Total Tardiness Criterion Research Articles

A tabu memory based iterated greedy algorithm for the distributed heterogeneous permutation flowshop scheduling problem with the total tardiness criterion

Distributed scheduling problems have been extensively studied due to their critical roles in industrial applications. Most research focuses on identical distributed factories and the objective of minimizing the makespan, ignoring the widely existing heterogeneous factories and delivery targets in reality. This paper aims to establish a distributed heterogeneous flowshop scheduling scenario with the objective of minimizing total tardiness (DHPFSP-t), and solve it using an improved iterative greedy algorithm. A mixed-integer programming model and several problem-specific properties are proposed for this novel scheduling scenario. Based on the distributed heterogeneous characteristics of the problem, four constructive algorithms are established to quickly generate initial solutions. Among them, the better solution is selected as the initial solution of the iterative greedy algorithm. To enhance the performance of the iterative greedy algorithm, the concept of tabu memory is incorporated and novel destruction and local search processes are devised. Thorough experiments are conducted to verify the effectiveness of the mixed-integer programming model of the scenario, the constructive heuristics and the improved iterative greedy algorithm. The result confirms the validity of the proposed model and the good performance of the proposed method.

A two-phase evolutionary algorithm for multi-objective distributed assembly permutation flowshop scheduling problem

• We study a multi-objective distributed assembly flowshop scheduling problem. • We present a two-phase evolutionary algorithm divided by time. • Two novel heuristics specific to different objectives are proposed. • Six crossover operators and two mutation operators are designed specifically. • The effectiveness of our algorithm is demonstrated by 810 benchmark instances. In recent years, multi-objective optimization problems have received extensive attention. This paper proposes a two-phase evolutionary algorithm (TEA) to solve the multi-objective distributed assembly permutation flowshop scheduling problem with total flowtime and total tardiness criteria. The first phase of the TEA uses a novel two-population structure to simultaneously optimize the two criteria. According to the characteristics of the structure, two construction heuristics are designed to obtain solutions with both high quality and diversity. Four crossover and two mutation operators are presented. The interaction between the two populations increases the diversity within each population. The second phase integrates the previous two populations and uses the method of normalized objective function to enhance efficiency. Two new crossover operators are proposed to improve the performance of the algorithm. The TEA first finds several approximate front solutions to provide ideal feasible areas, and then continuously expands the solutions to the Pareto front. It embodies convergence, diversity and uniformity in different phases. Finally, through 810 benchmark instances, the TEA is compared with five classical and popular algorithms. The effectiveness of the two mechanisms in the TEA is analyzed. Experimental results demonstrate the superior performance of the TEA in terms of distribution and coverage of solutions.

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.

An effective memetic algorithm for the distributed flowshop scheduling problem with an assemble machine

The distributed flowshop has been a hot topic in research in recent years. This paper considers a distributed permutation flowshop scheduling problem with an assemble machine, so-called the distributed assembly permutation flowshop scheduling problem (DAPFSP), with total tardiness criterion. We propose an effective memetic algorithm (EMA). Firstly, a constructive heuristic combining the well-known earliest due date rule and largest processing time rule is presented for producing a seed sequence. On this basis, an effective initialisation method is used to generate an initial population with a high level of quality and diversity. The EMA uses a new structure of a small iteration nested within a large iteration. Moreover, an improved crossover and mutation expand the solution space in a good direction. According to different operation situations and objects, we design four targeted and flexible local search methods. We evaluate the strategies of the EMA, compare and analyse it with seven efficient algorithms based on the 810 benchmark instances. The experimental results confirm the effectiveness and efficiency of the proposed EMA.

An effective water wave optimization algorithm with problem-specific knowledge for the distributed assembly blocking flow-shop scheduling problem

The distributed assembly blocking flow-shop scheduling problem (DABFSP), which is a promising area in modern supply chains and manufacturing systems, has attracted great attention from researchers and practitioners. However, minimizing the total tardiness in DABFSP has not captured much attention so far. For solving the DABFSP with the total tardiness criterion, a mixed integer linear programming method is utilized to model the problem, wherein the total tardiness during the production process and assembly process are optimized simultaneously. A constructive heuristic (KBNEH) and a water wave optimization algorithm with problem-specific knowledge (KWWO) are presented. KBNEH is designed by combining a new dispatching rule with an insertion-based improvement procedure to obtain solutions with high quality. In KWWO, effective technologies, such as the re-developed destruction–construction​ operator, four local search methods under the framework of the variable neighborhood search strategy (VNS), the path-relinking method are applied to improve the performance of the algorithm. Comprehensive numerical experiments based on 900 small-scale benchmark instances and 810 large-scale benchmark instances are conducted to evaluate the performance of the presented algorithm. The experimental results obtained by KWWO are 1 to 4 times better than those obtained by the other comparison algorithms, which demonstrate that the effectiveness of KWWO is superior to the compared state-of-the-art algorithms for the considered problem.

A referenced iterated greedy algorithm for the distributed assembly mixed no-idle permutation flowshop scheduling problem with the total tardiness criterion

In this paper, we study the distributed assembly mixed no-idle permutation flowshop scheduling problem (DAMNIPFSP) with total tardiness objective. We first formulate the problem. Second, based on the characteristics of the DAMNIPFSP, an improved Iterated Greedy algorithm, named RIG (Referenced Iterated Greedy), with two novel destruction methods, four new reconstruction methods and six new local search methods is presented. Among them, two of the reconstruction methods and four of the local search methods are based on a reference, which proves key to performance. Finally, RIG is compared with the related algorithms through experiments. The results show that the new RIG algorithm is a new state-of-the-art procedure for the DAMNIPFSP with the total tardiness criterion.

Minimization of total tardiness in no-wait flowshop production systems with preventive maintenance

Efficient business organizations must balance quality, cost, and time constraints in competitive environments. Reflecting the complexity of this task, we consider manufacturing systems including several stages of production chains requiring time measurement. When production scheduling is not prioritized in such enterprises, several negative effects may occur. A corporation may suffer financial penalties as well as negative brand exposure, and thus may find its credibility challenged. Therefore, in this study, we propose constructive methods to minimize a total tardiness criterion, considering preventative maintenance constraints to reflect the reality of industrial practice, focusing on a no-wait flowshop environment in which jobs are successively processed without operational interruptions. In addition to proposing constructive methods to solve the no-wait flowshop production scheduling problem, a metaheuristic is presented as an approach to improve results obtained by constructive methods. Computational experiments were designed and performed to compare several production scheduling algorithms. Among various constructive heuristics considered, an algorithm called HENLL using an insertion logic showed the best performance. The proposed metaheuristic is based on the iterated greedy (IG) search method, and the results obtained demonstrated significant improvement compared to the heuristics alone. It is expected that this study may be used by production planning and control (PPC) professionals to apply the proposed method to schedule production more efficiently. We show that the proposed method successfully presented a better solution in relation to total tardiness, considering the above mentioned environment.

Effective heuristics and metaheuristics to minimise total tardiness for the distributed permutation flowshop scheduling problem

ABSTRACT During recent years, the distributed permutation flowshop scheduling problem (DPFSP) has become a very active area of research. However, minimising total tardiness in DPFSP, a very essential and relevant objective for today's customer-orientated market, has not been studied much. In this paper, we address the DPFSP with the total tardiness criterion. We present a mixed-integer linear programming model, two heuristics, hybrid discrete Harris hawks optimisation and an enhanced variant of iterated greedy algorithm to solve the considered problem. Problem-specific knowledge is explored and effective technologies, such as path relinking and random sub-sequence/single-point local search, are employed to improve the presented algorithms. The operators and parameters of the algorithms are analysed and calibrated using the design of experiments. To evaluate the performance, the well-known benchmark problem set of Naderi and Ruiz for DPFSP is extended with due dates. We compare the presented algorithms against seven other well-known meta-heuristics from the literature. Statistically sound results demonstrate the effectiveness of the presented algorithms for the considered problem.

Robust (min–max regret) single machine scheduling with interval processing times and total tardiness criterion

This paper studies a robust (min–max regret) single machine scheduling problem with uncertain processing times represented by interval data. The objective is to obtain robust sequences of jobs that minimize the absolute deviation of total tardiness from the optimal solution under the worst-case scenario. The problem is first formulated as a mixed-integer linear programming (MILP) model and assuming that the corresponding deterministic NP-hard problem for the mid-point scenario can be solved optimally, an optimal schedule under the mid-point scenario is then proved to be a 2-approximation solution to the problem. Next, the worst-case scenarios are proved to be not necessarily at the upper or lower limits of the interval processing times. Utilizing these results, a 2-approximation algorithm (2AA), a worst-case scenario-based heuristic (WSH), and an approximate worst-case-based heuristic (AWH) are proposed and empirically evaluated, in which an iterative procedure for evaluating the maximum regret of a solution is integrated. Finally, the paper is concluded by suggesting some fruitful directions for future research in this area.

Heuristics and metaheuristics for the mixed no-idle flowshop with sequence-dependent setup times and total tardiness minimisation

Abstract This paper analyses the mixed no-idle flowshop scheduling problem by adding the sequence-dependent setup times constraint and focusing on minimising the total tardiness criterion. In the mixed no-idle flowshop environment, machines that allow idleness, and also those that do not, coexist. In this paper, an extension of this problem in which dependent setup times are included in machines that permit idleness is studied. In order to do so, a mixed integer linear programming (MILP) model is developed. Furthermore, a method to assess the total tardiness of a permutation sequence is provided. Moreover, a partial acceleration method is devised so as to compute the total tardiness in an insertion neighbourhood. Since this problem has not yet been studied in the literature, this research adapted the best known heuristics and metaheuristics available from related problems. Moreover, a new heuristic was developed in order to provide an efficient solving mechanism for the problem. The proposed heuristic was incorporated in the best metaheuristics found in the literature. The adapted methods, as well as our proposal, were tested and compared through statistical and computational experimentation in an extensive benchmark. The MILP was also evaluated and the optimal solutions were compared to those found by the new proposed heuristic. The results show that the proposed heuristic perform extremely well in terms of solution quality and computational efficiency, providing near optimal solutions in some cases.

A hybrid discrete water wave optimization algorithm for the no-idle flowshop scheduling problem with total tardiness criterion

The no-idle flowshop has attracted enormous attention owing to its widespread application in the manufacturing industry domain. In this paper, a hybrid discrete water wave optimization algorithm, named HWWO, is presented to solve the NIFSP with total tardiness. In order to improve the quality of a population, an initialize method based on a new priority rule combined with the modified NEH method is proposed to generate a population. In the propagation phase, a self-adaption selection neighborhood search structure is introduced to amplify the search range of waves and balance the exploration and exploitation ability of the HWWO. Afterwards, a variable neighborhood search is adopted to strengthen the local search and maintain the diversity of the population in the breaking phase. In the refraction operation, a perturbation sequence is generated and combined with the local optimal solution found by the breaking operation, in order to generate a new solution, and prevent the algorithm from becoming trapped in the local optimum. Furthermore, the control parameters and time complexity are analyzed. The experimental results and comparisons with the other state-of-the-art algorithms evaluated on Taillard's and Ruiz's benchmark sets reveal that the effectiveness and efficiency of the HWWO outperformed the compared algorithms for solving the NIFSP.

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.

Distributionally robust single machine scheduling with the total tardiness criterion

This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of each job is assumed to be an unknown random variable within a given distributional set, which is described by mean and variance information. The proposed DRO model aims to find an optimal sequence that minimizes the expected worst-case total tardiness. To the best of our knowledge, it is the first time in the relevant literature that a DRO approach is adopted to minimize the total tardiness criterion for machine scheduling. An explicit expression is derived as an upper bound approximation for the robust objective, and then we transform the DRO problem into a mixed integer second-order cone programming problem. To solve this problem, a branch-and-bound algorithm with several novel bounding procedures and dominance rules is designed. Computational experiments confirm that the bounding procedures and dominance rules contribute significantly to the algorithm’s efficiency, and problem instances with up to 30 jobs can be optimally solved within 40 s. To tackle large-scale problem instances, we further design a beam search algorithm with filtering and recovering phases. Additional experiments with instances beyond 30 jobs confirm the efficacy of this beam search algorithm. To test the effectiveness of the proposed DRO model, we compare the robust sequences to nominal sequences under different processing time distributions. Experimental results show that the robust sequences perform better than nominal sequences, especially when the due dates are relatively loose.

A hybrid discrete teaching-learning based meta-heuristic for solving no-idle flow shop scheduling problem with total tardiness criterion

This paper proposes a hybrid discrete teaching-learning based meta-heuristic (HDTLM) to solve the no-idle flow shop scheduling problem (NIFSP) with the total tardiness criterion. To imitate the teaching-learning phenomenon in the real world, the HDTLM is composed of three phases, i.e. discrete teaching phase based on probabilistic model, discrete learning phase based on hierarchical structure, and reinforcement learning. In the discrete teaching phase, a probabilistic model based on the elite learners and the best learner is used to generate a series of position sequences, and the concept of consensus permutation is employed to replace the mean individual in the teaching-learning based optimization (TLBO) algorithm. Each job of the consensus permutation is inserted into a new sequence according to the position sequence. In the discrete learning phase, according to different levels of learners, all learners are divided into three layers, i.e. top layer, middle layer, bottom layer, and then the proposed learning phase adopts the order of top-down to spread the knowledge. The reinforcement learning phase is applied to the best learner to further improve the knowledge level of teacher. The parameters of the HDTLM are calibrated by a design of experiments (DOE) on randomly generated testing instances. The computational results on Taillard and Ruiz's benchmark sets and statistical analyses show that the HDTLM is an efficient and effective method for solving the NIFSP.

A hybrid data envelopment analysis_decision tree approach to evaluate the bi-criteria flow shop with blocking problem

The purpose of this paper is to evaluate the overall performance of a bi-objective scheduling problem using a method based on a combination of data envelopment analysis and decision tree. The hybrid approach is applied to the blocking flow shop scheduling problem with both makespan and total tardiness objectives. For this end, we propose two families of three-phase heuristics. In phase one, several constructive heuristics are used to generate initial solutions and in phase two, two improving heuristics are used to generate non-dominated solutions. One of the improving heuristics is based on the makespan criteria and the other one is based on the total tardiness criteria. The non-dominated solutions are then compared using the free disposal hull (FDH) formulation of data envelopment analysis (DEA). The overall performance of the composed heuristics is measured using a decision tree approach.

A hybrid data envelopment analysis_decision tree approach to evaluate the bi-criteria flow shop with blocking problem

The purpose of this paper is to evaluate the overall performance of a bi-objective scheduling problem using a method based on a combination of data envelopment analysis and decision tree. The hybrid approach is applied to the blocking flow shop scheduling problem with both makespan and total tardiness objectives. For this end, we propose two families of three-phase heuristics. In phase one, several constructive heuristics are used to generate initial solutions and in phase two, two improving heuristics are used to generate non-dominated solutions. One of the improving heuristics is based on the makespan criteria and the other one is based on the total tardiness criteria. The non-dominated solutions are then compared using the free disposal hull (FDH) formulation of data envelopment analysis (DEA). The overall performance of the composed heuristics is measured using a decision tree approach.

Iterated-greedy-based algorithms with beam search initialization for the permutation flowshop to minimise total tardiness

The permutation flow shop scheduling problem is one of the most studied operations research related problems. Literally, hundreds of exact and approximate algorithms have been proposed to optimise several objective functions. In this paper we address the total tardiness criterion, which is aimed towards the satisfaction of customers in a make-to-order scenario. Although several approximate algorithms have been proposed for this problem in the literature, recent contributions for related problems suggest that there is room for improving the current available algorithms. Thus, our contribution is twofold: First, we propose a fast beam-search-based constructive heuristic that estimates the quality of partial sequences without a complete evaluation of their objective function. Second, using this constructive heuristic as initial solution, eight variations of an iterated-greedy-based algorithm are proposed. A comprehensive computational evaluation is performed to establish the efficiency of our proposals against the existing heuristics and metaheuristics for the problem.

Hybrid Algorithm Based on an Estimation of Distribution Algorithm and Cuckoo Search for the No Idle Permutation Flow Shop Scheduling Problem with the Total Tardiness Criterion Minimization

The no idle permutation flow shop scheduling problem (NIPFSP) is a popular NP-hard combinatorial optimization problem, which exists in several real world production processes. This study proposes a novel hybrid estimation of the distribution algorithm and cuckoo search (CS) algorithm (HEDA_CS) to solve the NIPFSP with the total tardiness criterion minimization. The problem model is built on the basis of the starting and ending time point of each job. A discrete solution representation method is applied in HEDA_CS to increase the operation efficiency. A novel probability matrix build method is also designed within the knowledge of the processing time matrix. The partially-mapped crossover operation works effectively during the CS phase. A suitable knowledge-based local search is also designed in the HEDA_CS to balance the exploitation and exploration. Finally, many simulations based on the new hard Ruiz benchmarks are conducted. Computational results demonstrate the effectiveness of the proposed HEDA_CS.

A discrete differential evolution algorithm for multi-objective permutation flowshop scheduling

The more practical and interesting versions of the permutation flowshop scheduling problem (PFSP) have a variety of objective criteria to be optimized simultaneously. Multi-objective PFSP is also a relevant combinatorial multi-objective optimization problem. In this paper we propose a multi-objecti ve evolutionary algorithm for PFSP by extending the previously proposed discrete differential evolution (DE) scheme for single-objective PFSP. This is the first application of the algebraic-based discrete DE to multi-objective problems. The algorithm is extended by adopting a variety of crossover and multi-objective selection operators. Among these, the multi-objective α-selection is a novelty of this work and can be decoupled from DE and used also in other evolutionary algorithms. The other crossover and selection operators have been taken from the existing literature and, where required, have been adapted to the problem at hand. An experimental evaluation has been conducted on all the three bi-objective PFSPs among the makespan, total flowtime and total tardiness criteria. The results show that the proposed approach is competitive with respect to the state-of-the-art algorithms.

A competitive memetic algorithm for multi-objective distributed permutation flow shop scheduling problem

Abstract In this paper, a competitive memetic algorithm (CMA) is proposed to solve the multi-objective distributed permutation flow-shop scheduling problem (MODPFSP) with the makespan and total tardiness criteria. Two populations corresponding to two different objectives are employed in the CMA. Some objective-specific operators are designed for each population, and a special interaction mechanism between two populations is designed. Moreover, a competition mechanism is proposed to adaptively adjust the selection rates of the operators, and some knowledge-based local search operators are developed to enhance the exploitation ability of the CMA. In addition, the influence of the parameters on the performance of the CMA is investigated by using the Taguchi method of design-of-experiment. Finally, extensive computational tests and comparisons are carried out to demonstrate the effectiveness of the CMA in solving the MODPFSP.