Ant colony optimization algorithm to parallel machine scheduling problem with setups

This study extends the best hybrid ant colony optimization variant developed by Liao et al. (2014) for crisp unrelated parallel machine scheduling problems to solve fuzzy unrelated parallel machine scheduling problems in consideration of trapezoidal fuzzy processing times, trapezoidal fuzzy sequencing dependent setup times and trapezoidal fuzzy release times. The objective is to find the best schedule taking minimum fuzzy makespan in completing all jobs. In this study, fuzzy arithmetic is used to determine fuzzy completion times of jobs and defuzzification function is used to convert fuzzy numbers back to crisp numbers for ranking. Eight fuzzy ranking methods are tested to find the most feasible one to be employed in this study. The fuzzy arithmetic testing includes four different cases and each case with the following operations separately, i.e., addition, subtraction, multiplication and division, to investigate the spread of fuzziness as fuzzy numbers are subject to more and more number of operations. The effect of fuzzy ranking methods on hybrid ant colony optimization (hACO) is investigated. To prove the correctness of our methodology and coding, unrelated parallel machine scheduling with fuzzy numbers and crisp numbers are compared based on scheduling problems up to 15 machines and 200 jobs. Relative percentage deviation (RPD) is used to evaluate the performance of hACO in solving fuzzy unrelated parallel machine scheduling problems. A numerical study on large-scale scheduling problems up to 20 machines and 200 jobs is conducted to assess the performance of the hACO algorithm. For comparison, a discrete particle swarm optimization (dPSO) algorithm is implemented for fuzzy unrelated parallel machine scheduling problem as well. The results show that the hACO has better performance than dPSO not only in solution quality in terms of RPD value, but also in computational time.

The problem dealt with in this study has job sequence-dependent setup times under suitable machine constraints and due date constraints. The performance criterion for this problem is to minimize the sum of makespan and total tardiness. In the literature, an application of ABC algorithm for the problems which includes all the properties that we have dealt has not been discussed. Because there is no appropriate test data, a real-life data was collected from a factory. In this study, a new approach has been proposed for the solution with meta-heuristics of unrelated parallel machine scheduling problems which is a combinatorial problem. This new neighborhood approach provides different machine assignments for every candidate job sequences. This approach is used by integrating into ABC and GA. To evaluate the performances of the algorithms, the real-life problem was solved by using ABC and GA algorithms under similar conditions. It was found that all jobs can be completed in two shifts without the need for a third shift. Computational results show that ABC algorithm has better performance than GA.

This paper addresses the problem of makespan minimization on unrelated parallel machines with sequence dependent setup times. The symbiotic organisms search (SOS) algorithm is a new and popular global optimization technique that has received wide acceptance in recent years from researchers in continuous and discrete optimization domains. An improved SOS algorithm is developed to solve the parallel machine scheduling problem. Since the standard SOS algorithm was originally developed to solve continuous optimization problems, a new solution representation and decoding procedure is designed to make the SOS algorithm suitable for the unrelated parallel machine scheduling problem (UPMSP). Similarly, to enhance the solution quality of the SOS algorithm, an iterated local search strategy based on combining variable numbers of insertion and swap moves is incorporated into the SOS algorithm. More so, to further improve the SOS optimization speed and performance, the longest processing time first (LPT) rule is used to design a machine assignment heuristic that assigns processing machines to jobs based on the machine dynamic load-balancing mechanism. Subsequently, the machine assignment scheme is incorporated into SOS algorithms and used to solve the UPMSP. The performances of the proposed methods are evaluated by comparing their solutions with other existing techniques from the literature. A number of statistical tests were also conducted to determine the variations in performance for each of the techniques. The experimental results showed that the SOS with LPT (SOS-LPT) heuristic has the best performance compared to other tested method, which is closely followed by SOS algorithm, indicating that the two proposed algorithms’ solution approaches are reasonable and effective for solving large-scale UPMSPs.

This article addresses a challenging industrial problem known as the unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times. In UPMSP, we have a set of machines and a group of jobs. The goal is to find the optimal way to schedule jobs for execution by one of the several available machines. UPMSP has been classified as an NP-hard optimisation problem and, thus, cannot be solved by exact methods. Meta-heuristic algorithms are commonly used to find sub-optimal solutions. However, large-scale UPMSP instances pose a significant challenge to meta-heuristic algorithms. To effectively solve a large-scale UPMSP, this article introduces a two-stage evolutionary variable neighbourhood search (EVNS) methodology. The proposed EVNS integrates a variable neighbourhood search algorithm and an evolutionary descent framework in an adaptive manner. The proposed evolutionary framework is employed in the first stage. It uses a mix of crossover and mutation operators to generate diverse solutions. In the second stage, we propose an adaptive variable neighbourhood search to exploit the area around the solutions generated in the first stage. A dynamic strategy is developed to determine the switching time between these two stages. To guide the search towards promising areas, a diversity-based fitness function is proposed to explore different locations in the search landscape. We demonstrate the competitiveness of the proposed EVNS by presenting the computational results and comparisons on the 1640 UPMSP benchmark instances, which have been commonly used in the literature. The experiment results show that our EVNS obtains better results than the compared algorithms on several UPMSP instances.

Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times

The Unrelated Parallel Machines Scheduling Problem (UPMSP) with sequence-dependent setup times has been widely applied to cloud computing, edge computing and so on. When the setup times are ignored, UPMSP will be a NP problem. Moreover, when considering the sequence related setup times, UPMSP is difficult to solve, and this situation will be more serious in the case of high-dimensional. This work firstly select the maximum completion time as the optimization objective, which establishes a mathematical model of UPMSP with sequence-dependent setup times. In addition, an improved firefly algorithm with courtship learning is proposed. Finally, in order to provide an approximate solution in an acceptable time, the proposed algorithm is applied to solve the UPMSP with sequence-dependent setup times. The experimental results show that the proposed algorithm has competitive performance when dealing with UPMSP with sequence-dependent setup times.

Unrelated parallel machine scheduling problem with special controllable processing times and setups

PurposeThe purpose of this paper is to present a hybrid meta-heuristic based on genetic algorithms (GAs), simulated annealing, variable neighborhood descent and path relinking for solving the variant of the unrelated parallel machine scheduling problem considering sequence-dependent setup times.Design/methodology/approachThe authors carried out computational experiments on literature problem instances proposed by Vallada and Ruiz (2011) and Arnaout et al. (2010) to test the performance of the proposed meta-heuristic. The objective function adopted was makespan minimization, and the authors used relative deviation, average and population standard deviation as performance criteria.FindingsThe results indicate the competitivity of the proposed approach and its superiority in comparison with several other algorithms. In small instances proposed by Vallada and Ruiz (2011) and on small and large instances proposed by Arnaout et al. (2010), the proposed approach presented the best results in most tested problem instances.Practical implicationsIn small instances proposed by Vallada and Ruiz (2011) and on small and large instances proposed by Arnaout et al. (2010), the proposed approach presented the best results in most tested problem instances.Originality/valueThe proposed approach presented high-quality results, with an innovative hybridization of a GA and neighborhood search algorithms, tested in diverse instances of literature. Furthermore, the case study demonstrated that the proposed approach is recommended for solving real-world problems.

With the increasing demand for hazardous materials (hazmat) from enterprises, port chemical industrial parks face growing risks in hazardous material transportation. By using internal road network information of parks, this study investigates the hazmat vehicle routing problem (HVRP) under different road conditions, with a bi-objective of minimizing total transportation risk and cost. The two main innovations are as follows. First, according to the grid-like road conditions in parks, the research scope of transportation segments of hazmat vehicles is divided into straight segments and curved segments. Second, the potential affected area of an accident is defined as a type of geometric shape associated with a series of factors refined from transportation situations. Finally, the effectiveness of the proposed two-stage ant colony optimization (TSACO) algorithm is verified through one instance using field data from a real port chemical industry park, and twelve instances from the classical capacitated vehicle routing problem (CVRP) resource.

Approximate dynamic programming for an energy-efficient parallel machine scheduling problem

This paper addresses a bi-objective cutting parallel machine scheduling problem aiming to minimize the total makespan and total tardiness. This problem is inspired from a structural metal-cutting plant that combines identical and unrelated parallel machine scheduling problems. To formulate this complicated problem, a new mixed-integer programming (MIP) model is presented in consideration of total makespan and total tardiness. The machine-job-dependent processing times are considered along with the setup times, pickup times, different delivery times, and machine eligibility constraints. Owing to the complex characteristics of the problem, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII) with an embedded variable neighborhood structure strategy (VNSGAIII) is developed. A number of randomly generated datasets are used to test the performance of VNSGAIII in comparison with NSGAII, and NSGAIII on solving the engineering problem addressed herein. The experimental results demonstrate that the suggested VNSGAIII statistically outperforms the compared algorithms, especially in the distribution of Pareto solutions. The e-constrained method is implemented in the direct MIP model by CPLEX for comparison with the proposed evolutionary algorithms. The proposed algorithm performs efficiently when obtaining the Pareto solutions.

In this paper, we present a new Imperialist Competitive Algorithm (ICA) to solve a bi-objective unrelated parallel machine scheduling problem where setup times are sequence dependent.The objectives include mean completion time of jobs and mean squares of deviations from machines workload from their averages.The performance of the proposed ICA (PICA) method is examined using some randomly generated data and they are compared with three alternative methods including particle swarm optimization (PSO), original version of imperialist competitive algorithm (OICA) and genetic algorithm (GA) in terms of the objective function values.The preliminary results indicate that the proposed study outperforms other alternative methods.In addition, while OICA performs the worst as alternative solution strategy, PSO and GA seem to perform better.

This study deals with an unrelated parallel machine scheduling problem with additional resources (UPMR). That is one of the important sub-problems in the scheduling. UPMR consists of scheduling a set of jobs on unrelated machines. In addition to that, a number of one or more additional resources are needed. UPMR is very important and its importance comes from the wealth of applications; they are applicable to engineering and scientific situations and manufacturing systems such as industrial robots, nurses, machine operators, bus drivers, tools, assembly plant machines, fixtures, pallets, electricity, mechanics, dies, automated guided vehicles, fuel, and more. The importance also comes from the concern about the limitation of resources that are dedicated for the production process. Therefore, researchers and decision makers are still working on UPMR problem to get an optimum schedule for all instances which have not been obtained to this day. The optimum schedule is able to increase the profits and decrease the costs whilst satisfying the customers’ needs. This research aims to review and discuss studies related to unrelated parallel machines and additional resources. Overall, the review demonstrates the criticality of resolving the UPMR problem. Metaheuristic techniques exhibit significant effectiveness in generating results and surpassing other algorithms. Nevertheless, continued improvement is essential to satisfy the evolving requirements of UPMR, which are subject to operational changes based on customer demand.

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource