Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillard’s instances for the blocking flow shop scheduling problem with the total flow time criterion.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

Scheduling algorithms for heterogeneous batch processors with incompatible job-families

We consider the problem of scheduling heterogeneous batch processors (i.e., batch processors with different capacity) with incompatible job-families and non-identical job sizes to maximize the utilization of the batch processors. We analyzed the computational complexity of this problem and showed that it is NP-hard and proposed eight variants of a fast greedy heuristic. A series of computational experiments were carried out to compare the performance of the heuristics and showed that the heuristics are capable of consistently obtaining near (estimated) optimal solutions with very low-computational burden for large-scale problems. We also carried out a study to find the effect of family processing time changes on the performance of the heuristics. This sensitivity analysis indicated that the processing time set of job-families influences the performance of the heuristic algorithms.     

Single machine interfering jobs problem with flowtime objective

Interfering jobs problems (or multi agents scheduling problems) are an emergent topic in the scheduling literature. In these decision problems, two or more sets of jobs have to be scheduled, each one with its own criteria. More specifically, we focus on a problem in which jobs belonging to two sets have to be scheduled in a single machine in order to minimize the total flowtime of the jobs in one set, while the total flowtime of the jobs in the other set should not exceed a given constant \(\epsilon \). This problem is known to be weakly NP-hard, and, in the literature, a dynamic programming (DP) algorithm has been proposed to find optimal solutions. In this paper, we first analyse the distribution of solutions of the problem in order to establish its empirical hardness. Next, a novel encoding scheme and a set of properties associated to the neighbourhood of this scheme are presented. These properties are used to develop both exact and approximate methods, i.e. a branch and bound (B&B) method, several constructive heuristics, and different versions of a genetic algorithm (GA). The computational experience carried out shows that the proposed B&B is more efficient than the existing DP algorithm. The results also show the advantages of the proposed encoding scheme, as the approximate methods yield close-to-optimum solutions for big-sized instances where exact methods are not feasible.     

The distributed permutation flowshop scheduling problem

This paper studies a new generalization of the regular permutation flowshop scheduling problem (PFSP) referred to as the distributed permutation flowshop scheduling problem or DPFSP. Under this generalization, we assume that there are a total of F identical factories or shops, each one with m machines disposed in series. A set of n available jobs have to be distributed among the F factories and then a processing sequence has to be derived for the jobs assigned to each factory. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. This production setting is necessary in today's decentralized and globalized economy where several production centers might be available for a firm. We characterize the DPFSP and propose six different alternative mixed integer linear programming (MILP) models that are carefully and statistically analyzed for performance. We also propose two simple factory assignment rules together with 14 heuristics based on dispatching rules, effective constructive heuristics and variable neighborhood descent methods. A comprehensive computational and statistical analysis is conducted in order to analyze the performance of the proposed methods.     

Evolutionary algorithms for flowshop sequencing with non-unique jobs

Sequencing problems are difficult combinatorial problems because of the extremely large search space of possible solutions and the large number of "local" optima that arise. Unlike other NP-hard combinatorial problems, the search space, in general, for sequencing problems (under the makespan objective) consists of sequences with objective function values that lie within only a relatively small amount of each other. This means that when a change is made to the sequence, an improvement or non-improvement is not easily recognised. This makes the problem much more difficult to solve. A number of constructive heuristics exist that obtain good solutions in a short period of time, however, the output of such algorithms is generally a single sequence which may not be feasible or preferred with respect to industry constraints. Other heuristic algorithms such as Simulated Annealing (SA) and Tabu Search (TS) have also been applied and successes have been reported. However, the performance is dependent upon a number of finely tuned parameters and the output is again only a single solution. For these reasons, Evolutionary Algorithms (EAs) may be suitable solution strategy, for which limited research has been performed. In this research, a number of new EAs have been proposed and a number of modifications have been made to several constructive algorithms to cope with non-unique jobs or jobs with multiple demands. A numerical comparison of a number of benchmark problems and real data of a truck assembly line has also been presented.     

Efficient constructive and composite heuristics for the Permutation Flowshop to minimise total earliness and tardiness

In this paper we address the problem of scheduling jobs in a permutation flowshop with a just-in-time objective, i.e. the minimisation of the sum of total tardiness and total earliness. Since the problem is NP-hard, there are several approximate procedures available for the problem, although their performance largely depends on the due dates of the specific instance to be solved. After an in-depth analysis of the problem, different cases or sub-problems are identified and, by incorporating this knowledge, four heuristics are proposed: a fast constructive heuristic, and three different local search procedures that use the proposed constructive heuristic as initial solution.The proposed Prod. Type: FLPheuristics have been compared on an extensive set of instances with the best-so-far heuristic for the problem, as well as with adaptations of efficient heuristics for similar scheduling problems. The computational results show the excellent performance of the proposed algorithms. Finally, the positive impact of the efficient heuristics is evaluated by including them as seed sequences for one of the best metaheuristic for the problem.     

An efficient stochastic hybrid heuristic for flowshop scheduling

The paper addresses the problem of flowshop scheduling in order to minimize the makespan objective. Three probabilistic hybrid heuristics are presented for solving permutation flowshop scheduling problem. The proposed methodology combines elements from both constructive heuristic search and a stochastic improvement technique. The stochastic method used in this paper is simulated annealing (SA). Experiments have been run on a large number of randomly generated test problems of varying jobs and machine sizes. Our approach is shown to outperform best-known existing heuristics, including the classical NEH technique (OMEGA, 1983) and the SA based on (OMEGA, 1989) of Osman and Potts . Statistical tests of significance are performed to substantiate the claims of improvement.     

Modeling and heuristics for scheduling of distributed job shops

This paper deals with the problem of distributed job shop scheduling in which the classical single-facility job shop is extended to the multi-facility one. The mathematical formulation of the problem is comprehensively discussed. Two different mixed integer linear programming models in form of sequence and position based variables are proposed. Using commercial software of CPLEX, the small sized problems are optimally solved. To solve large sized problems, besides adapting three well-known heuristics, three greedy heuristics are developed. The basic idea behind the developed heuristics is to iteratively insert operations (one at each iteration) into a sequence to build up a complete permutation of operations. The permutation scheme, although having several advantages, suffers from redundancy which is having many different permutations representing the same schedule. The issue is analyzed to recognize the redundant permutation. That improves efficiency of heuristics. Comprehensive experiments are conducted to evaluate the performance of the two models and the six heuristics. The results show sequence based model and greedy heuristics equipped with redundancy exclusion are effective for the problem.     

Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem

Hyper heuristics is a relatively new optimisation algorithm. Numerous studies have reported that hyper heuristics are well applied in combinatorial optimisation problems. As a classic combinatorial optimisation problem, the row layout problem has not been publicly reported on applying hyper heuristics to its various sub-problems. To fill this gap, this study proposes a parallel hyper-heuristic approach based on reinforcement learning for corridor allocation problems and parallel row ordering problems. For the proposed algorithm, an outer layer parallel computing framework was constructed based on the encoding of the problem. The simulated annealing, tabu search, and variable neighbourhood algorithms were used in the algorithm as low-level heuristic operations, and Q-learning in reinforcement learning was used as a high-level strategy. A state space containing sequences and fitness values was designed. The algorithm performance was then evaluated for benchmark instances of the corridor allocation problem (37 groups) and parallel row ordering problem (80 groups). The results showed that, in most cases, the proposed algorithm provided a better solution than the best-known solutions in the literature. Finally, the meta-heuristic algorithm applied to three low-level heuristic operations is taken as three independent algorithms and compared with the proposed hyper-heuristic algorithm on four groups of parallel row ordering problem instances. The effectiveness of Q-learning in selection is illustrated by analysing the comparison results of the four algorithms and the number of calls of the three low-level heuristic operations in the proposed method.     

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.     

A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimise total flowtime

This paper focuses on the blocking flow shop scheduling problem with the objective of total flowtime minimisation. This problem assumes that there are no buffers between machines and, due to its application to many manufacturing sectors, it is receiving a growing attention by researchers during the last years. Since the problem is NP-hard, a large number of heuristics have been proposed to provide good solutions with reasonable computational times. In this paper, we conduct a comprehensive evaluation of the available heuristics for the problem and for related problems, resulting in the implementation and testing of a total of 35 heuristics. Furthermore, we propose an efficient constructive heuristic which successfully combines a pool of partial sequences in parallel, using a beam-search-based approach. The computational experiments show the excellent performance of the proposed heuristic as compared to the best-so-far algorithms for the problem, both in terms of quality of the solutions and of computational requirements. In fact, despite being a relative fast constructive heuristic, new best upper bounds have been found for more than 27% of Taillard’s instances.     

A meta-heuristic approach to solve a JIT scheduling problem in hybrid flow shop

In this paper we address a hybrid flow shop scheduling problem considering the minimization of the sum of the total earliness and tardiness penalties. This problem is proven to be NP-hard, and consequently the development of heuristic and meta-heuristic approaches to solve it is well justified. So, we propose an ant colony optimization method to deal with this problem. Our proposed method has several features, including some heuristics that specifically take into account both earliness and tardiness penalties to compute the heuristic information values. The performance of our algorithm is tested by numerical experiments on a large number of randomly generated problems. A comparison with solutions performance obtained by some constructive heuristics is presented. The results show that the proposed approach performs well for this problem.     

Heuristics for scheduling in flowshops and flowline-based manufacturing cells to minimize the sum of weighted flowtime and weighted tardiness of jobs

The problem of scheduling in two different types of flowshops (all jobs available at time zero, different job availability times known a priori) and in flowline-based manufacturing cells is considered with the objective of minimizing the sum of weighted flowtime and weighted tardiness of jobs. First, heuristic preference relations are developed by the consideration of lower bounds on the completion times, operation due-dates, and weights for holding and tardiness of jobs. A heuristic algorithm for scheduling is then proposed by making use of the heuristic preference relations. Two more heuristic algorithms are developed by implementing an improvement scheme to enhance the quality of the solution given by the first heuristic algorithm. The proposed and the existing heuristics are evaluated with respect to the three problem classes under consideration by solving a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that all three proposed heuristics perform better than the existing heuristics in giving a solution of superior quality and that the first proposed heuristic yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the existing heuristics, and also the effectiveness of heuristics based on simulated annealing. The results are discussed in detail.     

A beam-search-based constructive heuristic for the PFSP to minimise total flowtime

In this paper we present a beam-search-based constructive heuristic to solve the permutation flowshop scheduling problem with total flowtime minimisation as objective. This well-known problem is NP-hard, and several heuristics have been developed in the literature. The proposed algorithm is inspired in the logic of the beam search, although it remains a fast constructive heuristic.The results obtained by the proposed algorithm outperform those obtained by other constructive heuristics in the literature for the problem, thus modifying substantially the state-of-the-art of efficient approximate procedures for the problem. In addition, the proposed algorithm even outperforms two of the best metaheuristics for many instances of the problem, using much lesser computation effort. The excellent performance of the proposal is also proved by the fact that the new heuristic found new best upper bounds for 35 of the 120 instances in Taillard’s benchmark.     

A biased random key genetic algorithm for the field technician scheduling problem

This paper addresses a problem that service companies often face: the field technician scheduling problem. The problem considers the assignment of a set of jobs or service tasks to a group of technicians. The tasks are in different locations within a city, with different time windows, priorities, and processing times. Technicians have different skills and working hours. The main objective is to maximize the sum of priority values associated with the tasks performed each day. Due to the complexity of this problem, constructive heuristics that explore specific characteristics of the problem are developed. A customized Biased Random Key Genetic Algorithm (BRKGA) is also proposed. Computational tests with 1040 instances are presented. The constructive heuristics outperformed a heuristic of the literature in 90% of the instances. In a comparative study with optimal solutions obtained for small-sized problems, the BRKGA reached 99% of the optimal values; for medium- and large-sized problems, the BRKGA provided solutions that are on average 3.6% below the upper bounds.     

Problem reduction heuristic for the 0-1 multidimensional knapsack problem

This paper introduces new problem-size reduction heuristics for the multidimensional knapsack problem. These heuristics are based on solving a relaxed version of the problem, using the dual variables to formulate a Lagrangian relaxation of the original problem, and then solving an estimated core problem to achieve a heuristic solution to the original problem. We demonstrate the performance of these heuristics as compared to legacy heuristics and two other problem reduction heuristics for the multi-dimensional knapsack problem. We discuss problems with existing test problems and discuss the use of an improved test problem generation approach. We use a competitive test to highlight the performance of our heuristics versus the legacy heuristic approaches. We also introduce the concept of computational versus competitive problem test data sets as a means to focus the empirical analysis of heuristic performance.     

Solving the feeder bus network design problem by genetic algorithms and ant colony optimization

This paper proposes the design and analysis of two metaheuristics, genetic algorithms and ant colony optimization, for solving the feeder bus network design problem. A study of how these proposed heuristics perform is carried out on several randomly generated test problems to evaluate their computational efficiency and the quality of solutions obtained by them. The results are also compared to those published in the literature. Computational experiments have shown that both heuristics are comparable to the state-of-the-art algorithms such as simulated annealing and tabu search.     

New approximate algorithms for the customer order scheduling problem with total completion time objective

In this paper, we study a customer order scheduling problem where a number of orders, composed of several product types, have to be scheduled on a set of parallel machines, each one capable to process a single product type. The objective is to minimise the sum of the completion times of the orders, which is related to the lead time perceived by the customer, and also to the minimisation of the work-in-process. This problem has been previously studied in the literature, and it is known to be NP-hard even for two product types. As a consequence, the interest lies on devising approximate procedures to obtain fast, good performing schedules. Among the different heuristics proposed for the problem, the ECT (Earliest Completion Time) heuristic by Leung et al. [6] has turned to be the most efficient constructive heuristic, yielding excellent results in a wide variety of settings. These authors also propose a tabu search procedure that constitutes the state-of-the-art metaheuristic for the problem. We propose a new constructive heuristic based on a look-ahead mechanism. The computational experience conducted shows that it clearly outperforms ECT, while having both heuristics the same computational complexity. Furthermore, we propose a greedy search algorithm using a specific neighbourhood that outperforms the existing tabu search procedure for different stopping criteria, both in terms of quality of solutions and of required CPU effort.     

An artificial neural network based heuristic for flow shop scheduling problems

The objective of this paper is to find a sequence of jobs in the flow shop to minimize makespan. A feed forward back propagation neural network is used to solve the problem. The network is trained with the optimal sequences of completely enumerated five, six and seven jobs, ten machine problem and this trained network is then used to solve the problem with greater number of jobs. The sequence obtained using artificial neural network (ANN) is given as the initial sequence to a heuristic proposed by Suliman and also to genetic algorithm (GA) as one of the sequences of the population for further improvement. The approaches are referred as ANN-Suliman heuristic and ANN-GA heuristic respectively. Makespan of the sequences obtained by these heuristics are compared with the makespan of the sequences obtained using the heuristic proposed by Nawaz, Enscore and Ham (NEH) and Suliman Heuristic initialized with Campbell Dudek and Smith (CDS) heuristic called as CDS-Suliman approach. It is found that the ANN-GA and ANN-Suliman heuristic approaches perform better than NEH and CDS-Suliman heuristics for the problems considered.