Application of improved immune algorithm in flow shop scheduling

Scheduling is an important task in manufacturing. It involves assigning jobs to machines in a particular order so as to meet the manufacturing target. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA), which is a new evolutionary algorithm, can be used to tackle complex scheduling problems and produce a reasonable manufacturing schedule within an acceptable time. This paper describes an IA approach to the scheduling of a flexible flow shop for PCB manufacturing. An overview of the flexible flow shop problem and the basic notions of an IA are first presented. Subsequently, the details of an IA approach are described and implemented. A case study of a flexible flow shop for the manufacture of PCBs for communication equipment was then conducted. The results obtained are compared with those computed by genetic algorithms (GAs), which are well-known evolutionary algorithms. From the case study, it was established that IAs outperformed GAs. The details of the case study as well as the comparative study are described.

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems

As an emerging novel evolutionary technique, the immune algorithm has gained a lot of attention and wide applications in various fields of engineering and management. To our knowledge, this paper first considers the application of immune algorithm for the classic permutation flow shop scheduling problem. We present a hybrid heuristic combining immune algorithm and simulated annealing for the n-job, m-machine permutation flow shop scheduling problem to minimize makespan and total flow time. A heuristically directed population-based construction approach in the immune algorithm and a forward/backward shift neighborhood search heuristic in the simulated annealing of the proposed method is utilized to explore the search process for better schedules of jobs as well to speed up the convergence speed of the proposed algorithm. The proposed method is tested with Taillard’s flow shop scheduling benchmark instances for different problems with job sizes varying from 20 to 500. The computational results demonstrate that the proposed heuristic is very competitive with the state-of-the-art procedures in terms of both solution quality and computational times.

A lot streaming based flow shop scheduling problem using simulated annealing algorithm

To study a scheduling problem of flexible flow shop, where at least one production stage is made up of unrelated parallel machines, and setup times are sequence- and machine-dependent. The objective is to find a schedule that minimizes the makespan and the number of tardy jobs in a static scheduling environment. For this problem, a 0-1 mixed integer programming is formulated. The model is, however, a combinatorial optimization problem which is too difficult to be solved for large-sized problems, and hence, a heuristic is developed to obtain good solutions in reasonable time. The heuristic has three phases. The first phase uses a constructive algorithm. It starts with the generation of the operating time representative for each operation. Then, it uses a dispatching rule or a simple flow shop makespan heuristic to determine an initial solution. The improvement algorithm based on shift moves or pairwise interchanges of jobs is applied to improve the solution in the second phase. After that, a metaheuristic is used to refine the solution in the final phase. Several well-known heuristics are tested in each phase. The performances of the heuristics are compared to one another based on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-sized problems. The computational results indicate that the Nawaz, Enscore, and Ham (NEH) algorithm is most suitable for determining the initial solution, the all-pairwise-interchange approach is good for improving the solution, and the simulated annealing algorithm is best metaheuristic for refining the solution.

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (Cmax). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.

In this paper, a network based formulation of a permutation flow shop problem is presented. Two nuances of flow shop problems with different levels of complexity are solved using different approaches to the linear programming formulation. Key flow shop parameters inclosing makespan of the flow shop problems were obtained without recourse to the traditional approach of using Gantt charts. The linear programming models of the flow shop problems considered were solved using LINGO 7.0. The present technique has been shown to be very effective and efficient.http://dx.doi.org/10.4314/njt.v34i2.11

Flow shop scheduling problems much studied by several researchers. One problem with scheduling is the tardiness. Total tardiness is the performance to minimize tardiness jobs. it is the right performance if there is a due date. This study proposes the Cross-Entropy Genetic Algorithm (CEGA) method to minimize the mean tardiness in the flow shop problem. In some literature, the CEGA algorithm is used in the case of minimizing the makespan. However, CEGA not used in the case of minimizing total tardiness. CEGA algorithm is a combination of the Cross-Entropy Algorithm which has a function to provide optimal sampling distribution and Genetic Algorithms that have functions to get new solutions. In some numeric experiments, the proposed algorithm provides better performance than some algorithms. For computing time, it is affected by the number of iterations. The higher the iteration, computing requires high time.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.

This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs’ completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NP-hard problem; a method based on decomposing the problem into sub-problem and solving each sub-problem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.

In this paper, we address the flowpath design issue of Automated Guided Vehicle Systems (AGVSs). In particular, we concentrate on the design of unidirectional flowpaths (i.e. vehicles are restricted to travel only in one direction along a given segment of the flowpath). We have developed intelligent heuristics — simulated annealing and tabu search algorithms for the design of unidirectional AGVSs. Different versions of simulated annealing and tabu search algorithms are implemented. Our extensive computational results indicate that both simulated annealing and tabu search yield solutions of adequate quality for all practical purposes. A tabu search implementation with the use of a frequency-based memory structure dominates all tested heuristics in terms of solution quality (i.e. percent deviation from optimality), with an impressive average performance over 45 test problems of less than 0.85% deviation from optimality.

This article examined the flow shop scheduling problem by considering the travel time between machines. The objective function of this problem was to provide a makespan. The Moth Flame Optimization (MFO) algorithm was proposed to solve the flow shop problem. The MFO experiment was carried out with a combination of iteration parameters and the population of the MFO algorithm to solve the flow shop scheduling problem. The computational results showed that MFO could produce a better solution than the actual scheduling method. Furthermore, the MFO Proposal Algorithm was able to reduce the makespan by up to 3%.

Flexible flow shop scheduling with uniform parallel machines

Minimizing the mean weighted absolute deviation from due dates in lot-streaming flow shop scheduling