No-idle Permutation Flowshop Scheduling Research Articles

An Iterative Greedy Algorithm With Q-Learning Mechanism for the Multiobjective Distributed No-Idle Permutation Flowshop Scheduling

An Iterative Greedy Algorithm With <i>Q</i>-Learning Mechanism for the Multiobjective Distributed No-Idle Permutation Flowshop Scheduling

A modified Aquila optimizer algorithm for optimization energy-efficient no-idle permutation flow shop scheduling problem

Increasing energy consumption has faced challenges and pressures for modern manufacturing operations. The production sector accounts for half of the world's total energy consumption. Reducing idle machine time by em­ploying No-Idle Permutation Flow Shop Scheduling (NIPFSP) is one of the best decisions for reducing energy consumption. This article modifies one of the energy consumption-solving algorithms, the Aquila Optimizer (AO) algo­rithm. This research contributes by 1) proposing novel AO procedures for solving energy consumption problems with NIPFSP and 2) expanding the literature on metaheuristic algorithms that can solve energy consumption problems with NIPFSP. To analyze whether the AO algorithm is optimal, we compared by using the Grey Wolf Optimizer (GWO) algorithm. It com­pares these two algorithms to tackle the problem of energy consumption by testing four distinct problems. Comparison of the AO and GWO algorithm is thirty times for each case for each population and iteration. The outcome of comparing the two algorithms is using a t-test on independent samples and ECR. In all case studies, the results demonstrate that the AO algorithm has a lower energy consumption value than GWO. The AO algorithm is there­fore recommended for minimizing energy consumption because it can produce more optimal results than the comparison algorithm.

Low-carbon no-idle permutation flow shop schedulling problem: giant trevally optimizer vs African vultures optimization algorithm

Greenhouse gas emissions continue to increase due to increased energy consumption. One of the largest emission-contributing sectors is the manufacturing industry. Therefore, the manufacturing industry is required to minimize carbon emissions. One of the efforts to solve the emission problem is to minimize machine downtime throughout the production procedure, which stands for no-idle permutation flowshop scheduling (NIPFSP). This article uses two metaheuristic algorithms, giant trevally optimizer (GTO) and African vultures optimization algorithm (AVOA), to solve the carbon emission problem. Both algorithms are tested on 3 cases with 30 runs for every population and iteration. To compare the outcomes of each algorithm, an independent sample t-test was employed. The results show that the GTO algorithm has better results than the AVOA algorithm on small and large case data. The findings indicate that both the GTO and AVOA algorithms yield comparable results when applied to medium-sized research datasets, suggesting their effectiveness in such scenarios.

A modified beluga whale optimization for optimizing energy-efficient no-idle permutation flow shop scheduling problem

Attention to energy-efficient permutation flow shop scheduling problems is increasing in the context of globalization and environmental awareness. However, the energy-efficient no-idle permutation flow shop scheduling problem (NIPFSP) has rarely been studied. This study proposes a procedure using Beluga Whale Optimization (BWO) to solve the energy-efficient NIPFSP issue to reduce total energy consumption (TEC). The offered procedure is tested using four job and machine variations and compared with the PSO algorithm. An independent sample t-test was performed to test the optimization results of the BWO and PSO in 4 cases. The results indicate that the offered procedure produces lower total energy consumption than the PSO algorithm. In addition, the algorithm also provides more competitive results when solving the energy-efficient NIPFSP problem with a larger number of jobs. The implications of this academic research show that the proposed procedure can be applied to solve the problem of energy-efficient NIPFSP, which is indicated by low energy consumption.

An Adaptive Iterated Greedy algorithm for distributed mixed no-idle permutation flowshop scheduling problems

Distributed flow shop scheduling is a very interesting research topic. This paper studies the distributed permutation flow shop scheduling problem with mixed no-idle constraints, which have important applications in practice. The optimization goal is to minimize total flowtime. A mixed-integer linear programming model is presented and an Adaptive Iterated Greedy (AIG) algorithm with the sample length changing according to the search process is designed. A restart strategy is also introduced to escape from local optima. Additionally, to further improve the performance of the algorithm, swap-based local search methods and acceleration algorithms for swap neighborhoods are proposed. Referenced Local Search (RLS), which shows better performance in solving scheduling problems, is also used in our algorithm. In the destruction stage, the job to be removed is selected according to the degree of influence on the total flowtime. In the initialization and construction phase, when a job is inserted, the jobs before and after the insertion position are removed and re-inserted into a better position to improve the algorithm search performance. A detailed design experiment is carried out to determine the best parameter configuration. Finally, large-scale experiments show that the proposed AIG algorithm is the best-performing one among all the algorithms in comparison.

Improved discrete cuckoo‐search algorithm for mixed no‐idle permutation flow shop scheduling with consideration of energy consumption

The increasing number and types of industrial tasks require factories to be more flexible in production. An improved discrete cuckoo search algorithm (CSA) is proposed and used to optimise the mixed no-idle permutation flow shop scheduling problem (MNPFSP). This problem considers MNPFSP energy consumption (MNPFSP_EC) an optimisation objective. Firstly, according to the characteristics of the individual update formula in the two stages of the standard CSA, the paper replaces the real number calculation or vector calculation in the original update formula with a discrete operation to keep the update mechanism of each stage unchanged. The change allows the algorithm to directly find a feasible solution in the discrete solution space that significantly improves the global search capability of cuckoo search. Secondly, an adaptive-starting local search based on quasi-entropy (QE) is constructed using swap, insert and 2-OPT operations with an exploitation that is adaptively executed based on QE, and QE is used to represent the diversity of population and control individuals in deciding whether to execute local search, thereby reducing computational complexity. Simulation experiments and comparisons of different instances demonstrate that the proposed algorithm can effectively solve MNPFSP_EC.

A new iterated greedy algorithm for no-idle permutation flowshop scheduling with the total tardiness criterion

With the no-idle constraint, a machine has to process a job after finishing the previous one without any interruption. The start time of the first job on each machine must thus be delayed to meet this condition. In this paper, a new Iterated Greedy Algorithm (IGA) is presented for no-idle flowshop scheduling with the objective of minimizing the total tardiness. For the initialization phase, a variant of the NEH procedure is developed. Then, we propose a new variable local search based on an insert move with two different job selection mechanisms. A tardiness-guided job selection procedure, a job-dependent parameter and an insert-swap based method are further introduced in the destruction-construction phases. While most of the related studies have used a fixed probability for accepting new or non-improving solutions, we propose a time-dependent probability that allows our algorithm to focus on exploration in early iterations and exploitation in later iterations. Comprehensive computational experiments show that the proposed IGA is superior in terms of solution quality than state-of-the-art algorithms for the problem at hand. As a result, more than 50% of the existing best solutions for the benchmark instances tested have been updated.

A collaborative optimization algorithm for energy-efficient multi-objective distributed no-idle flow-shop scheduling

Facing the energy crisis, manufacturers is paying much attention to the energy-efficient scheduling by taking both economic benefits and energy conservation into account. Meanwhile, with the economic globalization, it is significant to facilitate the advanced manufacturing and scheduling in the distributed way. This paper addresses the energy-efficient distributed no-idle permutation flow-shop scheduling problem (EEDNIPFSP) to minimize makespan and total energy consumption simultaneously. By analyzing the characteristics of the problem, several properties are derived. To solve the problem effectively, a collaborative optimization algorithm (COA) is proposed by using the properties and some collaborative mechanisms. First, two heuristics are collaboratively utilized for population initialization to guarantee certain quality and diversity. Second, multiple search operators collaborate in a competitive way to enhance the exploration adaptively. Third, different local intensification strategies are designed for the dominated and non-dominated individuals to enhance the exploitation. Fourth, a speed adjusting strategy for the non-critical operations is designed to improve total energy consumption. The effect of key parameters is investigated using the design-of-experiment with full factorial setting. Comparisons based on extensive numerical tests are carried out, which demonstrate the effectiveness of the proposed algorithm in solving the EEDNIPFSP.

Iterated reference greedy algorithm for solving distributed no-idle permutation flowshop scheduling problems

This paper investigates the Distributed No-idle Permutation Flowshop Scheduling Problem (DNIPFSP) with the objective of minimizing the makespan, which has not been discussed in any previous study. This study presents an Iterated Reference Greedy (IRG) algorithm for effectively solving this problem. The performance of the proposed IRG algorithm is compared with a state-of-the-art iterated greedy (IG) algorithm, as well as the Mixed Integer Linear Programming (MILP) model on two well-known benchmark problem sets. Computational results show that the proposed IRG algorithm outperforms the IG algorithm. Given the NP-Complete nature of the DNIPFSP problem, this paper is the first study to contribute a feasible approach for solving it effectively.

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.

Research on no-idle permutation flowshop scheduling with time-dependent learning effect and deteriorating jobs

This note considers no-idle permutation flowshop scheduling problems with time-dependent learning effect and deteriorating jobs. The objective functions are to minimize the makespan and the total (weighted) completion time, respectively. Low and Lin [1], showed that an optimal sequence for these problems can be solved in polynomial time. We demonstrate these results to be incorrect by counter-examples for the no-idle permutation flowshop scheduling problems with an increasing series of dominating machines (idm), then introduce new exact solution algorithms that polynomially solve these problems.

A bi-population EDA for solving the no-idle permutation flow-shop scheduling problem with the total tardiness criterion

In this paper, an effective bi-population estimation of distribution algorithm (BEDA) is presented to solve the no-idle permutation flow-shop scheduling problem (NIPFSP) with the total tardiness criterion. To enhance the search efficiency and maintain the diversity of the whole population, two sub-populations are used in the BEDA. The two sub-populations are generated by sampling the probability models that are updated differently for the global exploration and the local exploitation, respectively. Meanwhile, the two sub-populations collaborate with each other to share search information for adjusting the models. To well adjust the models for generating promising solutions, the global probability model is updated during the evolution with the superior population and the local probability model is updated with the best solution that has been explored. To further enhance exploitation in the promising region, the insertion operator is used iteratively as the local search procedure. To investigate the influence of parameter setting, numerical study based on the Taguchi method of design-of-experiment is carried out. The effectiveness of the bi-population strategy and local search procedure is shown by numerical comparisons, and the comparisons with the recently published algorithms by using the benchmarking instances also demonstrate the effectiveness of the proposed BEDA.

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.

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.

A differential evolution algorithm for the no-idle flowshop scheduling problem with total tardiness criterion

In this paper, we investigate the use of a continuous algorithm for the no-idle permutation flowshop scheduling (NIPFS) problem with tardiness criterion. For this purpose, a differential evolution algorithm with variable parameter search (vpsDE) is developed to be compared to a well-known random key genetic algorithm (RKGA) from the literature. The motivation is due to the fact that a continuous DE can be very competitive for the problems where RKGAs are well suited. As an application area, we choose the NIPFS problem with the total tardiness criterion in which there is no literature on it to the best of our knowledge. The NIPFS problem is a variant of the well-known permutation flowshop (PFSP) scheduling problem where idle time is not allowed on machines. In other words, the start time of processing the first job on a given machine must be delayed in order to satisfy the no-idle constraint. The paper presents the following contributions. First of all, a continuous optimisation algorithm is used to solve a combinatorial optimisation problem where some efficient methods of converting a continuous vector to a discrete job permutation and vice versa are presented. These methods are not problem specific and can be employed in any continuous algorithm to tackle the permutation type of optimisation problems. Secondly, a variable parameter search is introduced for the differential evolution algorithm which significantly accelerates the search process for global optimisation and enhances the solution quality. Thirdly, some novel ways of calculating the total tardiness from makespan are introduced for the NIPFS problem. The performance of vpsDE is evaluated against a well-known RKGA from the literature. The computational results show its highly competitive performance when compared to RKGA. It is shown in this paper that the vpsDE performs better than the RKGA, thus providing an alternative solution approach to the literature that the RKGA can be well suited.

A novel differential evolution algorithm for no-idle permutation flow-shop scheduling problems

A novel Discrete Differential Evolution (DDE) algorithm is proposed in this paper for solving no-idle permutation flow-shop scheduling problems with maximum completion time (makespan) criterion. Firstly, individuals of the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed. Secondly, a local search algorithm based on insert neighbourhood is embedded in the DDE algorithm to balance the exploration and exploitation and to enhance the local searching ability. In addition, we present two simple approaches to calculate makespan and a speed-up method for insert neighbourhood to improve the efficiency of the whole algorithm. Computational simulations and comparisons based on some well-known benchmarks demonstrate that the DDE algorithm is not only superior to the improved greedy and Kalczynski-Kamburowski heuristics in terms of searching quality, but also superior to the particle swarm optimisation and differential evolution algorithms according to searching quality, robustness and efficiency. [Received 9 July 2007; Revised 10 October 2007; Accepted 30 October 2007]

No-idle permutation flow shop scheduling based on a hybrid discrete particle swarm optimization algorithm

A novel hybrid discrete particle swarm optimization (HDPSO) algorithm is proposed in this paper to solve the no-idle permutation flow shop scheduling problems with the criterion to minimize the maximum completion time (makespan). Firstly, two simple approaches are presented to calculate the makespan of a job permutation. Secondly, a speed-up method is proposed to evaluate the whole insert neighborhood of a job permutation with (n−1)2 neighbors in time O(mn 2), where n and m denote the number of jobs and machines, respectively. Thirdly, a discrete particle swarm optimization (DPSO) algorithm based on permutation representation and a local search algorithm based on the insert neighborhood are fused to enhance the searching ability and to balance the exploration and exploitation. Then, computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is concluded that the proposed HDPSO algorithm is not only superior to two recently published heuristics, the improved greedy (IG) heuristic and Kalczynski–Kamburowski (KK) heuristic, in terms of searching quality, but also superior to the single DPSO algorithm and the PSO algorithm with variable neighborhood search (PSOvns) in terms of searching quality, robustness and efficiency.

Permutation flow shop scheduling with dominant machines to minimize discounted total weighted completion time

This paper deals with some special cases of general, no-wait and no-idle permutation flow shop scheduling problems, respectively. Special cases means that the machines form an increasing series of dominant machines, a decreasing series of dominant machines, an increasing–decreasing series of dominant machines and a decreasing–increasing series of dominant machines. Efficient polynomial time algorithms for finding the optimal schedules to minimize discounted total weighted completion time are developed.

No-wait or no-idle permutation flowshop scheduling with dominating machines

In this paper we study the no-wait or no-idle permutation flowshop scheduling problem with an increasing and decreasing series of dominating machines. The objective is to minimize one of the five regular performance criteria, namely, total weighted completion time, maximum lateness, maximum tardiness, number of tardy jobs and makespan. We establish that these five cases are solvable by presenting a polynomial-time solution algorithm for each case.