A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.     

Coordinated scheduling of production and delivery from multiple plants

This paper deals with the scheduling of orders and vehicle assignment for production and distribution planning in a scenario of no-wait, immediate delivery to the customer site. We first describe the problem and then present an integer programming model that maximizes the weighted value of the orders served. We consider a special case of the problem which can be solved in polinomial time by a minimum cost flow algorithm. Based on this approach we develop a heuristic procedure for the general case. Comparisons with an exact graph-based method attest that our heuristic produces good-quality solutions in short running times.     

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.     

An improved iterated greedy algorithm with a Tabu-based reconstruction strategy for the no-wait flowshop scheduling problem

This paper proposes a Tabu-mechanism improved iterated greedy (TMIIG) algorithm to solve the no-wait flowshop scheduling problem with a makespan criterion. The idea of seeking further improvement in the iterated greedy (IG) algorithm framework is based on the observation that the construction phase of the original IG algorithm may not achieve good performance in escaping from local minima when incorporating the insertion neighborhood search. To overcome this limitation, we have modified the IG algorithm by utilizing a Tabu-based reconstruction strategy to enhance its exploration ability. A powerful neighborhood search method that involves insert, swap, and double-insert moves is then applied to obtain better solutions from the reconstructed solution in the previous step. Empirical results on several benchmark problem instances and those generated randomly confirm the advantages of utilizing the new reconstruction scheme. In addition, our results also show that the proposed TMIIG algorithm is relatively more effective in minimizing the makespan than other existing well-performing heuristic algorithms.     

An improved heuristic for no-wait flow shop to minimize makespan

No-wait flow shop production has been widely applied in manufacturing, where no waiting time is allowed between intermediate operations. However, minimization of makespan for no-wait flow shop production is NP-hard. In this paper, we propose an average idle time (AIT) heuristic to minimize makespan in no-wait flow shop production. First, we take the current idle times and future idle times into consideration, proposing an initial sequence algorithm, and then use the insertion and neighborhood exchanging methods to further improve solutions. Compared with three existing best-known heuristics, our AIT heuristic can achieve the smallest deviations of 0.23% from optimum, based on Taillard’s benchmarks and 600 randomly generated instances, in the same computational complexity.     

A fast hybrid tabu search algorithm for the no-wait job shop problem

This paper describes a hybrid tabu search algorithm dedicated to a job shop problem with a no-wait constraint with a makespan criterion. The proposed here algorithm complexity is that the superior algorithm based on the tabu search technique selects parameters controlling the work of a certain constructional algorithm. This approach limits the checked solutions only to a group of solutions being able to be generated by the structural algorithm in question. It bears serious consequences both positive, for example it limits the research scope for a small fraction of relatively extremely well quality of acceptable solutions, and negative that is the lack of possibility of finding the optimal solution. In this paper numerical researches of the proposed algorithm are conducted as well as a comparative analysis with reference to the literature algorithms of the algorithm in question is made.     

Incorporating preventive maintenance into the m-machine no-wait flow-shop scheduling problem with total flow-time minimization: a computational study

In this article, the impact of preventive maintenance policies on the constructive heuristics performance for the no-wait flow-shop problem with total flow-time minimization is evaluated. The main constructive heuristics for the m-machine no-wait flow-shop scheduling problem with total flow-time minimization are compared through computational experiments with a set of 5760 problems. The results show that the adopted parameters significantly affect the performance of the constructive heuristics; also, the computational effort required to solve the problems increases owing to the complexity of the function-objective calculation. Heuristics proposed by Laha and Sapkal (LSH) and Framinan, Nagano and Moccellin (FNMH) provide the best solutions for both evaluated policies.     

The two-machine flowshop no-wait scheduling problem with a single server to minimize the total completion time

This work studies the scheduling problem where a set of jobs are available for processing in a no-wait and separate setup two-machine flow shop system with a single server. The no-wait constraint requires that the operations of a job have to be processed continuously without waiting between two machines. The setup time is incurred and attended by a single sever which can perform one setup at a time. The performance measure considered is the total completion time. The problem is strongly NP-hard. Optimal solutions for several restricted cases and some properties for general case are proposed. Both the heuristic and the branch and bound algorithms are established to tackle the problem. Computational experiments indicate that the heuristic and the branch and bound algorithm are superior to the existing ones in term of solution quality and number of branching nodes, respectively.     

实时无等待HFS调度的一种拉格朗日松弛算法

研究了实时无等待HFS调度问题,并建立一个整数规划模型,提出运用拉格朗日松弛算法来求解,在此算法中,常采用次梯度方法更新拉格朗日乘子,但它随着迭代数的增加收敛速度会减慢,因此设计了一个改进的bundle方法。将以前的次梯度累积到bundle中,以获得一个更好的乘子更新方向．仿真实验表明,与次梯度方法相比,所设计的bundle法不仅在较少的迭代数内得到了更快的收敛速度而且改进了优化性能,对于大规模问题效果更为显著。     

An improved heuristic to minimize total flow time for scheduling in the m-machine no-wait flow shop

In this paper, we present a constructive heuristic to minimize total flow time criterion for the well-known NP-hard no-wait flow shop scheduling problem. It is based on the assumption that the priority of a job in the initial sequence is given by the sum of its processing times on the bottleneck machines. The initial sequence of jobs thus generated is further improved using a new job insertion technique. We show, through computational experimentation, that the proposed method significantly outperforms the best-known heuristics while retaining its time complexity of O(n²). Statistical tests of significance are used to confirm the improvement in solution quality.