A class of order-based genetic algorithm for flow shop scheduling

Genetic ordinal optimisation for stochastic flow shop scheduling

“…Population size P(k); P t (k) Population; temporary population at the kth generation G max Maximum generation number θ; θ * Solution; the best solution found so far l Number of best solutions selected from the population S; |S| Search space; size of search space G Set of the p per cent "best" feasible solutions p e Desired solution quality for G p se Desired probability that at least one of the selected solutions is in G p m , p c Mutation and crossover probabilities J Performance expectation L Sample performance µ Theoretical mean σ 2 Theoretical variancē J i ; s 2 …”

“…Hybridisation is a practical and promising means to develop an effective and efficient algorithm by combining features of different methods [2,12]. In this section, OO, OCBA and the GA are briefly reviewed, and then GOO is proposed after providing the rationale and motivation behind hybridising these ideas.…”

“…Step 4 Perform order-based GA operations, including selection, crossover and mutation [2] with the top l solutions of P(k) to generate P s new solutions to form temporary population P t (k).…”

“…p e = |G|/|S|. Usually, |S| is extremely large, so it is very hard and time-consuming to find the best global solution in S. If we soften the goal to obtain at least one solution in G with the desired probability p se , then p se = 1 − (1 − p e ) m and m = ln(1 − p se )/ ln(1 − p e ), where m is the number required for uniformly sampling [2]. In Table 1, the required number m is summarised according to different p se and p e .…”

“…Due to the key role of scheduling in manufacturing systems, it is very important to develop efficient and effective advanced manufacturing and scheduling technologies and algorithms [2]. With strong industrial and engineering roots, flow shop scheduling, which is applicable to many real manufacturing systems, has been one of the most well-studied production scheduling problems [1][2][3][4][5][6][7][8][9][10][11][12]. The deterministic permutation flow shop problem with n jobs and m machines can be defined as follows: each of the n jobs is to be sequentially processed on machines 1 through m. At any time, no job can be processed on more than one machine, while no machine can process more than one job simultaneously.…”