A new approximation algorithm for two-machine flow shop scheduling with transporter coordinate

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).

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

A best possible on-line algorithm for two-machine flow shop scheduling to minimize makespan

This paper addresses a multiobjective scheduling problem in the permutation flow shop. The objectives are to minimize makespan and total flow time. The proposed approach is based on the framework of memetic algorithm, which is known as a hybrid of genetic algorithm and local search. The local search procedure is an iterative process repeating neighbor generation, neighbor evaluation, and neighbor selection. We take a problem-specific heuristic for neighbor generation and propose several strategies for neighbor evaluation and neighbor selection. Archive injection (adding non-dominated solutions to the population) is another issue under investigation. We examine the effects of the proposed strategies through experiments using forty widely used problem instances with different scales. We also evaluate the proposed approach by comparing it with other twenty-six ones in terms of three performance metrics. Our approach outperforms all benchmarks and updates a large portion of the sets of best known non-dominated solutions for large-scale instances.

No-wait flow shop scheduling problem has important applications in industrial systems. Migrating birds optimization (MBO) algorithm is a new meta-heuristic inspired by the V flight formation of the migrating birds which is proven to be an effective energy saving formation. This paper proposes an enhanced migrating birds optimization (EMBO) algorithm for no-wait flow shop scheduling with total flow time criterion. Because MBO is a neighborhood-based search heuristic, the population is divided into multiple migrating birds in proposed EMBO in an attempt to avoid local optima. Three heuristics are used for initializing the population. An effective neighborhood structure is used for each loop of EMBO. Extensive computational experiments are carried out based on a set of well-known flow shop benchmark instances that are considered as no-wait flow shop instances. Computational results and comparisons show that the proposed EMBO algorithm performs significantly better than the existing ones for no-wait flow shop scheduling problem with total flow time criterion.

The distributed hybrid flowshop scheduling (DHFS) problem, as one of the typical scheduling problems, has been researched in both academic and industrial fields during recent years. Consiering the DHFS with fuzzy processing time and setup time constraints, we develop an improved version of BSO, named IBSO. The objective is to minimize the maximize fuzzy completion time among all the factories. First, each solution is represented by a two-dimensional vectors. The two realistic constraints, i.e., the fuzzy processing time under uncertain enviornment and the setup time, make the problem close to the reality. Then, a novel constructive heuristic based on the Nawaz-Enscore-Ham (NEH) method, called distributed NEH, is proposed. Several local search heuristics considering the problem features and the objective are developed to enhance the local search abilities. Moreover a SA-based acceptance criterion is embeded to enhance the exploration abilities. Experimental results verify that the proposed algorithm is efficient and effective for solving the considered DHFS problems in comparison with other recently published efficient algorithms.

An ant colony optimization based algorithm for permutation flow shop scheduling was proposed.The key point of this algorithm is to integrate NEH heuristics with ant colony optimization.The proposed algorithm was tested on scheduling problem benchmarks.Theoretical analysis and experimental results show its effectiveness.

A permutation flowshop scheduling problem of optimizing the makespan and the total flow time, which can be expressed as Fm|prum|(C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> , ΣC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ), is considered in this paper. An improved multi-objective memetic algorithm (IMOMA) is proposed due to the NP-hardness of the problem. In order to effectively trade-off between two objectives, we propose a NEH and LR heuristic based initialization strategy and a powerful local search strategy, in the searching framework of memetic algorithm. Finally, we perform computational experiments by solving ten largest scale instances of Taillard benchmarks, with 500 jobs and 20 machines. The results demonstrate that the proposed IMOMA outperforms the NEHFF heuristic and two state-of-the-art evolutionary multi-objective algorithms, NSGA-II and MOEA/D with respect to convergence and diversity.

The estimation of distribution algorithm (EDA) has recently emerged as a promising alternative to traditional evolutionary algorithms for solving combinatorial optimisation problems. This paper presents a novel two-phase simulation-based EDA (TPSB-EDA) for minimising the makespan of a hybrid flow shop under stochastic processing times. To address the stochastic scheduling problem efficiently, the proposed TPSB-EDA incorporates a two-phase simulation model to estimate the performance of candidate solutions. In this model, an optimal back propagation network is firstly applied to identify a set of roughly good solutions, and then the selected solutions are further evaluated by a discrete-event simulation algorithm. Moreover, an annealing selection mechanism (ASM) is adopted to preserve the population diversity of EDA. Different from the selection operators of common EDAs, the ASM uses Boltzmann probability in the annealing algorithm to select part of population to establish the probabilistic model. Computation results indicate that the TPSB-EDA provides good solutions in the aspects of solution quality and computational efficiency.

The permutation flow shop problem (PFSSP) is a well-known difficult combinatorial optimization problem. In this paper, we present a new hybrid optimization algorithm named SIGSA to solve the PFSSP. This algorithm is composed by the LRV rule, SA-based local search and IIS-based local search. First, to make GSA suitable for PFSSP, a new LRV rule based on random key is introduced to convert the continuous position in GSA to the discrete job permutation. Second, to enhance the searching capability, the SA-based local search is designed to help the algorithm to escape from local minimum. Then, the IIS-based local search is used for enhancing the individuals in GSA with a certain probability. Additionally, Comparison with other results in the literature shows that the SIGSA is an efficient and effective approach for the PFSSP.

Parallel shifting bottleneck algorithms for non-permutation flow shop scheduling

The algorithm developed by Chen, Glass, Potts and Strusevich (CGPS) is by far the best one in terms of the worst-case performance ratio for the three-machine flow shop scheduling (3FSS) with minimum makespan criterion. This paper focuses on the experimental analysis of the CGPS algorithm. Three simulation experiments are conducted to compare and evaluate its performance in terms of six evaluation measures. It is shown that the CGPS algorithm is not empirically preferred for the 3FSS with minimum makespan criterion.

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

As a new analogy paradigm of human learning process, reinforcement learning (RL) has become an emerging topic in computational intelligence (CI). The synergy between the RL and CI is an emerging way to develop efficient solution algorithms for solving complex combinatorial optimization (CO) problems like machine scheduling problem. In this paper, we proposed an efficient optimization algorithm based on Deep RL for solving permutation flow-shop scheduling problem (PFSP) to minimize the maximum completion time. Firstly, a new deep neural network (PFSPNet) is designed for the PFSP to achieve the end-to-end output without limitation of problem sizes. Secondly, an actor-critic method of RL is used to train the PFSPNet without depending on the collection of high-quality labelled data. Thirdly, an improvement strategy is designed to refine the solution provided by the PFSPNet. Simulation results and statistical comparison show that the proposed optimization algorithm based on deep RL can obtain better results than the existing heuristics in similar computational time for solving the PFSP.

This paper proposes a self-adaptive hybrid population-based incremental learning algorithm (SHPBIL) for the m-machine reentrant permutation flow-shop scheduling problem (MRPFSSP) with makespan criterion. At the initial phase of SHPBIL, the information entropy (IE) of the initial population and an Interchange-based search are utilized to guarantee a good distribution of the initial population in the solution space, and a training strategy is designed to help the probability matrix to accumulate information from the initial population. In SHPBIL's global exploration, the IE of the probability matrix at each generation is used to evaluate the evolutionary degree, and then the learning rate is adaptively adjusted according to the current value of IE, which is helpful in guiding the search to more promising regions. Moreover, a mutation mechanism for the probability model is developed to drive the search to quite different regions. In addition, to enhance the local exploitation ability of SHPBIL, a local search based on critical path is presented to execute the search in some narrow and promising search regions. Simulation experiments and comparisons demonstrate the effectiveness of the proposed SHPBIL.