Estimation of distribution algorithm with path relinking for the blocking flow-shop scheduling problem

This article presents an effective estimation of distribution algorithm, named P-EDA, to solve the blocking flow-shop scheduling problem (BFSP) with the makespan criterion. In the P-EDA, a Nawaz–Enscore–Ham (NEH)-based heuristic and the random method are combined to generate the initial population. Based on several superior individuals provided by a modified linear rank selection, a probabilistic model is constructed to describe the probabilistic distribution of the promising solution space. The path relinking technique is incorporated into EDA to avoid blindness of the search and improve the convergence property. A modified referenced local search is designed to enhance the local exploitation. Moreover, a diversity-maintaining scheme is introduced into EDA to avoid deterioration of the population. Finally, the parameters of the proposed P-EDA are calibrated using a design of experiments approach. Simulation results and comparisons with some well-performing algorithms demonstrate the effectiveness of the P-EDA for solving BFSP.     

An effective estimation of distribution algorithm for the flexible job-shop scheduling problem with fuzzy processing time

Considering the fuzzy nature of the data in real-world scheduling, an effective estimation of distribution algorithm (EDA) is proposed to solve the flexible job-shop scheduling problem with fuzzy processing time. A probability model is presented to describe the probability distribution of the solution space. A mechanism is provided to update the probability model with the elite individuals. By sampling the probability model, new individuals can be generated among the search region with promising solutions. Moreover, a left-shift scheme is employed for improving schedule solution when idle time exists on the machine. In addition, some fuzzy number operations are used to calculate scheduling objective value. The influence of parameter setting is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Numerical testing results and comparisons with some existing algorithms are provided, which demonstrate the effectiveness of the proposed EDA.     

An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

This article proposes an extended continuous estimation of distribution algorithm (ECEDA) to solve the permutation flow-shop scheduling problem (PFSP). In ECEDA, to make a continuous estimation of distribution algorithm (EDA) suitable for the PFSP, the largest order value rule is applied to convert continuous vectors to discrete job permutations. A probabilistic model based on a mixed Gaussian and Cauchy distribution is built to maintain the exploration ability of the EDA. Two effective local search methods, i.e. revolver-based variable neighbourhood search and Hénon chaotic-based local search, are designed and incorporated into the EDA to enhance the local exploitation. The parameters of the proposed ECEDA are calibrated by means of a design of experiments approach. Simulation results and comparisons based on some benchmark instances show the efficiency of the proposed algorithm for solving the PFSP.     

基于多子种群和密度估计的高维多目标进化算法的冷轧负荷分配

提出一种基于多子种群和密度估计的高维多目标进化算法,通过生成参考向量来划分子种群,借助收敛性保持机制提高逼近帕累托前沿的程度.该算法通过计算个体与参考向量的欧式距离来评估个体密度,从而保持解集的多样性.数值仿真实验结果表明,该算法所得解集的收敛性和多样性明显优于对比算法.最后,使用该算法对冷轧负荷分配进行高维多目标优化...     

A modified teaching–learning-based optimisation algorithm for bi-objective re-entrant hybrid flowshop scheduling

In this paper, a modified teaching–learning-based optimisation (mTLBO) algorithm is proposed to solve the re-entrant hybrid flowshop scheduling problem (RHFSP) with the makespan and the total tardiness criteria. Based on the simple job-based representation, a novel decoding method named equivalent due date-based permutation schedule is proposed to transfer an individual to a feasible schedule. At each generation, a number of superior individuals are selected as the teachers by the Pareto-based ranking phase. To enhance the exploitation ability in the promising area, the insertion-based local search is embedded in the search framework as the training phase for the TLBO. Due to the characteristics of the permutation-based discrete optimisation, the linear order crossover operator and the swap operator are adopted to imitate the interactions among the individuals in both the teaching phase and the learning phase. To store the non-dominated solutions explored during the search process, an external archive is used and updated when necessary. The influence of the parameter setting on the mTLBO in solving the RHFSP is investigated, and numerical tests with some benchmarking instances are carried out. The comparative results show that the proposed mTLBO outperforms the existing algorithms significantly.     

基于速度交流的多种群多目标粒子群算法研究

为提高多目标优化算法的收敛精度和搜索性能,提出一种基于速度交流的多种群多目标粒子群算法。算法引入速度交流机制,将种群划分为多个子种群以实现速度信息共享,改善粒子单一搜索模式,提高算法的全局搜索能力。采用混沌映射优化惯性权重,提高粒子搜索遍历性和全局性,为降低算法在运行后期陷入局部最优Pareto前沿的可能性,对各个子种群执行不同的变异操作。将算法与NSGA-Ⅱ、SPEA2、Ab YSS、MOPSO、SMPSO和GWASF-GA先进多目标优化算法进行对比,实验结果表明:该算法得到的解集具有更好的收敛性和分布性。     

Minimizing makespan in a no-wait flowshop with two batch processing machines using estimation of distribution algorithm

This paper studies the problem of minimising makespan in a no-wait flowshop with two batch processing machines (comprised of a parallel batch processing machine and a serial batch processing machine), non-identical job sizes and unequal ready times. We propose a population-based evolutionary method named estimation of distribution algorithm (EDA). Firstly, the individuals in the population are coded into job sequences. Then, a probabilistic model is built to generate new population and an incremental learning method is developed to update the probabilistic model. Thirdly, the best-fit heuristic is used to group jobs into batches and a least idle/waiting time approach is proposed to sequence the batches on batch processing machines. In addition, some problem-dependent local search heuristics are incorporated into the EDA to further improve the searching quality. Computational simulation and comparisons with some existing algorithms demonstrate the effectiveness and robustness of the proposed algorithm. Furthermore, the effectiveness of embedding the local search method in the EDA is also evaluated.     

Solving the blocking flow shop scheduling problem with makespan using a modified fruit fly optimisation algorithm

The flow shop scheduling problem with blocking has important applications in a variety of industrial systems but is under-represented in the research literature. In this paper, a modified fruit fly optimisation (MFFO) algorithm is proposed to solve the above scheduling problem for makespan minimisation. The MFFO algorithm mainly contains three key operators. One is related to the initialisation scheme in which a problem-specific heuristic is adopted to generate an initial fruit fly swarm location with high quality. The second is concerned with the smell-based search in which a neighbourhood strategy is designed to generate a new location. To further enhance the exploitation of the proposed algorithm considered, a speed-up insert-neighbourhood-based local search is applied with a probability. Finally, the last is for the vision-based search in which an update criterion is proposed to induce the fruit fly into a better searching space. The simulation experimental results demonstrated the efficiency of the proposed algorithm, in spite of its simple structure, in comparison with a state-of-the-art algorithm. Moreover, new best solutions for Taillard’s instances are reported for this problem, which can be used as a basis of comparison in future studies.     

An artificial immune network for multiobjective optimization problems

Multiobjective optimization is an important problem of great complexity and evolutionary algorithms have been established as a dominant approach in the field. This article suggests a method for approximating the Pareto front of a given function based on artificial immune networks. The proposed method uses cloning and mutation on a population of antibodies to create local subsets of the Pareto front. Elements of these local fronts are combined, in a way that maximizes diversity, to form the complete Pareto front of the function. The method is tested on a number of well-known benchmark problems, as well as an engineering problem. Its performance is compared against state-of-the-art algorithms, yielding promising results.     

A hybrid approach combining modified artificial bee colony and cuckoo search algorithms for multi-objective cloud manufacturing service composition

This paper proposes a multi-objective hybrid artificial bee colony (MOHABC) algorithm for service composition and optimal selection (SCOS) in cloud manufacturing, in which both the quality of service and the energy consumption are considered from the perspectives of economy and environment that are two pillars of sustainable manufacturing. The MOHABC uses the concept of Pareto dominance to direct the searching of a bee swarm, and maintains non-dominated solution found in an external archive. In order to achieve good distribution of solutions along the Pareto front, cuckoo search with Levy flight is introduced in the employed bee search to maintain diversity of population. Furthermore, to ensure the balance of exploitation and exploration capabilities for MOHABC, the comprehensive learning strategy is designed in the onlooker search so that every bee learns from the external archive elite, itself and other onlookers. Experiments are carried out to verify the effect of the improvement strategies and parameters’ impacts on the proposed algorithm and comparative study of the MOHABC with typical multi-objective algorithms for SCOS problems are addressed. The results show that the proposed approach obtains very promising solutions that significantly surpass the other considered algorithms.     

An innovative artificial bee colony algorithm and its application to a practical intercell scheduling problem

In this article, an innovative artificial bee colony (IABC) algorithm is proposed, which incorporates two mechanisms. On the one hand, to provide the evolutionary process with a higher starting level, genetic programming (GP) is used to generate heuristic rules by exploiting the elements that constitute the problem. On the other hand, to achieve a better balance between exploration and exploitation, a leading mechanism is proposed to attract individuals towards a promising region. To evaluate the performance of IABC in solving practical and complex problems, it is applied to the intercell scheduling problem with limited transportation capacity. It is observed that the GP-generated rules incorporate the elements of the most competing human-designed rules, and they are more effective than the human-designed ones. Regarding the leading mechanism, the strategies of the ageing leader and multiple challengers make the algorithm less likely to be trapped in local optima.     

A Pareto firefly algorithm for multi-objective disassembly line balancing problems with hazard evaluation

The safety hazards existing in the process of disassembling waste products pose potential harms to the physical and mental health of the workers. In this article, these hazards involved in the disassembly operations are evaluated and taken into consideration in a disassembly line balancing problem. A multi-objective mathematical model is constructed to minimise the number of workstations, maximise the smoothing rate and minimise the average maximum hazard involved in the disassembly line. Subsequently, a Pareto firefly algorithm is proposed to solve the problem. The random key encoding method based on the smallest position rule is used to adapt the firefly algorithm to tackle the discrete optimisation problem of the disassembly line balancing. To avoid the search being trapped in a local optimum, a random perturbation strategy based on a swap operation is performed on the non-inferior solutions. The validity of the proposed algorithm is tested by comparing with two other algorithms in the existing literature using a 25-task phone disassembly case. Finally, the proposed algorithm is applied to solve a refrigerator disassembly line problem based on the field investigation and a comparison of the proposed Pareto firefly algorithm with another multi-objective firefly algorithm in the existing literature is performed to further identify the superior performance of the proposed Pareto firefly algorithm, and eight Pareto optimal solutions are obtained for decision makers to make a decision.     

Two enhanced differential evolution algorithms for job shop scheduling problems

This paper proposes two new differential evolution algorithms (DE) for solving the job shop scheduling problem (JSP) that minimises two single objective functions: makespan and total weighted tardiness. The proposed algorithms aim to enhance the efficiency of the search by dynamically balancing exploration and exploitation ability in DE and avoiding the problem of premature convergence. The first algorithm allows DE population to simultaneously perform different mutation strategies in order to extract the strengths of various strategies and compensate for the weaknesses of each individual strategy to enhance the overall performance. The second algorithm allows the whole DE population to change the search behaviour whenever the solutions do not improve. This study also introduces a modified local mutation operation embedded in the two proposed DE algorithms to promote exploitation in different areas of the search space. In addition, a local search technique, called Critical Block (CB) neighbourhood, is applied to enhance the quality of solutions. The performances of the proposed algorithms are evaluated on a set of benchmark problems and compared with results obtained from an efficient existing Particle Swarm Optimisation (PSO) algorithm. The numerical results demonstrate that the proposed DE algorithms yield promising results while using shorter computing times and fewer numbers of function evaluations.     

An improved label fusion approach with sparse patch‐based representation for MRI brain image segmentation

The multi‐atlas patch‐based label fusion (LF) method mainly focuses on the measurement of the patch similarity which is the comparison between the atlas patch and the target patch. To enhance the LF performance, the distribution probability about the target can be used during the LF process. Hence, we consider two LF schemes: in the first scheme, we keep the results of the interpolation so that we can obtain the labels of the atlas with discrete values (between 0 and 1) instead of binary values in the label propagation. In doing so, each atlas can be treated as a probability atlas. Second, we introduce the distribution probability of the tissue (to be segmented) in the sparse patch‐based LF process. Based on the probability of the tissue and sparse patch‐based representation, we propose three different LF methods which are called LF‐Method‐1, LF‐Method‐2, and LF‐Method‐3. In addition, an automated estimation method about the distribution probability of the tissue is also proposed. To evaluate the accuracy of our proposed LF methods, the methods were compared with those of the nonlocal patch‐based LF method (Nonlocal‐PBM), the sparse patch‐based LF method (Sparse‐PBM), majority voting method, similarity and truth estimation for propagated segmentations, and hierarchical multi‐atlas LF with multi‐scale feature representation and label‐specific patch partition (HMAS). Based on our experimental results and quantitative comparison, our methods are promising in the magnetic resonance image segmentation. © 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 23–32, 2017     

Credit where credit’s due: accounting for co-authorship in citation counts

I propose a new method (Pareto weights) to objectively attribute citations to co-authors. Previous methods either profess ignorance about the seniority of co-authors (egalitarian weights) or are based in an ad hoc way on the order of authors (rank weights). Pareto weights are based on the respective citation records of the co-authors. Pareto weights are proportional to the probability of observing the number of citations obtained. Assuming a Pareto distribution, such weights can be computed with a simple, closed-form equation but require a few iterations and data on a scholar, her co-authors, and her co-authors’ co-authors. The use of Pareto weights is illustrated with a group of prominent economists. In this case, Pareto weights are very different from rank weights. Pareto weights are more similar to egalitarian weights but can deviate up to a quarter in either direction (for reasons that are intuitive).     

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.     

An extension of the directed search domain algorithm to bilevel optimization

A method is developed for generating a well-distributed Pareto set for the upper level in bilevel multiobjective optimization. The approach is based on the Directed Search Domain (DSD) algorithm, which is a classical approach for generation of a quasi-evenly distributed Pareto set in multiobjective optimization. The approach contains a double-layer optimizer designed in a specific way under the framework of the DSD method. The double-layer optimizer is based on bilevel single-objective optimization and aims to find a unique optimal Pareto solution rather than generate the whole Pareto frontier on the lower level in order to improve the optimization efficiency. The proposed bilevel DSD approach is verified on several test cases, and a relevant comparison against another classical approach is made. It is shown that the approach can generate a quasi-evenly distributed Pareto set for the upper level with relatively low time consumption.     

A competitive memetic algorithm for the distributed two-stage assembly flow-shop scheduling problem

This article addresses the distributed two-stage assembly flow-shop scheduling problem (DTSAFSP) with makespan minimisation criterion. A mixed integer linear programming model is presented, and a competitive memetic algorithm (CMA) is proposed. When designing the CMA, a simple encoding scheme is proposed to represent the factory assignment and the job processing sequence; and a ring-based neighbourhood structure is designed for competition and information sharing. Moreover, some knowledge-based local search operators are developed to enhance the exploitation ability. The influence of parameter setting on the CMA is investigated using the analysis of variance method. Extensive computational tests and comparisons are carried out, which demonstrate the effectiveness of the proposed CMA in solving the DTSAFSP.     

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.     

ENGINEERING DESIGN OPTIMIZATION USING A SWARM WITH AN INTELLIGENT INFORMATION SHARING AMONG INDIVIDUALS

In this paper a new swarm algorithm for single objective design optimization problems is presented. A swarm is a collection of individuals having a common goal to reach the best value (minimum or maximum) of a function. Among the individuals in a swarm, there are some better performers (leaders) who set the direction of search for the rest of the individuals. An individual that is not in the better performer list (BPL) improves its performance by deriving information from its closest neighbour in the BPL. In an unconstrained problem, the objective values are used to generate the BPL while a multilevel Pareto ranking scheme is implemented to generate the BPL for constrained problems. The information sharing strategy also ensures that all the individuals in the swarm are unique as in a real swarm, where at a given time instant two individuals cannot share the same location. The uniqueness among the individuals result in a set of near optimal individuals at the final stage that is useful for sensitivity analysis. Three well-studied engineering design examples are solved to illustrate the benefits of the proposed swarm strategy