Parallel machine scheduling with step-deteriorating jobs and setup times by a hybrid discrete cuckoo search algorithm

Abstract

This article considers the parallel machine scheduling problem with step-deteriorating jobs and sequence-dependent setup times. The objective is to minimize the total tardiness by determining the allocation and sequence of jobs on identical parallel machines. In this problem, the processing time of each job is a step function dependent upon its starting time. An individual extended time is penalized when the starting time of a job is later than a specific deterioration date. The possibility of deterioration of a job makes the parallel machine scheduling problem more challenging than ordinary ones. A mixed integer programming model for the optimal solution is derived. Due to its NP-hard nature, a hybrid discrete cuckoo search algorithm is proposed to solve this problem. In order to generate a good initial swarm, a modified heuristic named the MBHG is incorporated into the initialization of population. Several discrete operators are proposed in the random walk of Lévy Flights and the crossover search. Moreover, a local search procedure based on variable neighborhood descent is integrated into the algorithm as a hybrid strategy in order to improve the quality of elite solutions. Computational experiments are executed on two sets of randomly generated test instances. The results show that the proposed hybrid algorithm can yield better solutions in comparison with the commercial solver CPLEX with one hour time limit, discrete cuckoo search algorithm and the existing variable neighborhood search algorithm.

An Improved Discrete Artificial Bee Colony Algorithm for Flexible Flowshop Scheduling with Step Deteriorating Jobs and Sequence‐Dependent Setup Times

“…Stage3 Stage2 M11 M31 M21 M13 M33 M23 M12 M32 M22 53 68 13 104 68 7 9 15 80 23 66 29 3 87 61 10 37 56 45 98 53 59 26 36 20 25 41 33 30 12 28 20 20 44 23 21 44 25 40 31 33 22 25 22 10 h ijk = e initial job sequence [4,5,1,3,2] at stage 1 is given and consistent with the instance illustrated in Figure 2. e machine allocation and completion time of all jobs are computed as follows.…”

“…e comparison with GA, GH, and MVNS verifies the effectivity and efficiency of the IDABC algorithm, especially for large-scale problems. Some future work may be done from the following aspects: (1) our study involves the single-objective problem of total weighted completion time; the application of the developed algorithm may be extended to solve other single or multiobjective scheduling problems; (2) it is interesting to present some heuristic algorithms to generate initial population instead of the random procedure used in the paper so as to further improve the algorithm performance.…”

“…In the classical FFSP, the processing times of jobs are always assumed to be known and fixed. However, it might not be true in realistic industrial processes such as steel production and equipment maintenance [2]. e actual processing time may become longer due to equipment wear, physical properties of jobs, fatigue of the workers, and so on.…”

“…ere is a relatively little research on step deterioration. To solve identical parallel machine scheduling, Guo et al [2] considered sequencedependent setup times and applied a hybrid discrete cuckoo algorithm to minimize total tardiness; Cheng et al [9] presented a modified weight-combination search algorithm and a variable neighborhood search to minimize total completion time. For two-stage FFSP with identical parallel machines at stage 1 and a single batching machine at stage 2, Gong and Tang [10] proposed a heuristic algorithm to minimize makespan plus the total penalty cost of batching-machine utilization ratio where the job processing time at stage 2 is a step function of its waiting time between the two stages.…”

Adaptive Autotuning Mathematical Approaches for Integrated Optimization of Automated Container Terminal

“…Although the basic metaheuristic algorithms may not obtain the exact solution, it can obtain the suboptimal solution and the complexity of computing time is relatively low, and comparatively, its applicability and stability are better than those of the accurate algorithm [26][27][28]. However, taking more factors into consideration in automated terminals, the model is more complex and the basic metaheuristic algorithm has shown up the disadvantages such as longer computing time and slow convergence speed [29,30].…”