A holonic approach to flexible flow shop scheduling under stochastic processing times

Elite Particle Swarm Optimization Algorithm for Solving the Bi-criteria No-wait Flexible Flow Shop Problem

“…Secondly, it is essential to randomly produce the selective information  ,which shares the same dimension with particle and whose domain is in   0,1 . Apart from the aforesaid fixed particle information, other positions should be updated in accordance with  ; if the corresponding information of  is 1, the information of particle 1 x should be replaced with the information at the position 1 v ; if the aforesaid information is 0, the operation should be omitted. The rest position information is decided by the workpieces to be arranged in 1 x .…”

“…Apart from the aforesaid fixed particle information, other positions should be updated in accordance with  ; if the corresponding information of  is 1, the information of particle 1 x should be replaced with the information at the position 1 v ; if the aforesaid information is 0, the operation should be omitted. The rest position information is decided by the workpieces to be arranged in 1 x . E.g.1: There are seven workpieces to be processed 1 2 3 4 5 6 7 { , , , , , , } J J J J J J J in a flexible flow shop problem.…”

“…Consequently, it is essential to modify the formula of particle position and velocity updating, and the modified formula of velocity updating is showed as follows: 1 12…”

“…4) EDD: The workpiece sort is ranked according to the ascending order of due date of the workpiece to be processed. 5) SOH (Single Objective Hybrid algorithm): Solutions should be got respectively with the aforesaid NEH algorithm, applying makespan and the maximum delay time as the optimal scheduling 1  , 2  of optimal objectives, and combining 1  , 2  as the optimal scheduling of sort  . Among them, the workpiece sorts with the same positions in 1  , 2  should be copied to the corresponding positions in  , and the rest sorts are copied after random number selects a corresponding position information in 1  , 2  .…”

“…Flexible flow shop problem is a crucial branch of scheduling issue [1] and a frequent model in actual industrial production. General flow shop problem i nvolves allocation of fixed processing machine tools, while the flexible flow shop problem [2] allows the application of parallel machines, during which, the wor kpiece in each working procedure can arbitrarily select parallel machine to process.…”