A scatter search algorithm with a novel solution representation for flexible open shop scheduling: a multi-objective optimization

An efficient tabu search approach for the two-machine preemptive open shop scheduling problem

A genetic algorithm for scheduling open shops with sequence-dependent setup times

Scheduling two-machine preemptive open shops to minimize total completion time

This paper deals with the open shop scheduling problem (OSP) with makespan minimization. An exact dynamic programming algorithm is proposed for solving the OSP to optimality. This approach is applied to the OSP for the first time. Computational results show that the proposed algorithm is able to solve moderate benchmark instances.

Approximation algorithms for the multiprocessor open shop scheduling problem

It is known that in many real industrial settings, some setup is carried out before the process of a job. Usually, the magnitude of this setup depends on the order of two consecutive jobs. In this case, the setup is called sequence-dependent. This paper deals with open shop scheduling with sequence-dependent setup times to minimize the total completion time. The problem is formulated as an effective mixed integer linear programming model that best characterizes and solves to optimality small-sized instances of the problem under consideration. Since the electromagnetism-like metaheuristic (EM) is successfully applied to some NP-hard problems, we have been motivated to employ and assess the effectiveness of EM to solve the open shop with setup times. To further enhance EM, a local search engine in form of a fast and simple simulated annealing is incorporated. In order to evaluate the performance of the proposed algorithms, an experiment is designed where the proposed methods are compared against some algorithms in the literature. The related results are analyzed by statistical tools. The experimental results and statistical analyses demonstrate that the proposed model and EM are effective for the problem.

Flow shop and open shop scheduling with a critical machine and two operations per job

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence's benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

Binary relations or interactions among bio-entities, such as proteins, set up the essential part of any living biological system. Protein-protein interactions are usually structured in a graph data structure called "protein-protein interaction networks" (PPINs). Analysis of PPINs into complexes tries to lay out the significant knowledge needed to answer many unresolved questions, including how cells are organized and how proteins work. However, complex detection problems fall under the category of non-deterministic polynomial-time hard (NP-Hard) problems due to their computational complexity. To accommodate such combinatorial explosions, evolutionary algorithms (EAs) are proven effective alternatives to heuristics in solving NP-hard problems. The main aim of this study is to make a close examination of the performance of the EAs where modularity and modularity density are selected as two different objective functions. Topology-based modularity and topology-based modularity density are designed to examine the detection ability of the EAs and to compare their performance. To conduct the experiments, two yeast Saccharomyces cerevisiae PPINs are used and evaluated under nine evaluation metrics. The results reveal the potential impact of the topology-based modularity density to outperform the counterpart modularity functions in almost all evaluation metrics.

Objectives: Scheduling is an optimization problem in computer science and operation research in which ideal jobs are assigned to particular times. Nowadays, the problem is presented as an online problem, that is, each job is presented and the online algorithm needs to make a decision about the job before the next job is presented. Methods and Statstical Analysis: The proposed approach is used to solve the open job scheduling problem in which any job can be connected with the available machine. That was implemented in matlab to available best results with hybrid evolutionary algorithm. Findings: In this paper, a hybrid algorithm based on the particle swarm optimization is proposed, for flexible, open shop scheduling problem, to minimize the make-span. First an effective new approach using two decisions based on parallel priories dispatching rules is applied. Next we develop a hybridizing HPSO, that presents new components for updating velocity and position using evolutionary operators, with an adaptive neighbourhood procedure based on the insert-interchange fitness function, selection, mutation, crossover. Application/Improvements: The performance of the proposed a new hybrid algorithm is compared to other benchmark problems. Keywords: Dispatching Rules, Evolutionary Operators, Flexible Open Shop Problem, Local Search, Particle Swarm Optimization

In this chapter, we consider the open shop scheduling problem which can be described as follows. A set of n jobs J1, J2, . . . , Jn has to be processed on a set of m machines M1,M2, . . . , Mm. The processing of job Ji on machine Mj is denoted as operation (i, j), and the sequence in which the operations of a job are processed on the machines is arbitrary. Moreover, each machine can process at most one job at a time and each job can be processed on at most one machine at a time. Such an open shop environment arises in many industrial applications. For example, consider a large aircraft garage with specialized work-centers. An airplane may require repairs on its engine and electrical circuit system. These two tasks may be carried out in any order but it is not possible to do these tasks on the same plane simultaneously. Further applications of open shop scheduling problems in automobile repair, quality control centers, semiconductor manufacturing, teacher-class assignments, examination scheduling, and satellite communications are described by Kubiak et al. (1991), Liu and Bulfin (1987) and Prins (1994). For each job Ji, i = 1, 2, . . . , n, there may be given a release date ri ≥ 0 which is the earliest possible time when the first operation of this job may start, a weight wi and a due date di ≥ 0 by which the job should be completed. The processing time of operation (i, j) is denoted as tij. It is assumed that the processing times of all operations are assumed to be given in advance. Let Ci be the completion time of job Ji, i.e. the time when the last operation of this job is completed. Traditional optimization criteria are basically partitioned into two types: either

In this paper we study multiprocessor and open shop scheduling problems from several points of view. We explore a tight dependence of the polynomial solvability/intractability on the number of allowed preemptions. For an exhaustive interrelation, we address the geometry of problems by means of a novel graphical representation. We use the so-called preemption and machine-dependency graphs for preemptive multiprocessor and shop scheduling problems, respectively. In a natural manner, we call a scheduling problem acyclic if the corresponding graph is acyclic. There is a substantial interrelation between the structure of these graphs and the complexity of the problems. Acyclic scheduling problems are quite restrictive; at the same time, many of them still remain NP-hard. We believe that an exhaustive study of acyclic scheduling problems can lead to a better understanding and give a better insight of general scheduling problems.

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

Open shop scheduling problem is a typical NP problem with wide engineering background. It is of importance with respect of theory and application. In this paper, a mixed integer programming model was established with the objective to minimize the makespan based on the characteristics of the open shop, and a evolution genetic algorithm(EGA) was proposed. The representation of chromosome used in this paper was composed of two layers: operation layer and machine layer, which can be encoded and decoded easily. In generating initial population, DS/LTRP heuristic was used in order to improve the quality of the population. And particular crossover operation was proposed, which generated multiple offspring at a time, so that the efficiency of the algorithm can be well improved. At last, the proposed algorithm was tested on taillard benchmark, and numerical example showed good result.