Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion

The hybrid flow shop scheduling problem

“…This is sometimes referred to as operation processing order or exact representation. [83] employ this scheme and propose several TS and SA methods. In order to cope with such large search space, the schedule is constructed, at each stage, after the solution of a linear program.…”

“…F Hm, ((P M (k) ) m k=1 ))|avail|several simulation, heuristics, SA [16] F H3, ((P M (k) ) 3 k=1 ))||Cmax agent-based approach [20] F Hm, ((P M (k) ) m k=1 ))|recrc|Ū w MPF, GA, lower bounds,checks processing [47] F Hm, ((P M (k) ) m k=1 ))||Cmax Artificial Immune Systems [91] F Hm, ((P M (k) ) m k=1 ))|blocking, skip|Cmax flow lines, MPF, TS, huristics F H2, ((1 (1) , P 2 (2) ))||Cmax B&B, GA, heuristics [41] F Hm, ((P M (k) ) m k=1 ))|recrc|T w dispatching rules, heuristics [61] F H2, ((1 (1) , P 2 (2) ))|no − wait, (p j = 1) 1 |Cmax exact method [96] F Hm, ((P M (k) ) m k=1 ))||{Cmax,C} review on exact solution methods [121] F H2, ((1 (1) , P M (2) ))|avail|Cmax B&B, heuristics, complexity [38] F H3, ((RM (k) ) 3 k=1 ))|prec, block, S nsd |Cmax MPR-TS [70] F H2, ((P M (k) ) 2 k=1 )||Cmax B&B [88] F Hm, ((P M (k) ) m k=1 ))||Cmax MPR-SA, lower bounds [107] F H2, ((P 2 (1) , 1 (2) ))|batch|Cmax TSP-based heuristics [37] F H3, ((RM (k) ) 3 k=1 ))|S sd , block, prec|Cmax MPF, lower bounds, TS [50] F Hm, ((P M (k) ) m k=1 ))|assign|ĒT TS, special problem [83] F Hm, ((P M (k) ) m k=1 ))|r j |Cost TS, SA, heuristics [85] F Hm, ((RM (k) ) m k=1 ))|lot, skip|Cost GA, SA, flow lines [100] F H3, ((P M (k) ) 3 k=1 ))||Cmax heuristics [151] (1) , P 2 (2) ))|assembly (2) |F heuristics [195] F Hm, ((P M (k) ) m k=1 ))|size jk |Cmax Particle Swarm Optimization [196] F H2, ((1 (1) , P 2 (2) ))|skip (1) |Cmax heuristics 2009 [90] F Hm, ((RM (k) ) m k=1 ))|S sd , r j |αCmax + (1 − α)Ū MPF, heuristics, dispatching rules, GA [95] F H2, ((P M (1) , 1 (2) ))||Cmax heuristics, product-mix [191] F Hm, ((P M (k) ) m k=1 ))|skip, block, reentry|Cmax GA mixed with LS [229] F Hm, ((P M (k) ) m k=1 ))|size jk |Cmax Iterated Greedy (IG) [19] F H2, ((P M (1) , P M (2) ))|batch (2) |Cmax heuris...…”

A Firefly Algorithm for the Mono-Processors Hybrid Flow Shop Problem

“…With the same purpose, a branch-and-bound algorithm was addressed in [11]. Several heuristics were studied to schedule multiprocessor tasks in the two-stage extension of the same problem in order to minimize makespan as simulating analytics (SA) and TS [12]. In [13] and with recirculation to minimize the weighted number of tardy tasks, authors compare a greedy algorithm with a genetic algorithm (GA) on solving a three-stage HFS scheduling problem.…”

Solving a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment by a genetic algorithm

“…Hybrid flow shop problems can be shown as flexible flow lines (FFL) enabling us to represent most of the production environments. Several industries, such as chemical and tile [2], textile [3], and metallurgical industry [4], can be modeled as a hybrid flow shop.…”