Minimising total tardiness in the m-machine flowshop problem: A review and evaluation of heuristics and metaheuristics

In this work, a review and comprehensive evaluation of heuristics and metaheuristics for the m-machine flowshop scheduling problem with the objective of minimising total tardiness is presented. Published reviews about this objective usually deal with a single machine or parallel machines and no recent methods are compared. Moreover, the existing reviews do not use the same benchmark of instances and the results are difficult to reproduce and generalise. We have implemented a total of 40 different heuristics and metaheuristics and we have analysed their performance under the same benchmark of instances in order to make a global and fair comparison. In this comparison, we study from the classical priority rules to the most recent tabu search, simulated annealing and genetic algorithms. In the evaluations we use the experimental design approach and careful statistical analyses to validate the effectiveness of the different methods tested. The results allow us to clearly identify the state-of-the-art methods.     

An improved NEH-based heuristic for the permutation flowshop problem

NEH is an effective heuristic for solving the permutation flowshop problem with the objective of makespan. It includes two phases: generate an initial sequence and then construct a solution. The initial sequence is studied and a strategy is proposed to solve job insertion ties which may arise in the construct process. The initial sequence which is generated by combining the average processing time of jobs and their standard deviations shows better performance. The proposed strategy is based on the idea of balancing the utilization among all machines. Experiments show that using this strategy can improve the performance of NEH significantly. Based on the above ideas, a heuristic NEH-D (NEH based on Deviation) is proposed, whose time complexity is O(mn²), the same as that of NEH. Computational results on benchmarks show that the NEH-D is significantly better than the original NEH.     

两台流水机器协调分解调度问题

研究钢管加工流程中一类新型两台机器流水车间调度问题,工件在第一台机器上加工后被分解成多个子工件.对于最小化最大完成时间的情况,给出一个多项式时间的最优算法;对于最小化最大完成时间与惩罚费用之和的情况,给出一个拟多项式时间的动态规划算法;对于考虑生产前运输的最小化最大完成时间的情况,分析了问题的复杂性.证明了第一种情况的最优算法可作为后两种情况的2-近似算法.数值实验表明了算法的有效性.     

An ant colony optimization approach to a permutational flowshop scheduling problem with outsourcing allowed

This paper deals with the scheduling problem of minimizing the makespan in a permutational flowshop environment with the possibility of outsourcing certain jobs. It addresses this problem by means of the development of an ant colony optimization-based algorithm. This new algorithm, here named as flowshop ant colony optimization is composed of two combined ACO heuristics. The results show that this new approach can be used to solve the problem efficiently and in a short computational time.     

Bi-criteria minimization for the permutation flowshop scheduling problem with machine-based learning effects

In traditional scheduling problems, the processing time for the given job is assumed to be a constant regardless of whether the job is scheduled earlier or later. However, the phenomenon named “learning effect” has extensively been studied recently, in which job processing times decline as workers gain more experience. This paper discusses a bi-criteria scheduling problem in an m-machine permutation flowshop environment with varied learning effects on different machines. The objective of this paper is to minimize the weighted sum of the total completion time and the makespan. A dominance criterion and a lower bound are proposed to accelerate the branch-and-bound algorithm for deriving the optimal solution. In addition, the near-optimal solutions are derived by adapting two well-known heuristic algorithms. The computational experiments reveal that the proposed branch-and-bound algorithm can effectively deal with problems with up to 16 jobs, and the proposed heuristic algorithms can yield accurate near-optimal solutions.     

A generalized constructive algorithm using insertion-based heuristics

In this paper, a generalized constructive algorithm referred to as GCA is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework, referred to as PERMGEN, forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of GCA are identified. Features and benefits of the generalized algorithm are presented through the extension of the NEH heuristic, a successful heuristic solution approach of Nawaz, Enscore, and Ham for the permutation flowshop problem (PFSP). The goal of the experimental study is to improve the performance of the NEH heuristic on the PFSP. To achieve this goal, the space of algorithmic control arguments is searched for a combination of values that define an algorithm providing lower makespan solutions than NEH, in a linear increase of CPU time. Computational experiments on a set of 120 benchmark problem instances, originally proposed by Taillard, are performed to establish a more robust version of the original NEH constructive heuristic. The proposed procedures outperform NEH, preserving its efficiency and simplicity.     

Two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times

Two-machine no-wait flowshop scheduling problems in which the processing time of a job is a function of its position in the sequence and its resource allocation are considered in the study. The primary objective is to find the optimal sequence of jobs and the optimal resource allocation separately. Here we propose two separate models: minimizing a cost function of makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function of makespan, total waiting time, total absolute differences in waiting times and total resource cost. Since each model is strongly NP-hard, we solve both models by breaking them down to two sub-problems, the optimal resource allocation problem for any job sequence and the optimal sequence problem with its optimal resource allocation. Specially, we transform the second sub-problem into the minimum of the bipartite graph optimal matching problem (NP-hard), and solve it by using the classic KM (Kuhn–Munkres) algorithm. The solutions of the two sub-problems demonstrate that the target problems remain polynomial solvable under the proposed model.     

Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools

Several grammar-based genetic programming algorithms have been proposed in the literature to automatically generate heuristics for hard optimization problems. These approaches specify the algorithmic building blocks and the way in which they can be combined in a grammar; the best heuristic for the problem being tackled is found by an evolutionary algorithm that searches in the algorithm design space defined by the grammar.In this work, we propose a novel representation of the grammar by a sequence of categorical, integer, and real-valued parameters. We then use a tool for automatic algorithm configuration to search for the best algorithm for the problem at hand. Our experimental evaluation on the one-dimensional bin packing problem and the permutation flowshop problem with weighted tardiness objective shows that the proposed approach produces better algorithms than grammatical evolution, a well-established variant of grammar-based genetic programming. The reasons behind such improvement lie both in the representation proposed and in the method used to search the algorithm design space.     

Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.