Mathematical Problems in Engineering

Research Article

New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing

Algorithm 1

Sequential simulated annealing for the CAC problem.
( 1 )    I N I T I A L I Z E ( 𝑀 , 𝑇 , 𝐿 )  /* Create the 𝑖 𝑛 𝑖 𝑡 𝑖 𝑎 𝑙 𝑠 𝑜 𝑙 𝑢 𝑡 𝑖 𝑜 𝑛 . */
( 2 )    𝑀 ⋆ ← 𝑀 ;   /* Memorize the 𝑏 𝑒 𝑠 𝑡 𝑠 𝑜 𝑙 𝑢 𝑡 𝑖 𝑜 𝑛 . */
( 3 )    𝑇 = 𝑇 0 ;   /* Initial 𝑡 𝑒 𝑚 𝑝 𝑒 𝑟 𝑎 𝑡 𝑢 𝑟 𝑒 of SA. */
( 4 )   repeat
( 5 )   for   𝑖 ← 1   to   𝐿   do
( 6 )    𝑀 𝑖 ← G E N E R A T E ( 𝑀 ) ;    /* Perturb current state. */
( 7 )    Δ 𝒞 ← 𝒞 ( 𝑀 𝑖 ) − 𝒞 ( 𝑀 ) ;    /* Evaluate cost function. */
( 8 )    𝑥 ← r a n d o m ;     /* 𝑥 in the range [0,1). */
( 9 )   if   Δ 𝒞 < 0 𝐨 𝐫 𝑒 − Δ 𝒞 / 𝑇 > 𝑥   then
( 1 0 )     𝑀 ← 𝑀 𝑖 ;     /* Accept new state.*/
( 1 1 )    if   𝒞 ( 𝑀 ) < 𝒞 ( 𝑀 ⋆ )   then
( 1 2 )      𝑀 ⋆ ← 𝑀 ; /* Memorize the 𝑏 𝑒 𝑠 𝑡 𝑠 𝑜 𝑙 𝑢 𝑡 𝑖 𝑜 𝑛 . */
( 1 3 )    end if
( 1 4 )   end if
( 1 5 )  end for
( 1 6 )   C A L C U L A T E _ C O N T R O L ( 𝑇 , 𝜙 )
( 1 7 )   until   𝑡 𝑒 𝑟 𝑚 𝑖 𝑛 𝑎 𝑡 𝑖 𝑜 𝑛 𝑐 𝑜 𝑛 𝑑 𝑖 𝑡 𝑖 𝑜 𝑛 is satisfied;