Improvements for multi-objective flow shop scheduling by Pareto Iterated Local Search

The flow shop scheduling problem consists in the assignment of a set of jobs J = {J1, . . . , Jn}, each of which consists of a set of operations Jj = {Oj1, . . . , Ojoj} onto a set of machines M = {M1, . . . ,Mm} [5, 18]. Each operation Ojk is processed by at most one machine at a time, involving a non-negative processing time pjk. The result of the problem resolution is a schedule x, defining for each operation Ojk a starting time sjk on the corresponding machine. Several side constraints are present which have to be respected by any solution x belonging to the set of feasible schedules X. Precedence constraints Ojk ⊲ Ojk+1∀j = 1, . . . , n, k = 1, . . . , oj − 1 between the operations of a job Jj assure that processing of Ojk+1 only commences after completion of Ojk, thus sjk+1 > sjk + pjk. In flow shop scheduling, the machine sequence in which the operations are processed by the machines is identical for all jobs, and for the specific case of the permutation flow shop scheduling the job sequence must also be the same on all machines.