A scatter search algorithm for the distributed permutation flowshop scheduling problem

The distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs. Distributed manufacturing is a common situation for large enterprises that compete in a globalized market. The problem has two dimensions: assigning jobs to factories and scheduling the jobs assigned to each factory. Despite being recently introduced, this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature. In this paper we present a scatter search (SS) method for this problem to optimize makespan. SS has seldom been explored for flowshop settings. In the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search. A comprehensive computational campaign including 10 existing algorithms, together with statistical analyses, shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin. Moreover all 720 known best solutions for this problem are improved.     

A comparison of local search methods for flow shop scheduling

Local search techniques are widely used to obtain approximate solutions to a variety of combinatorial optimization problems. Two important categories of local search methods are neighbourhood search and genetic algorithms. Commonly used neighbourhood search methods include descent, threshold accepting, simulated annealing and tabu search. In this paper, we present a computational study that compares these four neighbourhood search methods, a genetic algorithm, and a hybrid method in which descent is incorporated into the genetic algorithm. The performance of these six local search methods is evaluated on the problem of scheduling jobs in a permutation flow shop to minimize the total weighted completion time. Based on the results of extensive computational tests, simulated annealing is found to generate better quality solutions than the other neighborhood search methods. However, the results also indicate that the hybrid genetic descent algorithm is superior to simulated annealing.     

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.     

A hybrid genetic local search algorithm for the permutation flowshop scheduling problem

Traditionally, the permutation flowshop scheduling problem (PFSP) was with the criterion of minimizing makespan. The permutation flowshop scheduling problem to minimize the total flowtime has attracted more attention from researchers in recent years. In this paper, a hybrid genetic local search algorithm is proposed to solve this problem with each of both criteria. The proposed algorithm hybridizes the genetic algorithm and a novel local search scheme that combines two local search methods: the Insertion Search (IS) and the Insertion Search with Cut-and-Repair (ISCR). It employs the genetic algorithm to do the global search and two local search methods to do the local search. Two local search methods play different roles in the search process. The Insertion Search is responsible for searching a small neighborhood while the Insertion Search with Cut-and-Repair is responsible for searching a large neighborhood. Furthermore, the orthogonal-array-based crossover operator is designed to enhance the GA’s capability of intensification. The experimental results show the advantage of combining the two local search methods. The performance of the proposed hybrid genetic algorithm is very competitive. For the PFSP with the total flowtime criterion, it improved 66 out of the 90 current best solutions reported in the literature in short-term search and it also improved all the 20 current best solutions reported in the literature in long-term search. For the PFSP with the makespan criterion, the proposed algorithm also outperforms the other three methods recently reported in the literature.     

An Application of a Multi-Objective Tabu Search Algorithm to a Bicriteria Flowshop Problem

This paper proposes a new tabu search algorithm for multi-objective combinatorial problems with the goal of obtaining a good approximation of the Pareto-optimal or efficient solutions. The algorithm works with several paths of solutions in parallel, each with its own tabu list, and the Pareto dominance concept is used to select solutions from the neighborhoods. In this way we obtain at each step a set of local nondominated points. The dispersion of points is achieved by a clustering procedure that groups together close points of this set and then selects the centroids of the clusters as search directions. A nice feature of this multi-objective algorithm is that it introduces only one additional parameter, namely, the number of paths. The algorithm is applied to the permutation flowshop scheduling problem in order to minimize the criteria of makespan and maximum tardiness. For instances involving two machines, the performance of the algorithm is tested against a Branch-and-Bound algorithm proposed in the literature, and for more than two machines it is compared with that of a tabu search algorithm and a genetic local search algorithm, both from the literature. Computational results show that the heuristic yields a better approximation than these algorithms.     

A proposal for a hybrid meta-strategy for combinatorial optimization problems

In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.     

Scheduling coupled-operation jobs with exact time-lags

Scheduling coupled-operation jobs with exact time-lags on a single machine has a wide range of applications. In that problem, each job consists of two operations with given processing times, which should be scheduled on a single machine observing a given time-lag. The general case of the problem with arbitrary processing times of operations and arbitrary time lags is known to be NP-hard in the strong sense and the problem remains NP-hard for many special cases. In order to develop a local search algorithm for the problem, we first explore two possible approaches for representing feasible solutions and their neighborhoods based on maintaining a permutation of first operations of the jobs or maintaining a full permutation of all operations. The first representation appears to be unpromising since, as we prove, the problem of finding an optimal sequence of second operations for a fixed sequence of first operations is NP-hard in the strong sense even in the case of unit processing times. We elaborate the second approach by developing a tabu search heuristic based on efficient job re-insertion. Empirical evaluation demonstrates superiority of the developed algorithm in comparison with the earlier published algorithms.     

A permutation flow-shop scheduling problem with convex models of operation processing times

The paper is an extension of the classical permutation flow-shop scheduling problem to the case where some of the job operation processing times are convex decreasing functions of the amounts of resources (e.g., financial outlay, energy, raw material) allocated to the operations (or machines on which they are performed). Some precedence constraints among the jobs are given. For this extended permutation flow-shop problem, the objective is to find a processing order of the jobs (which will be the same on each machine) and an allocation of a constrained resource so as to minimize the duration required to complete all jobs (i.e., the makespan). A computational complexity analysis of the problem shows that the problem is NP-hard. An analysis of the structure of the optimal solutions provides some elimination properties, which are exploited in a branch-and-bound solution scheme. Three approximate algorithms, together with the results of some computational experiments conducted to test the effectiveness of the algorithms, are also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

In this paper, a particle swarm optimization algorithm (PSO) is presented to solve the permutation flowshop sequencing problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. For this purpose, a heuristic rule called the smallest position value (SPV) borrowed from the random key representation of Bean [J.C. Bean, Genetic algorithm and random keys for sequencing and optimization, ORSA Journal of Computing 6(2) (1994) 154–160] was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems. In addition, a very efficient local search, called variable neighborhood search (VNS), was embedded in the PSO algorithm to solve the well known benchmark suites in the literature. The PSO algorithm was applied to both the 90 benchmark instances provided by Taillard [E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research, 64 (1993) 278–285], and the 14,000 random, narrow random and structured benchmark instances provided by Watson et al. [J.P. Watson, L. Barbulescu, L.D. Whitley, A.E. Howe, Contrasting structured and random permutation flowshop scheduling problems: Search space topology and algorithm performance, ORSA Journal of Computing 14(2) (2002) 98–123]. For makespan criterion, the solution quality was evaluated according to the best known solutions provided either by Taillard, or Watson et al. The total flowtime criterion was evaluated with the best known solutions provided by Liu and Reeves [J. Liu, C.R. Reeves, Constructive and composite heuristic solutions to the P∥∑C_i scheduling problem, European Journal of Operational Research 132 (2001) 439–452], and Rajendran and Ziegler [C. Rajendran, H. Ziegler, Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs, European Journal of Operational Research, 155(2) (2004) 426–438]. For the total flowtime criterion, 57 out of the 90 best known solutions reported by Liu and Reeves, and Rajendran and Ziegler were improved whereas for the makespan criterion, 195 out of the 800 best known solutions for the random and narrow random problems reported by Watson et al. were improved by the VNS version of the PSO algorithm.     

A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution. Additionally, a strategy based on subpopulations is implemented to avoid the direct computation of descent directions for the entire population. The evaluation of the proposed algorithm is performed on a set of benchmark test problems allowing a comparison with the most representative state-of-the-art multiobjective algorithms. The results show that the proposed approach is highly competitive in terms of the quality of non-dominated solutions and robustness.     

Local search algorithms for the min-max loop layout problem

In the min-max loop layout problem, machines are to be arranged around a loop of conveyor belt. The ordering of the machines dictates the number of circuits of the conveyor belt required to manufacture each of several products. The goal is to find an ordering of the machines that minimises the maximum number of circuits required for the manufacture of any of the products. Since the problem is strongly NP-hard, the study of heuristic methods is of interest. This paper proposes iterated descent and tabu search algorithms, and a randomised insertion algorithm. Results of extensive computational tests show that all of our algorithms outperform a previously known algorithm that applies a greedy heuristic to the solution of a linear programming relaxation. The best quality solutions are obtained with iterated descent. This adds further evidence to the belief that iterated descent can produce high quality solutions to a variety of combinatorial optimisation problems. Moreover, unlike some other local search algorithms, iterated descent does not require much tuning in order to be competitive.     

Optimal location with equitable loads

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn ³) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented.     

Minimizing energy consumption and makespan in a two-machine flowshop scheduling problem

Energy consumption has become a key concern for manufacturing sector because of negative environmental impact of operations. We develop constructive heuristics and multi-objective genetic algorithms (MOGA) for a two-machine sequence-dependent permutation flowshop problem to address the trade-off between energy consumption as a measure of sustainability and makespan as a measure of service level. We leverage the variable speed of operations to develop energy-efficient schedules that minimize total energy consumption and makespan. As minimization of energy consumption and minimization of makespan are conflicting objectives, the solutions to this problem constitute a Pareto frontier. We compare the performance of constructive heuristics and MOGAs with CPLEX and random search in a wide range of problem instances. The results show that MOGAs hybridized with constructive heuristics outperform regular MOGA and heuristics alone in terms of quality and cardinality of Pareto frontier. We provide production planners with new and scalable solution techniques that will enable them to make informed decisions considering energy consumption together with service objectives in shop floor scheduling.     

Total completion time with makespan constraint in no-wait flowshops with setup times

The m-machine no-wait flowshop scheduling problem with the objective of minimizing total completion time subject to the constraint that the makespan value is not greater than a certain value is addressed in this paper. Setup times are considered non-zero values, and thus, setup times are treated as separate from processing times. Several recent algorithms, an insertion algorithm, two genetic algorithms, three simulated annealing algorithms, two cloud theory-based simulated annealing algorithms, and a differential evolution algorithm are adapted and proposed for the problem. An extensive computational analysis has been conducted for the evaluation of the proposed algorithms. The computational analysis indicates that one of the nine proposed algorithms, one of the simulated annealing algorithms (ISA-2), performs much better than the others under the same computational time. Moreover, the analysis indicates that the algorithm ISA-2 performs significantly better than the earlier existing best algorithm. Specifically, the best performing algorithm, ISA-2, proposed in this paper reduces the error of the existing best algorithm in the literature by at least 90% under the same computational time. All the results have been statistically tested.     

A branch-and-bound-based local search method for the flow shop problem

It is well-known that exact branch and bound methods can only solve small or moderately sized ????-hard combinatorial optimization problems. In this paper, we address the issue of embedding an approximate branch and bound algorithm into a local search framework. The resulting heuristic has been applied to the problem of finding a minimum makespan in the permutation flow shop problem. Computational experiments carried out on a large set of benchmark problems show that the proposed method consistently yields optimal or near-optimal solutions for instances with up to 200 jobs and 10 machines. In particular, for 19 instances, the heuristic produces solutions that outperform the best known ones.     

A new dominance rule to minimize total weighted tardiness with unequal release dates

We present a new dominance rule by considering the time-dependent orderings between each pair of jobs for the single machine total weighted tardiness problem with release dates. The proposed dominance rule provides a sufficient condition for local optimality. Therefore, if any sequence violates the dominance rule then switching the violating jobs either lowers the total weighted tardiness or leaves it unchanged. We introduce an algorithm based on the dominance rule, which is compared to a number of competing heuristics for a set of randomly generated problems. Our computational results indicate that the proposed algorithm dominates the competing algorithms in all runs, therefore it can improve the upper bounding scheme in any enumerative algorithm. The proposed time-dependent local dominance rule is also implemented in two local search algorithms to guide these algorithms to the areas that will most likely contain the good solutions.     

A composite algorithm for multiprocessor scheduling

A composite algorithm is developed for the classical problem of scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. The algorithm at first obtains a family of initial partial solutions and combines these partial solutions until a feasible solution is generated. Then local search procedures are used for improving the solution. The effectiveness of this approach is evaluated through extensive computational comparisons with recent improvement heuristics for different classes of benchmark instances.     

Tabu search and GRASP for the maximum diversity problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naïve ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. The constructive method can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.     

An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives

Iterated Greedy (IG) algorithms are based on a very simple principle, are easy to implement and can show excellent performance. In this paper, we propose two new IG algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines, a characteristic that is often found in industrial settings. The first IG algorithm is a straightforward adaption of the IG principle, while the second incorporates a simple descent local search. Furthermore, we consider two different optimization objectives, the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness. Extensive experiments and statistical analyses demonstrate that, despite their simplicity, the IG algorithms are new state-of-the-art methods for both objectives.     

Cooperative metaheuristics for the permutation flowshop scheduling problem

In this work, we propose cooperative metaheuristic methods for the permutation flowshop scheduling problem considering two objectives separately: total tardiness and makespan. We use the island model where each island runs an instance of the algorithm and communications start when the islands have reached certain level of evolution, that is, communication is not allowed from the beginning of the execution. Subsequent ones occur when new better solutions are found. We carry out an exhaustive comparison of the cooperative methods against the sequential counterparts running in completely comparable scenarios. Results have been carefully analysed by means of statistical procedures and we can conclude that the cooperative methods yield much better results than the sequential algorithms and state-of-the-art methods running in the same number of processors but without communications. The proposed cooperative schemes are easy to apply to other algorithms and problems.