Some effective heuristics for no-wait flowshops with setup times to minimize total completion time

In this work, we consider a complex flowshop scheduling problem in which both no-wait and separate setup times are considered. The optimisation criterion is the minimisation of the total completion time. We propose an effective dominance rule for the four machine case that can also be used for m machines. Five simple and fast heuristics are proposed along with two easy to code stochastic local search methods, one of them being based on Iterated Local Search (ILS). An extensive computational evaluation is carried out with two sets of 5,400 instances. All seven methods are compared to two recent algorithms. The results, confirmed by thorough statistical analyses, show that the proposed methods are more effective and efficient when compared to the best existing algorithms in the literature for the considered problem.     

Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization

In this paper, a HGA (hybrid genetic algorithm) is proposed for permutation flowshop scheduling problems (PFSP) with total flowtime minimization, which are known to be NP-hard. One of the chromosomes in the initial population is constructed by a suitable heuristic and the others are yielded randomly. An artificial chromosome is generated by a weighted simple mining gene structure, with which a new crossover operator is presented. Additionally, two effective heuristics are adopted as local search to improve all generated chromosomes in each generation. The HGA is compared with one of the most effective heuristics and a recent meta-heuristic on 120 benchmark instances. Experimental results show that the HGA outperforms the other two algorithms for all cases. Furthermore, HGA obtains 115 best solutions for the benchmark instances, 92 of which are newly discovered.     

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.     

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.     

The minimum shift design problem

The min-Shift Design problem (MSD) is an important scheduling problem that needs to be solved in many industrial contexts. The issue is to find a minimum number of shifts and the number of employees to be assigned to these shifts in order to minimize the deviation from workforce requirements. Our research considers both theoretical and practical aspects of the min-Shift Design problem. This problem is closely related to the minimum edge-cost flow problem (MECF), a network flow variant that has many applications beyond shift scheduling. We show that MSD reduces to a special case of MECF and, exploiting this reduction, we prove a logarithmic hardness of approximation lower bound for MSD. On the basis of these results, we propose a hybrid heuristic for the problem, which relies on a greedy heuristic followed by a local search algorithm. The greedy part is based on the network flow analogy, and the local search algorithm makes use of multiple neighborhood relations. An experimental analysis on structured random instances shows that the hybrid heuristic clearly outperforms our previous commercial implementation. Furthermore, it highlights the respective merits of the composing heuristics for different performance parameters.     

A note on a greedy heuristic for flow-shop makespan minimization with no machine idle-time

We study makespan minimization on an m machine flowshop. No idle time is allowed between consecutive operations on each machine. We introduce an efficient (O(n²)) greedy algorithm, which is shown numerically to perform better than a recently published heuristic.     

Local search methods for the flowshop scheduling problem with flowtime minimization

Flowshop scheduling is a very active research area. This problem still attracts a considerable amount of interest despite the sheer amount of available results. Total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years. New best solutions have been found for common benchmarks at a rapid pace. However, these improvements many times come at the cost of sophisticated algorithms. Complex methods hinder potential applications and are difficult to extend to small problem variations. Replicability of results is also a challenge. In this paper, we examine simple and easy to implement methods that at the same time result in state-of-the-art performance. The first two proposed methods are based on the well known Iterated Local Search (ILS) and Iterated Greedy (IG) frameworks, which have been applied with great success to other flowshop problems. Additionally, we present extensions of these methods that work over populations, something that we refer to as population-based ILS (pILS) and population-based IG (pIGA), respectively. We calibrate the presented algorithms by means of the Design of Experiments (DOE) approach. Extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature. The results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective. Furthermore, we show that, despite their simplicity, the presented methods are able to improve 12 out of 120 best known solutions of Taillard’s flowshop benchmark with total flowtime criterion.     

EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.     

Group-shop scheduling with sequence-dependent set-up and transportation times

This paper considers a group-shop scheduling problem (GSSP) with sequence-dependent set-up times (SDSTs) and transportation times. The GSSP provides a general formulation including the job-shop and the open-shop scheduling problems. The consideration of set-up and transportation times is among the most realistic assumptions made in the field of scheduling. In this paper, we study the GSSP with transportation and anticipatory SDSTs, where jobs are released at different times and there are several transporters to carry jobs. The objective is to find a job schedule that minimizes the makespan, that is, the time at which all jobs are completed and transported to the warehouse (or to the customer). The problem is formulated as a disjunctive programming problem and then prepared in a form of mixed integer linear programming (MILP). Due to the non-deterministic polynomial-time hardness (NP-hardness) of the GSSP, large instances cannot be optimally solved in a reasonable amount of time. Therefore, a genetic algorithm (GA) hybridized with an active schedule generator is proposed to tackle large-sized instances. Both Baldwinian and Lamarckian versions of the proposed hybrid algorithm are then implemented and evaluated through computational experiments.     

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.     

Heuristic Techniques for Single Line Train Scheduling

Optimising a train schedule on a single line track is known to be NP-Hard with respect to the number of conflicts in the schedule. This makes it difficult to determine optimum solutions to real life problems in reasonable time and raises the need for good heuristic techniques. The heuristics applied and compared in this paper are a local search heuristic with an improved neighbourhood structure, genetic algorithms, tabu search and two hybrid algorithms. When no time constraints are enforced on solution time, the genetic and hybrid algorithms were within five percent of the optimal solution for at least ninety percent of the test problems.     

A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop

In this paper a new mixed-integer linear programming (MILP) model is proposed for the multi-processor open shop scheduling (MPOS) problems to minimize the makespan with considering independent setup time and sequence dependent removal time. A hybrid imperialist competitive algorithm (ICA) with genetic algorithm (GA) is presented to solve this problem. The parameters of the proposed algorithm are tuned by response surface methodology (RSM). The performance of the algorithm to solve small, medium and large sized instances of the problem is evaluated by introducing two performance metrics. The quality of obtained solutions is compared with that of the optimal solutions for small sized instances and with the lower bounds for medium sized instances. Also some computational results are presented for large sized instances.     

Job-shop local-search move evaluation without direct consideration of the criterion’s value

This article focuses on the evaluation of moves for the local search of the job-shop problem with the makespan criterion. We reason that the omnipresent ranking of moves according to their resulting value of a criterion function makes the local search unnecessarily myopic. Consequently, we introduce an alternative evaluation that relies on a surrogate quantity of the move’s potential, which is related to, but not strongly coupled with, the bare criterion. The approach is confirmed by empirical tests, where the proposed evaluator delivers a new upper bound on the well-known benchmark test yn2. The line of the argumentation also shows that by sacrificing accuracy the established makespan estimators unintentionally improve on the move evaluation in comparison to the exact makespan calculation, in contrast to the belief that the reliance on estimation degrades the optimization results.     

Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In a lot of cases, the combination of goals and resource exponentially increases search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multi-objective problem and to generate a set of diversified “optimal” solutions in order to help decision maker. We are interested in one of the problems occurring in the production workshops where the list of demands is split into firm (certain) jobs and predicted jobs. One wishes to maximize the produced quantity, while minimizing as well as possible the makespan and the production costs. Genetic algorithms are used to find the scheduling solution of the firm jobs because they are well adapted to the treatment of the multi-objective optimization problems. The predicted jobs will be inserted in the real solutions (given by genetic algorithms). The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the quality and robustness of our proposed approach.     

New solution methods for single machine bicriteria scheduling problem: Minimization of average flowtime and number of tardy jobs

We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer’s position, and the latter reflects the manufacturer’s perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.     

Global and Local Search Algorithms for Concave Cost Transshipment Problems

Traditionally, the minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Recently, some advanced local search algorithms have been developed that can directly solve concave cost bipartite network problems. However, they are not applicable to general transshipment problems. Moreover, the effectiveness of these modified local search algorithms for solving general concave cost transshipment problems is doubtful. In this research, we propose a global search algorithm for solving concave cost transshipment problems. Effecient methods for encoding, generating initial populations, selection, crossover and mutation are proposed, according to the problem characteristics. To evaluate the effectiveness of the proposed global search algorithm, four advanced local search algorithms based on the threshold accepting algorithm, the great deluge algorithm, and the tabu search algorithm, are also developed and are used for comparison purpose. To assist with the comparison of the proposed algorithms, a randomized network generator is designed to produce test problems. All the tests are performed on a personal computer. The results indicate that the proposed global search algorithm is more effective than the four advanced local algorithms, for solving concave cost transshipment problems.     

Iterated greedy local search methods for unrelated parallel machine scheduling

This work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m   parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machine problem. Similarly to most of the literature, this paper deals with the minimization of the maximum completion time of the jobs, commonly referred to as makespan (_Cmax)$(C_{\text{max}})$. Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time. Extensive computational campaigns show that these solutions are, most of the time, better than the current state-of-the-art methodologies by a statistically significant margin.     

A local search using solution fragments for the 2-machine bicriteria scheduling problem

In this work, we introduce a local search strategy for combinatorial optimization problems which explores neighborhoods obtained using fragments of current solutions. We apply the approach to the well-known -hard 2-machine bicriteria flowshop scheduling problem. Computational experiments using benchmark data show the approach to be effective when compared to other algorithms available for the problem.     

Hybrid Flow-Shop: a Memetic Algorithm Using Constraint-Based Scheduling for Efficient Search

The paper considers the hybrid flow-shop scheduling problem with multiprocessor tasks. Motivated by the computational complexity of the problem, we propose a memetic algorithm for this problem in the paper. We first describe the implementation details of a genetic algorithm, which is used in the memetic algorithm. We then propose a constraint programming based branch-and-bound algorithm to be employed as the local search engine of the memetic algorithm. Next, we present the new memetic algorithm. We lastly explain the computational experiments carried out to evaluate the performance of three algorithms (genetic algorithm, constraint programming based branch-and-bound algorithm, and memetic algorithm) in terms of both the quality of the solutions produced and the efficiency. These results demonstrate that the memetic algorithm produces better quality solutions and that it is very efficient.     

An Algorithm for the Job Shop Scheduling Problem based on Global Equilibrium Search Techniques

The job shop scheduling problem is considered, and an algorithm based on the global equilibrium search method is proposed for its solution. Computational experiments using well-known benchmark problems are presented. Several new upper bounds for these problems are obtained.Research partially supported by NSF and AirForce grants.