Permutation Flow-shop Problem Research Articles

On a bi-objective distributed permutation flow shop problem with batch processing machines

On a bi-objective distributed permutation flow shop problem with batch processing machines

Minimizing the maximum tardiness for a permutation flow shop problem under the constraint of sequence independent setup time

In this work, we will study a permutation flow shop scheduling problem under the constraint of sequence independent setup time. In our case, each machine requires a certain setup time to process all the different jobs assigned to it. Hence, this setup time will be independent of sequence of jobs, but will depend only on the nature of machine. The optimization objective is to minimize the maximum tardiness criterion. To solve this optimization problem, an exact method, heuristics and metaheuristics are the three main resolution methods that we have used. The exact method is represented by the mixed integer linear programming (MILP) model. In terms of the second category of resolution methods, we have been focused on two methods, the first is a modified heuristic based on Johnson rule (HBJR) while the second is based on the Nawaz–Enscore–Ham (NEH) algorithm. Finally, three metaheuristics have been used, namely the iterated local search (ILS) method, the iterated greedy (IG) algorithm and the genetic algorithm (GA). Our numerical results indicate that for the problems with small size instances, the NEH heuristic outperforms HBJR approach, while for relatively large size instances, the developed IG algorithm gives best results than both other metaheuristics ILS and GA.

Evaluating procedures in the NEH heuristic for the PFSP - SIST

The development and assessment of 48 heuristics for the sequence-independent setup time permutation flow shop problem (PFSP-SIST) are presented in this article. This contribution combines four tie-breaking solutions with twelve priority rules for the NEH heuristic fourth and first stage, respectively. Heuristics are evaluated on Ruiz and Allahverdi (2007) benchmark problem instances, that covers small, medium and large-size problems. The popular accelerations of Taillard were used in all tests, which were adapted to the sequence-independent setup time constraint. The aim is to reduce the longest job completion time, which is also referred to as makespan. Computation results show that using different tie-breaking strategies has a greater impact on performance than using different priority rules. The heuristics that presented the best results in relatively low computation time are those that use the FFs tie-breaking strategy procedure to the sequence-independent setup time problem.

An improved iterated greedy algorithm for distributed mixed no-wait permutation flowshop problems with makespan criterion

The distributed permutation flowshop scheduling is a critical issue in various industries, involving jobs allocation and scheduling among multiple flowshops. This paper extends the research to explore the Distributed Mixed No-Wait Permutation Flowshop Scheduling Problems (DMNWPFSP) with minimizing makespan. The innovation lies in an optimized mathematical model, hybrid heuristic algorithms, an improved iterated greedy algorithm (IIG), and high-quality solutions. Extensive experimental results demonstrate the effectiveness and superiority of the proposed IIG in terms of scheduling quality, computational efficiency, and robustness compared to existing approaches. The outcomes of this work contribute to the field of distributed flowshop scheduling, providing valuable insights for practitioners seeking to enhance production efficiency and competitiveness.

AVOA and ALO Algorithm for Energy-Efficient No-Idle Permutation Flow Shop Scheduling Problem: A Comparison Study

Global energy consumption is a pressing issue and is predicted to continue increasing between 2010 and 2040. Among the various sectors, the industrial sector, particularly manufacturing, is the main driver of this increase. To effectively address this growing problem and support energy conservation efforts, reducing idle time on production-related machines is critical. The No-Idle Permutation Flow Shop Problem (NIPFSP) and, indirectly, the need to reduce energy consumption in manufacturing processes are the driving forces behind this study. The African Vultures Optimization Algorithm (AVOA) and the Ant Lion Optimizer (ALO) are two novel meta-heuristic algorithms designed to achieve this goal. The effectiveness of both AVOA and ALO was rigorously evaluated across three distinct scenarios: small, medium, and large. Statistical analysis, in the form of independent sample t-tests, was employed to compare the performance of these algorithms. We found that, while both algorithms yielded similar results in the small case, AVOA demonstrated a superior capability in optimizing the NIPFSP in the medium and large cases and, consequently, in curbing energy consumption. This implies that AVOA offers a more promising approach to addressing energy consumption concerns in the manufacturing sector, particularly in scenarios involving medium- to large-scale production processes. The implementation of such innovative meta-heuristic algorithms holds the potential to significantly contribute to global energy conservation efforts while enhancing the efficiency of industrial operations.

A problem-specific knowledge based artificial bee colony algorithm for scheduling distributed permutation flowshop problems with peak power consumption

A distributed permutation flowshop scheduling problem (DPFSP) with peak power consumption is addressed in this work. The instantaneous energy consumption of each factory cannot exceed a threshold. First, a mathematical model is developed to describe the concerned problem. Second, an improved artificial bee colony (IABC) algorithm is proposed. Based on problem-specific knowledge, three new solution generation operators, e.g., shift, swap, and speed adjust, are designed for employ bees and onlooker bees. A local search operation is developed to improve the quality of current best-known solution in each iteration. 450 instances are solved to evaluate the performance of IABC via comparing to seven state-of-the-art algorithms. The average relative percentage increase (ARPI) of IABC ranks 1 among all compared algorithms. The results and discussions show that the proposed IABC algorithm has strong competitiveness for solving the DPFSP with peak power consumption.

Nondominated sorting genetic algorithm-II with Q-learning for the distributed permutation flowshop rescheduling problem

The distributed permutation flowshop problem (DPFSP) has been extensively studied in recent years. However, most of the research has overlooked the disturbance factors in the processing environment, such as the arrival of new jobs. To address this issue, a nondominated sorting genetic algorithm-II (NSGA-II) with Q-learning has been developed. First, an iterated greedy algorithm (IG) is proposed to generate an initial solution for the first stage. Then, the NSGA-II algorithm is designed to optimize dual-objective problems in the second stage, and the Q-learning algorithm is used to adjust the algorithm parameters. Next, two local search strategies based on key factories are adopted, including critical factory-based insert and swap operations. Finally, a comprehensive experiment of the proposed algorithm against other advanced multiobjective algorithms is conducted. The results confirm that the proposed algorithm can solve the distributed permutation flowshop rescheduling problem with high efficiency.

On some lower bounds for the permutation flowshop problem

The permutation flowshop problem with makespan objective is a classic machine scheduling problem, known to be NP-hard in the strong sense. We analyse some of the existing lower bounds for the problem, including the “job-based” and “machine-based” bounds, a bound from linear programming (LP), and a recent bound of Kumar and co-authors. We show that the Kumar et al. bound dominates the machine-based bound, but the LP bound is stronger still. On the other hand, the LP bound does not, in general, dominate the job-based bound. Based on this, we devise simple iterative procedures for strengthening the Kumar et al. and LP bounds. Computational results are encouraging. In particular, we are able to obtain improved lower bounds for the “hard, small” instances of Vallada, Ruiz and Framinan.

Problem-specific knowledge MOEA/D for energy-efficient scheduling of distributed permutation flow shop in heterogeneous factories

With the development of the global economy and the enhancement of environmental awareness, energy-efficient permutation flow shop scheduling gets more attention. Nevertheless, research on distributed scheduling with heterogeneous factories is scarce. In this paper, a knowledge-driven MOEA/D (KMOEA/D) is proposed to address the energy-efficient scheduling of distributed permutation flow shop problem in heterogeneous factories (DPFSP-HF) with the criteria of minimizing the makespan (Cmax) and total energy consumption (TEC). First, an efficient energy-saving strategy is proposed to reduce the TEC criteria. Second, a constructive heuristic is designed to generate a high-quality solution set. Third, an ingenious genetic operator is utilized to maintain population diversity. Fourth, the knowledge-driven local search operator combined the problem-specific knowledge is constructed according to the properties of DPFSP-HF. Additionally, the Taguchi approach is used to calibrate the parameter configuration of KMOEA/D. We evaluate the effectiveness of each improvement of KMOEA/D and compare it to other well-known multi-objective optimization algorithms on different instances. The results indicate the effectiveness of each improvement of KMOEA/D, and verify that KMOEA/D is an efficient approach to address DPFSP-HF.

Permutation flowshop problems minimizing core waiting time and core idle time

Waiting time and idle time are among the main cost sources in production systems. They can also affect the feasibility of operations from a technological perspective; hence, both such times have to be kept as small as possible. This paper studies four single-objective variants of the permutation flowshop scheduling problem, where two objectives are considered: the weighted sum of the makespan and the core waiting time, and the weighted sum of the makespan and the core idle time. For each objective, both the problem with the assumption of semi-active solution and the one without it are considered.A general solution framework for tackling the above-mentioned problems is provided. First, two Mixed Integer Linear Programming (MILP) formulations (based on positional and precedence variables, respectively) and one Constraint Programming (CP) formulation are presented. Second, a MILP-based local search approach based on the positional MILP formulation and the concept of sliding windows are defined. An extensive set of computational experiments on benchmark instances show that the positional MILP formulation strongly outperforms the other two formulations in all the considered cases. The experiments also show that the sliding window local search heuristic achieves much better performances than other state-of-the-art local search heuristics. Indeed, it is able to improve the state-of-the-art in 2384 instances out of 2400.

Fitness Approximation Surrogate-assisted Hyper-heuristic for the Permutation Flowshop Problem

Hyper-heuristics can be applied to solve complex optimization problems. However, they need a substantial number of fitness function evaluations to discover a good approximation to the global optimum, especially for large-scale problems. Recently, surrogate-assisted algorithms have drawn increasing attention, and have shown their potential to deal with expensive complex optimization problems. This paper aims to use surrogates to approximate HHGA's (Ahmed Bacha et al., 2019) fitness functions, an efficient hyper-heuristic for solving the permutation flowshop problem, one of the most important scheduling types in modern industries. The objective is to approximate, in an online approach, the fitness function, reducing considerably the execution time of HHGA while maintaining its quality. The proposed online surrogate model is mainly designed to capture the details of the fitness function to enhance the accuracy estimation. The experimental results on Taillard's widely used benchmark problems show that the proposed fitness approximation-assisted HHGA is able to achieve competitive performance on a limited computational budget.

An Analysis of Effective Per-instance Tailored GAs for the Permutation Flowshop Scheduling Problem

In this paper, we analyze the results of two hyper-heuristics HHGA and HHabs that generate per-instances genetic algorithms for the permutation flow shop problem. They are competitive with literature approaches for most of instances of the benchmark of Taillard. Nevertheless, they are not effective enough for some difficult instances. For this purpose, we propose a workflow to analyse GAs configurations and their results in order to detect which components influence the most on generated GAs quality in order to enhance the quality of these hyper-heuristics.

Robust permutation flow shop total weighted completion time problem: Solution and application to the oil and gas industry

This work proposes exact solution approaches for the m-machine robust permutation flow shop problem, where operation processing times are uncertain and vary in a given interval. Following the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the total weighted completion time of the restricted worst-case scenario, in which only a subset of operation processing times will deviate to worst-case values. We develop several robust counterpart formulations, which can be used to derive optimal solutions for medium-sized problem instances by using a Column-and-Constraint Generation algorithm. The efficacy of the solution methods is validated through experiments on three sets of randomly-generated instances. Finally, a case study for the maintenance schedule of Brazilian oil platforms is presented.

A discrete artificial bee colony method based on variable neighborhood structures for the distributed permutation flowshop problem with sequence-dependent setup times

• The DPFSP with SDST under minimization of total flowtime is investigated in the paper; • We propose a constructive heuristic framework, which contains three constructive heuristics, to obtain good initial solutions for our DABC vns ; • By analyzing the characteristics of problem-specific, four different neighborhood structures are proposed and selectively applied in three stages to obtain more feasible neighborhood solutions; • A new population update strategy is adopted in scout bee phase to help algorithm explore new promising area; • The experimental evaluation is used to verify the validity of constructive heuristics and DABC vns . In today's global economy, distributed manufacturing has become increasingly appropriate. Job setup time is invariably a factor in manufacturing, and needs to be considered when making scheduling decisions. This study aims to minimize the total flow time by solving a distributed permutation flowshop scheduling problem (DPFSP) with a sequence-dependent setup time (SDST) to minimize total flowtime. First, to manage the DPFSP/SDST effectively, we propose a constructive heuristic framework based on the LR heuristic, which contains three constructive heuristics to obtain good initial solutions. Second, a discrete artificial bee colony (DABC) method based on variable neighborhood structures (DABC vns ) is proposed. By analyzing the problem-specific characteristics in the DABC vns , four different neighborhood structures are proposed, which are selectively applied in three stages of DABC vns to obtain more feasible neighborhood solutions. In addition, two variable neighborhood descent algorithms are proposed, which are each based on local search methods. The algorithms are developed to improve the best solution obtained in initial population and the best solution generated in the three stages. Finally, we conduct an experiment to calibrate the parameter of the DABC vns method. To evaluate the performance of the proposed method compared to six other algorithms, comprehensive computational experiments are conducted. The simulation results indicate that the proposed method delivers the best quality solutions for the DPFSP/SDST in the minimization of total flowtime.

An Effective Iterated Greedy Algorithm for a Robust Distributed Permutation Flowshop Problem With Carryover Sequence-Dependent Setup Time

A new scheduling problem, the distributed permutation flowshop scheduling problem with uncertain processing times and carryover sequence-dependent setup time (DPUC), is addressed. The DPUC is an important application problem in modern electronics manufacturing. A robust model is established for the DPUC with makespan criterion. A counter-intuitive paradox is found, that is, adding a new job to one of the production lines can reduce the completion time of the production line. Two acceleration methods are provided to save computational efforts. An iterated greedy algorithm called IG_FS is proposed to solve the DPUC. A heuristic based on the well-known NEH is proposed to generate the initial solution for the IG_FS. In the destruction phase of the IG_FS, dynamic sizes based on both adaptability and randomness are provided to improve the exploration capability. During the local search phase of the IG_FS, a hybrid local search method consisting of shift and swap operators is presented to exploit more diverse search areas. Extensive experiments show that the proposed IG_FS performs significantly better than the six competing algorithms adapted from the closely related scheduling literature.

Adaptive search space to generate a per-instance genetic algorithm for the permutation flow shop problem

This study introduces, HHABS, a new hyper-heuristic for permutation-based problems. It is a high-level local search that generates tailored genetic algorithms for considered problem instances. The motivation of this work is to reduce the time needed to design a dedicated genetic algorithm for a new instance increasing the chance to explore undiscovered search spaces. It uses three search spaces to build genetic algorithms. In the first one, standard blind operators are used. In the second one, problem-oriented ones are used and finally, in the last one, knowledge extracted during the search process is taken into consideration through diversification and intensification strategies. HHABS’s solving process explores the three search spaces starting from the standard one and jumps to the next search spaces until it gets the best found solution so far, for the given instance, or all search spaces are covered. Extensive experiments have been conducted on the well-known PFSP. The performance comparison, on the Taillard instances, against state-of-the-art algorithms verified the reliability of the proposed organization of the search space on its performance. Besides, it allowed us to classify instances into easy, medium and difficult.

A critical-path based iterated local search for the green permutation flowshop problem

The permutation flowshop scheduling problem is a widely studied combinatorial optimization problem with several real-world applications. In this paper we address a green variant of the problem with controllable processing times and two objective functions: one related to the service level of the factory (makespan) and another one related to the total cost or the total energy/carbon consumption. For this problem we propose a novel Critical-Path based Iterated Local Search. This metaheuristic incorporates several theoretical results to accelerate the search of solutions in the intensification phase. The proposed algorithm has been compared on an extensive benchmark with the most promising algorithms in the literature. The computational results show the excellent performance of the proposal.

A Fuzzy Simheuristic for the Permutation Flow Shop Problem under Stochastic and Fuzzy Uncertainty

Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with both stochastic and fuzzy processing times. The main goal is to find the solution (permutation of jobs) that minimizes the expected makespan. However, due to the existence of uncertainty, other characteristics of the solution are also taken into account. In particular, we illustrate how survival analysis can be employed to enrich the probabilistic information given to decision-makers. To solve the aforementioned optimization problem, we extend the concept of a simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated in the PFSP. In order to test our approach, classical PFSP instances have been adapted and extended, so that processing times become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones.

MILP-based local search procedures for minimizing total tardiness in the No-idle Permutation Flowshop Problem

We consider the No-idle Permutation Flowshop Scheduling Problem (NPFSP) with a total tardiness criterion. We present two Mixed Integer Linear Programming (MILP) formulations based on positional and precedence variables, respectively. We study six local search procedures that explore two different neighborhoods by exploiting the MILP formulations. Our computational experiments show that two of the proposed procedures strongly outperform the state-of-the-art metaheuristic. We update 63% of the best known solutions of the instances in Taillards’ benchmark, and 77% if we exclude those instances for which we proved that the previous best known solutions are optimal.

A Pareto-based collaborative multi-objective optimization algorithm for energy-efficient scheduling of distributed permutation flow-shop with limited buffers

Energy-efficient scheduling of distributed production systems has become a common practice among large companies with the advancement of economic globalization and green manufacturing. Nevertheless, energy-efficient scheduling of distributed permutation flow-shop problem with limited buffers (DPFSP-LB) does not receive adequate attention in the relevant literature. This paper is therefore the first attempt to study this DPFSP-LB with objectives of minimizing makespan and total energy consumption ( T E C ). To solve this energy-efficient DPFSP-LB, a Pareto-based collaborative multi-objective optimization algorithm (CMOA) is proposed. In the proposed CMOA, first, the speed scaling strategy based on problem property is designed to reduce T E C . Second, a collaborative initialization strategy is presented to generate a high-quality initial population. Third, three properties of DPFSP-LB are utilized to develop a collaborative search operator and a knowledge-based local search operator. Finally, we verify the effectiveness of each improvement component of CMOA and compare it against other well-known multi-objective optimization algorithms on instances. Experiment results demonstrate the effectiveness of CMOA in solving this energy-efficient DPFSP-LB. Especially, the CMOA is able to obtain excellent results on all problems regarding the comprehensive metric, and is also competitive to its rivals regarding the convergence metric. • A green criterion is considered in the studied problem. • A new constraint of the limited buffers is introduced into this problem. • A multi-objective optimization algorithm is presented to solve this problem. • An effective energy saving strategy is proposed. • An initialization strategy and local search strategy are proposed.