International Scholarly Research Notices

Research Article

Ant Colony Algorithm for Just-in-Time Job Shop Scheduling with Transportation Times and Multirobots

Algorithm 1

initialization step
𝐷 𝑒 𝑝 𝑜 𝑡 _ 𝑖 𝑛 𝑖 𝑡 𝑖 𝑎 𝑙 ← { 𝑓 𝑖 𝑟 𝑠 𝑡 𝑜 𝑝 𝑒 𝑟 𝑎 𝑡 𝑖 𝑜 𝑛 𝑠 𝑜 𝑓 𝑗 𝑜 𝑏 𝑠 }
𝐶 ℎ 𝑎 𝑟 𝑖 𝑜 ( 𝑟 ) ← 𝑂 𝑟 , ∀ 𝑟 = 1 , … , 𝑅 ( 𝑂 𝑟 ⊂ 𝑖 𝑛 𝑖 𝑡 𝑖 𝑎 𝑙 _ 𝑑 𝑒 𝑝 𝑜 𝑠 𝑖 𝑡 )
𝑑 ( 𝑟 , 0 ) ← 𝑑 𝑒 𝑝 𝑙 𝑎 𝑐 𝑒 𝑟 _ 𝑟 𝑜 𝑏 𝑜 𝑡 ( 𝑟 ) , ∀ 𝑟 = 1 , … , 𝑅 / / ℎ 𝑒 𝑢 𝑟 𝑖 𝑠 𝑡 𝑖 𝑐 𝑡 𝑜 𝑚 𝑜 𝑣 𝑒 𝑡 ℎ 𝑒 𝑡 𝑟 𝑎 𝑛 𝑠 𝑝 𝑜 𝑟 𝑡 𝑒 𝑟 𝑣 𝑒 ℎ 𝑖 𝑐 𝑙 𝑒
𝑐 ( 𝑟 , 0 ) = 𝑑 ( 𝑟 , 0 ) , ∀ 𝑟 = 1 , … , 𝑅
𝐹 𝑜 𝑟 ( 𝑖 𝑡 1 = 1 , … , 𝑁 1 m a x ) 𝑑 𝑜
  𝐹 𝑜 𝑟 ( 𝑖 𝑡 = 1 , … , 𝑁 2 m a x ) 𝑑 𝑜
   / / 𝑔 𝑒 𝑛 𝑒 𝑟 𝑎 𝑡 𝑒 𝑜 𝑛 𝑒 𝑠 𝑜 𝑙 𝑢 𝑡 𝑖 𝑜 𝑛
   𝐹 𝑜 𝑟 ( 𝑡 = 1 , … , ℎ 𝑜 𝑟 𝑖 𝑧 𝑜 𝑛 ) 𝑑 𝑜
     / / 𝑐 𝑦 𝑐 𝑙 𝑒 𝑜 𝑓 𝑝 𝑟 𝑜 𝑑 𝑢 𝑐 𝑡 𝑖 𝑜 𝑛
     𝐹 𝑜 𝑟 ( 𝑠 = 1 , … , 𝑆 ) 𝑑 𝑜
        𝑇 𝑟 𝑎 𝑖 𝑡 𝑒 𝑟 _ 𝑠 𝑡 𝑎 𝑡 𝑖 𝑜 𝑛 ( 𝑠 ) / / 𝑡 𝑟 𝑒 𝑎 𝑡 𝑚 𝑒 𝑛 𝑡 𝑜 𝑓 𝑠 𝑡 𝑎 𝑡 𝑖 𝑜 𝑛 𝑠
     𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
     𝐹 𝑜 𝑟 ( 𝑟 = 1 , … , 𝑅 ) 𝑑 𝑜
       𝑑 ( 𝑟 , 𝑡 ) ← 𝑡 𝑟 𝑎 𝑖 𝑡 𝑒 𝑟 _ 𝑟 𝑜 𝑏 𝑜 𝑡 ( 𝑟 ) / / 𝑡 𝑟 𝑒 𝑎 𝑡 𝑚 𝑒 𝑛 𝑡 𝑜 𝑓 𝑡 𝑟 𝑎 𝑛 𝑠 𝑝 𝑜 𝑟 𝑡 𝑒 𝑟 𝑣 𝑒 ℎ 𝑖 𝑐 𝑙 𝑒 𝑠
       𝑐 ( 𝑟 , 𝑡 ) ← 𝑑 ( 𝑟 , 𝑡 )
       / / 𝑙 𝑜 𝑐 𝑎 𝑙 𝑢 𝑝 𝑑 𝑎 𝑡 𝑒 𝑜 𝑓 𝑝 ℎ 𝑒 𝑟 𝑜 𝑚 𝑜 𝑛 𝑒
       𝜏 𝑐 𝑑 = 𝜏 𝑐 𝑑 + 𝜏 0 ( 1 − 𝜌 0 )
       𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
       𝐹 𝑜 𝑟 ( 𝑠 = 1 , … , 𝑆 ) 𝑑 𝑜
         𝑀 𝑖 𝑠 𝑒 _ 𝑎 𝑗 𝑜 𝑢 𝑟 _ 𝑠 𝑡 𝑎 𝑡 𝑖 𝑜 𝑛 ( 𝑠 ) / / 𝑢 𝑝 𝑑 𝑎 𝑡 𝑒 𝑜 𝑓 𝑠 𝑡 𝑎 𝑡 𝑖 𝑜 𝑛 𝑠
       𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
   𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
  𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
  𝑆 𝑜 𝑙 ← 𝑐 ℎ 𝑜 𝑖 𝑠 𝑖 𝑟 _ 𝑚 𝑒 𝑖 𝑙 𝑙 𝑒 𝑢 𝑟 𝑒 ( ) / / 𝑐 ℎ 𝑜 𝑠 𝑒 𝑜 𝑓 𝑡 ℎ 𝑒 𝑏 𝑒 𝑠 𝑡 𝑠 𝑜 𝑙 𝑢 𝑡 𝑖 𝑜 𝑛
  / / 𝐺 𝑙 𝑜 𝑏 𝑎 𝑙 𝑢 𝑝 𝑑 𝑎 𝑡 𝑒 𝑜 𝑓 𝑝 ℎ 𝑒 𝑟 𝑜 𝑚 𝑜 𝑛 𝑒 .
  𝜏 𝑚 ( 𝑖 ) 𝑚 ( 𝑖 + 1 ) = 𝜏 𝑚 ( 𝑖 ) 𝑚 ( 𝑖 + 1 ) + 𝜏 0 ( 1 − 𝜌 0 ) ,for each pair of successive operation of sol
  𝐸 𝑛 𝑑 𝐹 𝑜 𝑟
  𝐸 𝑛 𝑑 𝑎 𝑙 𝑔 𝑜 𝑟 𝑖 𝑡 ℎ 𝑚