A new constructive heuristic for the flowshop scheduling problem

This paper presents a simple constructive heuristic (HFC) for the flowshop makespan problem which is capable of producing non-permutation schedules when it deems it appropriate. HFC determines the order of any two jobs in the final schedule based on their order in all two-machine problems embedded in the problem. Computational experiments indicate that HFC performs as well as NEH which is the currently best available constructive heuristic on problems where a permutation schedule is expected to be optimal. However, HFC outperforms NEH on problems where a non-permutation schedule may be optimal.     

A fuzzy greedy heuristic for permutation flow-shop scheduling

This paper describes a polynomial-time heuristic for the permutation flow-shop scheduling problem with the makespan criterion. The proposed method consists of two phases: arranging the jobs in priority order and then constructing a sequence. A fuzzy greedy evaluation function is employed to prioritize the jobs for incorporating into the construction phase of the heuristic. Computational experiments using standard benchmark problems indicate an improvement of the new heuristic over the well-known Nawaz, Enscore and Ham (NEH) heuristic. It will be seen that the NEH heuristic is a special case of our more general heuristic.     

A partial enumeration heuristic for multi-objective flowshop scheduling problems

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.     

A New Heuristic Method for the Permutation Flow Shop Scheduling Problem

A new heuristic method for the permutation flow shop scheduling problem is presented and compared with two other heuristics named NEH and SPIRIT. The new heuristic method is based on a property of the scheduling problem that provides an upper bound on the idle time of the last machine between any two adjacent jobs regardless of their position in the sequence of jobs. The results from computational experience have shown that the new heuristic outperforms, in solution quality, all others for problems having up to 50 jobs and 30 machines.     

On the automatic discovery of variants of the NEH procedure for flow shop scheduling using genetic programming

We use genetic programming to find variants of the well-known Nawaz, En-score and Ham (NEH) heuristic for the permutation flow shop problem. Each variant uses a different ranking function to prioritize operations during schedule construction. We have tested our ideas on problems where jobs have release times, due dates, and weights and have considered five objective functions: makespan, sum of tardiness, sum of weighted tardiness, sum of completion times and sum of weighted completion times. The implemented genetic programming system has been carefully tuned and used to generate one variant of NEH for each objective function. The new NEHs, obtained with genetic programming, have been compared with the original NEH and randomized NEH versions on a large set of benchmark problems. Our results indicate that the NEH variants discovered by genetic programming are superior to the original NEH and its stochastic version on most of the problems investigated.     

An empirical analysis of the optimality rate of flow shop heuristics

If a certain optimization problem is NP-hard or even harder, one could expect that the chances of solving it optimally should rather decrease with an increase of the problem size. We reveal, however, that the opposite occurs for a strongly NP-hard problem, which requires sequencing n jobs through an m machine flow shop so as to minimize the makespan. In particular, we empirically examine optimality rates (the probability of being optimal) of the famous NEH heuristic of Nawaz et al. [Nawaz, M., Enscore, Jr., E., Ham, I., 1983. A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, The International Journal of Management Science 11, 91–95] and two improved versions of NEH. By using millions of simulation trials and a new effective lower bound on the shortest makespan, we observe relatively high optimality rates of the three heuristics for small values of m. Rather surprisingly, for larger values of n, the heuristics become more frequently optimal as n increases. Neither theoretical nor empirical studies of optimality rates of flow shop heuristics have been conducted so far, and – to the best of our knowledge – no similar studies are known in the field of operations research.     

Technical note: a systematic procedure based on CALIBRA and the Nelder & Mead algorithm for fine-tuning metaheuristics

The problem of setting the parameter values of a metaheuristic algorithm that optimise its performance is complex and time-consuming. Although the performance of a metaheuristic can be very sensitive to the parameter values, it is usual in the literature that the selection of the value parameters is not enough justified. There are in the literature two procedures that facilitate the task of fine-tuning: CALIBRA and the Nelder & Mead (N&M) algorithm. We propose a hands-off systematic procedure for fine-tuning metaheuristics that takes the advantages of CALIBRA and the N&M algorithm.     

改进二元分布估计算法求解置换流水车间调度问题

针对置换流水车间调度这类组合最优化问题的求解,提出了一种改进二元分布估计算法(Improved binary estimation distribution algorithm, I-EDA)。算法以二元分布估计算法为架构,使用NEH(Nawaz-Enscore-Ham)启发式算法生成初始解,提高了初始解的质量;通过对优势解的统计采样构建位置矩阵模型和链接矩阵模型,依照两个矩阵模型的合并概率组合链接区块产生子代。提出了NEH插入式重组策略和基于位置概率的交换策略和两种全新局部搜索机制替代原二元分布估计算法的相邻交换法,以进一步筛选优势解。最后通过对Reeves标准测试集的仿真实验和算法比较验证了所提出算法的有效性。     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

Density Based Problem Space Search for the Capacitated Clustering p-Median Problem

In the Capacitated Clustering Problem (CCP), a given set of n weighted points is to be partitioned into p clusters such that, the total weight of the points in each cluster does not exceed a given cluster capacity. The objective is to find a set of p centers that minimises total scatter of points allocated to them. In this paper a new constructive method, a general framework to improve the performance of greedy constructive heuristics, and a problem space search procedure for the CCP are proposed. The constructive heuristic finds patterns of natural subgrouping in the input data using concept of density of points. Elements of adaptive computation and periodic construction–deconstruction concepts are implemented within the constructive heuristic to develop a general framework for building efficient heuristics. The problem-space search procedure is based on perturbations of input data for which a controlled perturbation strategy, intensification and diversification strategies are developed. The implemented algorithms are compared with existing methods on a standard set of bench-marks and on new sets of large-sized instances. The results illustrate the strengths of our algorithms in terms of solution quality and computational efficiency.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

Constructive and composite heuristic solutions to the P//∑Ci scheduling problem

In this paper, we study the permutation flowshop scheduling problem with the criterion of minimising the total flow time. We propose a new constructive heuristic procedure to solve the problem. This procedure is flexible in the computational effort required, as it can be adjusted to the requirements of the problem. We combine this procedure with local search methods, whose computational requirements can also be varied, to study the efficiency and effectiveness of different ways of forming composite solution methods. Computational experiments on standard benchmark problems are carried out. The results show that the new heuristic performs significantly better than previous ones and that combining constructive and search heuristics not only further improves the solution quality but also saves computation time. Discussions on the results are provided and future research is suggested.     

An adaptive memory algorithm for the split delivery vehicle routing problem

The split delivery vehicle routing problem (SDVRP) relaxes routing restrictions forcing unique deliveries to customers and allows multiple vehicles to satisfy customer demand. Split deliveries are used to reduce total fleet cost to meet those customer demands. We provide a detailed survey of the SDVRP literature and define a new constructive algorithm for the SDVRP based on a novel concept called the route angle control measure. We extend this constructive approach to an iterative approach using adaptive memory concepts, and then add a variable neighborhood descent process. These three new approaches are compared to exact and heuristic approaches by solving the available SDVRP benchmark problem sets. Our approaches are found to compare favorably with existing approaches and we find 16 new best solutions for a recent 21 problem benchmark set.     

Minimizing the total completion time in a two-machine flowshop with sequence-independent setup times

We consider the problem of minimizing the sum of completion times in a two-machine permutation flowshop subject to setup times. We propose a new priority rule, several constructive heuristics, local search procedures, as well as an effective multiple crossover genetic algorithm. Computational experiments carried out on a large set of randomly generated instances provide evidence that a constructive heuristic based on newly derived priority rule dominates all the proposed constructive heuristics. More specifically, we show that one of our proposed constructive heuristics outperforms the best constructive heuristic in the literature in terms of both error and computational time. Furthermore, we show that one of our proposed local search-based heuristics outperforms the best local search heuristic in the literature in terms of again both error and computational time. We also show that, in terms of quality-to-CPU time ratio, the multiple crossover genetic algorithm performs consistently well.     

The examination timetabling problem at Universiti Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution

This paper presents a real-world, capacitated examination timetabling problem from Universiti Malaysia Pahang (UMP), Malaysia. The problem has constraints which have not been modelled before, these being the distance between examination rooms and splitting exams across several rooms. These constraints provide additional challenges in defining a suitable model and in developing a constructive heuristic. One of the contributions of this paper is to formally define this real-world problem. A further contribution is the constructive heuristic that is able to produce good quality solutions for the problem, which are superior to the solutions that are produced using the university’s current software. Moreover, our method adheres to all hard constraints which the current systems fails to do.     

Heuristic algorithms for the minmax regret flow-shop problem with interval processing times

An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion’s value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion.

     

Improvement heuristic for the flow-shop scheduling problem: An adaptive-learning approach

We propose an improvement-heuristic approach for the general flow-shop problem (n/m/C_max) based on the idea of adaptive learning. The approach employs a one-pass heuristic to give a good starting solution in the search space and uses a weight parameter to perturb the data of the original problem to obtain improved solutions. The weights are then adjusted employing a learning strategy which involves reinforcement and backtracking. The learning is similar to that in neural networks. The random perturbation allows a non-deterministic local search. We apply the improvement-heuristic approach in conjunction with three well-known heuristics in the literature, namely, Palmer’s Slope Index, CDS and NEH. We test our approach on several benchmark problem sets including Taillard’s, Carlier’s, Heller’s and Reeves’. We compare our results to the best-known upper-bound solutions and find that for many problems we match the best-known upper bound. For one problem we discover a new upper bound.     

A hybrid tabu search/branch & bound approach to solving the generalized assignment problem

A new approach for solving the generalized assignment problem (GAP) is proposed that combines the exact branch & bound approach with the heuristic strategy of tabu search (TS) to produce a hybrid algorithm for solving GAP. The algorithm described uses commercial software to solve sub-problems generated by the TS guiding strategy. The TS approach makes use of the concept of referent domain optimisation and introduces novel add/drop strategies. In addition, the linear programming relaxation of GAP that forms part of the branch & bound approach is itself helpful in suggesting which variables might take binary values. Computational results on benchmark test instances are presented and compared with results obtained by the standard branch & bound approach and also several other heuristic approaches from the literature. The results show the new algorithm performs competitively against the alternatives and is able to find some new best solutions for several benchmark instances.     

A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing

The three-dimensional bin packing problem consists of packing a set of boxes into the minimum number of bins. In this paper we propose a new GRASP algorithm for solving three-dimensional bin packing problems which can also be directly applied to the two-dimensional case. The constructive phase is based on a maximal-space heuristic developed for the container loading problem. In the improvement phase, several new moves are designed and combined in a VND structure. The resulting hybrid GRASP/VND algorithm is simple and quite fast and the extensive computational results on test instances from the literature show that the quality of the solutions is equal to or better than that obtained by the best existing heuristic procedures.     

A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem

Over the last decade, many metaheuristics have been applied to the flowshop scheduling problem, ranging from Simulated Annealing or Tabu Search to complex hybrid techniques. Some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated. In fact, several published methods require substantial implementation efforts, exploit problem specific speed-up techniques that cannot be applied to slight variations of the original problem, and often re-implementations of these methods by other researchers produce results that are quite different from the original ones. In this work we present a new iterated greedy algorithm that applies two phases iteratively, named destruction, were some jobs are eliminated from the incumbent solution, and construction, where the eliminated jobs are reinserted into the sequence using the well known NEH construction heuristic. Optionally, a local search can be applied after the construction phase. Our iterated greedy algorithm is both very simple to implement and, as shown by experimental results, highly effective when compared to state-of-the-art methods.