An estimation of distribution algorithm for hybrid flow shop scheduling under stochastic processing times

This paper deals with job shop scheduling with stochastic processing time in normal distribution. The extended Giffler-Thompson procedure in the stochastic context is first presented and some operations on the stochastic processing time are defined. A new permutation-based representation method is then proposed, in which the substring related to each machine is a permutation. The conflict among the competing operations is eliminated by giving priority to the operation with the minimum gene value in the same permutation. An efficient genetic algorithm is proposed to minimize the maximum completion time of jobs. The proposed algorithm is tested on a set of benchmark problems and compared when it is endowed with different crossover and mutation. The computational results demonstrate the effectiveness of the proposed genetic algorithm.

This paper presents a simulation optimization with genetic algorithm and optimal computing budget allocation for semiconductor back-end assembly scheduling problem to achieve minimal average order flow time. In particular, this research explores characteristics of hybrid flow shop scheduling problem in complicated identical and unrelated parallel machines, orders with specific product and demand scheduled with different release time, order split for parallel and merges for batch processing during manufacturing under product-machine dedication with stochastic processing times and sequence-dependent setup times. As this is a real-life stochastic event system and discrete simulation is usually the only resort for performance. Coupling genetic algorithms in simulation optimization as the solution space is large. Optimal computing budget allocation was used to reduce simulation budget usage while stochastic situation. Numerical result shows it is effective to improve performance better than practical heuristics and efficient to generate few replications which conquer the barriers utilize the advantages of simulation-based approach. This work can be as solution architecture for providing superior scheduling decision on allocation of orders and subsequent jobs to machines in a complex hybrid flow shop.

The layout positioning problem of facilities on a straight line is known as Single Row Facility Layout Problem (SRFLP). The objective of SRFLP, categorized as NP-Complete problem, is to arrange the layout such that the sum of distances between all facilities’ pairs can be minimized. Extended Artificial Chromosome Genetic Algorithm (eACGA) is a promising algorithm that has been proposed recently. eACGA extends the probabilistic model in Estimation of Distribution Algorithms (EDAs) and then hybridize it with Genetic Algorithms (GAs). eACGA is proven to produce an excellent solution for scheduling problem. In this paper, we modify the eACGA to solve SRFLP. Computational results on benchmark problems show the effectiveness of eACGA for solving SRFLP. Key Words: single row facility layout, estimation distribution algorithm, genetic algorithm.

In this paper, we have proposed a hybrid approach combining Artificial Bee Colony Algorithm (ABC) with Estimation of Distribution Algorithm (EDA) for Minimum Weight Dominating Set (MWDS) problem. By combining ABC algorithm with EDA, we are able to guide the search process toward more promising solutions in comparison with any of the two constituent approaches. We have also used a solution improvement method which further trims down the solution in order to minimize its fitness value. Computational results on standard benchmark instances of the MWDS problem show that the hybrid ABC-EDA performs as good as or better than existing approaches in terms of solution quality on most of the instances.

Summary Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty-quantification study, reservoir models must be updated using the observed response from the reservoir by a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir. However, this requires multiple expensive multiphase-flow simulations. Thus, uncertainty-quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory because of slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by estimation-of-distribution algorithms (EDAs). EDAs are population-based algorithms that use models to estimate the probability distribution of promising solutions and then generate new candidate solutions. This paper explores the application of EDAs, including univariate and multivariate models. We discuss two histogram-based univariate models and one multivariate model, the Bayesian optimization algorithm (BOA), which employs Bayesian networks for modeling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDAs can accelerate the search process while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian network allows the BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. The BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir-uncertainty quantification. We demonstrate the effectiveness of EDA by applying the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well-controlled case. Results show better estimation of uncertainty when compared with some other traditional population-based algorithms.

The aim of this chapter is to propose a new heuristic for Machine Part Cell Formation problem. The Machine Part Cell Formation problem is the important step in the design of a Cellular Manufacturing system. The objective is to identify part families and machine groups and consequently to form manufacturing cells with respect to minimizing the number of exceptional elements and maximizing the grouping efficacy. The proposed algorithm is based on a hybrid algorithm that combines a Variable Neighborhood Search heuristic with the Estimation of Distribution Algorithm. Computational results are presented and show that this approach is competitive and even outperforms existing solution procedures proposed in the literature.

This paper investigates the multistage hybrid flow shop (HFS) scheduling problems using the new bat algorithm. A HFS is the generalisation of flowshop with multiple machines. HFS is one of the important scheduling problems that represent many industries like iron and steel, chemical, textile and ceramic industries. The HFS scheduling problems have been proved to be NP-hard. A recently developed bat meta-heuristic algorithm is proposed to solve the HFS problems. The proposed algorithm is validated with a well-chosen set of benchmark problems in the literature. Computational results indicate that the proposed bat algorithm is more efficient than the genetic algorithm and particle swarm optimisation.

Flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are multiobjective and are subjected to a wide range of uncertainties. Although evolutionary algorithms are commonly used to solve multiobjective and stochastic problems, very few approaches combine simultaneously these two aspects. In the paper the multiobjective flow shop scheduling problem is modeled with the stochastic processing time and the machine breakdown. A mathematical scheme is designed for the largest flow of time and the largest delay time. A hybrid multiobjective genetic algorithm is proposed to solve the optimization problems iteratively on uncertain condition. The results of simulation experiments are shown that the algorithm can provide a good performance for the flow shop scheduling problems on the uncertain condition.

ABSTRACTIn the context of Industry 4.0, a production line must be flexible and adaptable to stochastic or real‐world environments. As a result, the assembly line balancing (ALB) problem involves managing uncertainty or stochasticity. Several methods have been proposed, including stochastic mathematical programming models and simulations. However, programming models can only incorporate a few sources of uncertainty that result in impractical or unfeasible solutions to implement due to overlooked complexities, while simulation is only used to test solutions from deterministic approaches or adjust parameters without maintaining their optimum value. The proposed methodology uses a deterministic mathematical model to minimize the cycle time, followed by the simulation to measure the impact of selected sources of uncertainty on the cycle time. Finally, the optimum value of the stochastic parameters is computed using simulation‐based optimization to maintain the average cycle time close to the deterministic one. A real‐life assembly line balancing problem for a motorcycle manufacturing company is solved to test the proposed methodology. The sources of uncertainty are the tasks' stochastic processing times, inter‐arrival time, the number of workers in each station, and the speed of the material handling system. Results show that the average cycle time is above 2.7% from the deterministic value computed by the programming model when the inter‐arrival time is set to 270 60 s; the processing times are allowed to increase or decrease by 3 s; the material handling system's speed is 1.5 m/s; and the number of workers in cells is between 4 and 6, with a speed of 2 m/s. The reader can download the source code and the simulation model to apply the methodology to other instances.

In this paper, we consider a variant of vehicle routing problem with multiple trip and time windows. In this alternative problem, we think about the scheduling of trucks to a number of customers in the presence of fixed fleet and time windows constraints. This type of problem can be described as determining a number of vehicle trips minimising total travelled distance complying with the time windows and the multiple use of vehicles. We call this problem a multiple trips fixed fleet vehicle routing problems with time windows (MTFFVRPTW). To solve this variant, a new hybrid evolutionary algorithm for transport optimisation problems, called estimation of distribution algorithm with local search is used. The proposed algorithm integrates a double structure of distribution technique, which is used to introduce the variables dependency. To evaluate our approach we provide a number of experimentation to a modified Solomon's instances for the case of multiple trips. The results show that the hybrid proposed algorithm offer a good quality solution in the term of objective functions, also in the running time.

Shop scheduling problems are known to be notoriously intractable, both in theory and practice. In this paper we give a randomized approximation algorithm for flow shop scheduling where the number of machines is part of the input problem. Our algorithm has a multiplicative factor of 2(1 + δ) and an additive term of O(mln(m+ n)pmax)/δ2).

In this study, we propose a reinforcement learning (RL) approach for minimizing the number of work overload situations in the mixed model sequencing (MMS) problem with stochastic processing times. The learning environment simulates stochastic processing times and penalizes work overloads with negative rewards. To account for the stochastic component of the problem, we implement a state representation that specifies whether work overloads will occur if the processing times are equal to their respective 25%, 50%, and 75% probability quantiles. Thereby, the RL agent is guided toward minimizing the number of overload situations while being provided with statistical information about how fluctuations in processing times affect the solution quality. To the best of our knowledge, this study is the first to consider the stochastic problem variation with a minimization of overload situations.

As a typical model-based evolutionary algorithm, estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied in global optimization. However, the commonly used Gaussian EDA (GEDA) usually suffers from premature convergence, which severely limits its search efficiency. This paper first systematically analyzes the reasons for the deficiency of traditional GEDA, then tries to enhance its performance by exploiting the evolution direction, and finally develops a new GEDA variant named EDA2. Instead of only utilizing some good solutions produced in the current generation to estimate the Gaussian model, EDA2 preserves a certain number of high-quality solutions generated in the previous generations into an archive and employs these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model, which in turn can guide EDA2 toward more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA2 since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA2, we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs. The experimental results demonstrate that EDA2 is efficient and competitive.

The current work contributes to stochastic hybrid flow shop scheduling. After a thorough literature analysis, it is firstly evident that works on stochastic flow shop scheduling are still limited in number; moreover, they often rely on simplifying assumptions; eventually, they may lack in a full viability for industrial application of the proposed models or algorithms. Considering these limitations, the present work proposes a scheduling framework based on Discrete Event Simulation and on Genetic Algorithms. The work stems from a previously published work, therefore, contributes by identifying some inconsistencies in the original algorithm in the so called “limit cases”. Overall, the paper proposes an alternative fitness function to avoid the generation of such inconsistencies; besides, it considers a realistic probability distribution to describe the stochastic processing times for robust scheduling of a hybrid flow shop. The end purpose is to move towards a viable application of optimization algorithms in industrial environments.

A hybrid flow shop (HFS) scheduling is characterized of “[Formula: see text]” jobs “[Formula: see text]” machines with “[Formula: see text]” stages by unidirectional flow of work with a variety of jobs being processed sequentially in a single-pass manner. The HFS scheduling problem is known to be strongly NP-hard in nature. Hence, the essential complexity of the problem necessitates the application of meta-heuristics to solve HFS scheduling problems. A population-based genetic algorithm (GA) and a simulated annealing (SA) algorithm have been proposed to solve the multi-stage HFS scheduling problem with missing operations to minimize the mean tardiness. The computational results observed that the GA is efficient in finding out good quality solutions.