Abstract
Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N, in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed.
Highlights
As a part of production scheduling and combinatorial optimization problems, job-shop scheduling problem (JSP) attracts more and more researchers from all walks of life in the recent decades [1,2,3,4,5].Flexible job-shop scheduling problem (FJSP) inherits the characteristics of the JSP, in which each operation is allowed to be processed by any machine in a given set rather than one specified machine, and it has been proved that the FJSP is strong NP-hard [6]
The nondominated sorting genetic algorithm (NSGA)-II algorithm with T iteration times is first used to obtain the initial population N which consists of three parts changing with the iteration times
The proposed BEG-nondominated sorting genetic algorithm II (NSGA-II) algorithm was coded in MATLAB R2014a and implemented on a computer configured with Intel Core i3 CPU with 2.67 GHz frequency and 4 GB RAM
Summary
As a part of production scheduling and combinatorial optimization problems, job-shop scheduling problem (JSP) attracts more and more researchers from all walks of life (e.g., mechanical engineering, mathematics, and computer software engineering) in the recent decades [1,2,3,4,5]. Brandimarte [9] proposed a hybrid tabu search (TS) algorithm which was based on decomposition to solve the FJSP. A genetic algorithm (GA) combined with a variable neighbourhood search (VNS) was presented by Gao et al [14], and a GA with different strategies was proposed by Pezzella et al [15]. The nondominated sorting genetic algorithm (NSGA) [30] was one of the first methods used to solve the multiobjective problem. We found that the NSGA-II algorithm has the disadvantage of premature convergence to local solution and the algorithms with a twostage optimization scheme have the disadvantages of being unable to gain stable and high quality initial population in the first stage.
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