random sub-sequence local

   search

(22)  Evaluate fitness for each individual 𝑥;

(23)   𝐸𝑆←𝐸𝑙𝑖𝑡𝑒_Set(𝑥);

(24)   𝐸𝑆_∗←𝑆𝑒𝑙𝑒𝑐𝑡_Best_Elite(𝐸𝑆);

(25)   𝑥←𝑆𝑖𝑛𝑔𝑙𝑒-point_Local_Search (𝐸𝑆_∗)  //carry out random single-point local search

(26)  Evaluate fitness for each individual 𝑥;

(27)   𝐸𝑆←𝐸𝑙𝑖𝑡𝑒_Set(𝑥);

(28)  𝑡=𝑡+1

(29) end

(30) Output result and plot