Three-machine flowshop with two operations per job to minimize makespan

This work studies three variants of a three-machine flowshop problem with two operations per job to minimize makespan (F3/o = 2/C_max). A set of n jobs are classified into three mutually exclusive families A, B and C. The families A, B and C are defined as the set of jobs that is scheduled in machine sequence (M₁, M₂), (M₁, M₃) and (M₁, M₃), respectively, where (M_x, M_y) specifies the machine sequence for the job that is processed first on M_x, and then on M_y. Specifically, jobs with the same route (machine sequence) are classified into the same family. Three variants of F3/o = 2/C_max are studied. First, F3/GT, no-idle, o = 2/C_max, in which both machine no-idle and GT restrictions are considered. The GT assumption requires that all jobs in the same family are processed contiguously on the machine and the machine no-idle assumption requires that all machines work continuously without idle time. Second, the problem F3/GT, o = 2/C_max, in which the machine no-idle restriction in the first variant is relaxed, is considered. Third, the problem F3/no-idle, o = 2/C_max with the GT assumption in the first variant relaxed is considered. Based on the dominance conditions developed, the optimal solution is polynomially derived for each variant. These results may narrow down the gap between easy and hard cases of the general problem.     

A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem

This paper presents a variable iterated greedy algorithm (IG) with differential evolution (vIG_DE), designed to solve the no-idle permutation flowshop scheduling problem. In an IG algorithm, size d of jobs are removed from a sequence and re-inserted into all possible positions of the remaining sequences of jobs, which affects the performance of the algorithm. The basic concept behind the proposed vIG_DE algorithm is to employ differential evolution (DE) to determine two important parameters for the IG algorithm, which are the destruction size and the probability of applying the IG algorithm to an individual. While DE optimizes the destruction size and the probability on a continuous domain by using DE mutation and crossover operators, these two parameters are used to generate a trial individual by directly applying the IG algorithm to each target individual depending on the probability. Next, the trial individual is replaced with the corresponding target individual if it is better in terms of fitness. A unique multi-vector chromosome representation is presented in such a way that the first vector represents the destruction size and the probability, which is a DE vector, whereas the second vector simply consists of a job permutation assigned to each individual in the target population. Furthermore, the traditional IG and a variable IG from the literature are re-implemented as well. The proposed algorithms are applied to the no-idle permutation flowshop scheduling (NIPFS) problem with the makespan and total flowtime criteria. The performances of the proposed algorithms are tested on the Ruben Ruiz benchmark suite and compared to the best-known solutions available at http://soa.iti.es/rruiz as well as to those from a recent discrete differential evolution algorithm (HDDE) from the literature. The computational results show that all three IG variants represent state-of-art methods for the NIPFS problem.     

解决零空闲流水线调度问题的离散粒子群算法

研究了以最大完工时间为目标的零空闲流水线调度问题.提出一种复杂度为O(nm)的最大完工时间算法和一种快速插入邻域搜索算法;提出了解决该问题的离散粒子群调度算法,并结合简化邻域搜索算法给出了提高调度算法性能的措施.仿真实验表明了所得算法的有效性.     

Exact resolution of the one-machine sequencing problem with no machine idle time

This paper investigates the one-machine sequencing problem in a workshop where the machine has to satisfy the no-idle constraint, that is, the machine must process jobs without interruption. The objective is to minimize the makespan. Each job has a release date for which it is available for processing on the machine and a delivery time during which it must remain in the system after being processed by the machine. This problem has been studied without adding the no-idle constraint. It is solved in polynomial time, when the preemption of jobs is allowed, applying Jackson’s rule. But, when the preemption of jobs is not allowed, it becomes strongly NP-hard. Although, it can be solved in a very short time using Carlier’s branch and bound algorithm. Below, we propose to adapt Carlier’s branch and bound method in order to calculate an optimal nonpreemptive schedule for the problem when adding the no-idle constraint.     

Memetic algorithm with node and edge histogram for no-idle flow shop scheduling problem to minimize the makespan criterion

This paper presents a memetic algorithm with hybrid node and edge histogram (MANEH) to solve no-idle permutation flow shop scheduling problem (NIPFSP) with the criterion to minimize the maximum completion time (the makespan criterion). The MANEH mainly composes of two components: population-based global search and local refinements for individuals. At the initialization stage, a modified speed-up NEH method and the random initialization are utilized to generate more promising solutions with a reasonable running time. At the population-based global search stage, a random sample crossover is first proposed to construct a hybrid node and edge histogram matrix (NEHM) with superior solutions in the population, and then a new sequence is generated by sampling the NEHM or selecting jobs from a template sequence. At the local refinements stage, an improved general variable neighborhood search with the simulated annealing acceptance (GVNS-SA) is developed to improve the current best individual. The GVNS-SA adopts a random referenced local search in the inner loop and the probability of SA to decide whether accept the incumbent solution for the next iteration. Moreover, the influence of key parameters in the MANEH is investigated based on the approach of a design of experiments (DOE). Finally, numerical simulation based on the benchmark of Ruiz and thorough statistical analysis are provided. The comparisons between MANEH and some existing algorithms as well as MA-based algorithms demonstrate the effectiveness and superiority of the proposed MANEH in solving the NIPFSP. Furthermore, the MANEH improves 89 out of the 250 current best solutions reported in the literature.     

A hybrid discrete differential evolution algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion

This paper presents a hybrid discrete differential evolution (HDDE) algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion, which is not so well studied. The no-idle condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. A novel speed-up method based on network representation is proposed to evaluate the whole insert neighborhood of a job permutation and employed in HDDE, and moreover, an insert neighborhood local search is modified effectively in HDDE to balance global exploration and local exploitation. Experimental results and a thorough statistical analysis show that HDDE is superior to the existing state-of-the-art algorithms by a significant margin.     

Flowshop scheduling of deteriorating jobs on dominating machines

In this paper we consider the general, no-wait and no-idle permutation flowshop scheduling problem with deteriorating jobs, i.e., jobs whose processing times are increasing functions of their starting times. We assume a linear deterioration function with identical increasing rates for all the jobs and there are some dominating relationships between the machines. We show that the problems to minimize the makespan and the total completion time remain polynomially solvable when deterioration is considered, although these problems are more complicated than their classical counterparts without deterioration.