双目标可重入混合流水车间调度问题的离散灰狼优化算法

可重入混合流水车间调度问题普遍存在于许多高科技制造产业中,如半导体晶圆制造和TFT-LCD面板生产过程等,但目前关于可重入调度问题的相关研究还比较少。本文设计了一种改进多目标灰狼优化算法(IMOGWO)解决最小化最大完工时间和总拖期时间最小的可重入混合流水车间调度问题,针对该问题特点对基本灰狼优化算法进行了一系列改进操作。通过对小规模测试问题基准算例的数值实验,验证了所设计的IMOGWO算法求解该调度问题的有效性。实验结果表明IMOGWO算法在非劣解的收敛性和支配性方面显著优于已有的NSGA-II和MOGWO算法,在解的分布性指标方面IMOGWO稍微优于其他两种算法。     

New simulation-based frameworks for multi-objective reliability-based design optimization of structures

In the present study, two new simulation-based frameworks are proposed for multi-objective reliability-based design optimization (MORBDO). The first is based on hybrid non-dominated sorting weighted simulation method (NSWSM) in conjunction with iterative local searches that is efficient for continuous MORBDO problems. According to NSWSM, uniform samples are generated within the design space and, then, the set of feasible samples are separated. Thereafter, the non-dominated sorting operator is employed to extract the approximated Pareto front. The iterative local sample generation is then performed in order to enhance the accuracy, diversity, and increase the extent of non-dominated solutions. In the second framework, a pseudo-double loop algorithm is presented based on hybrid weighted simulation method (WSM) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) that is efficient for problems including both discrete and continuous variables. According to hybrid WSM-NSGA-II, proper non-dominated solutions are produced in each generation of NSGA-II and, subsequently, WSM evaluates the reliability level of each candidate solution until the algorithm converges to the true Pareto solutions. The valuable characteristic of presented approaches is that only one simulation run is required for WSM during entire optimization process, even if solutions for different levels of reliability be desired. Illustrative examples indicate that NSWSM with the proposed local search strategy is more efficient for small dimension continuous problems. However, WSM-NSGA-II outperforms NSWSM in terms of solutions quality and computational efficiency, specifically for discrete MORBDOs. Employing global optimizer in WSM-NSGA-II provided more accurate results with lower samples than NSWSM.     

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature.     

Multi-objective open shop scheduling by considering human error and preventive maintenance

This study presents an open shop scheduling model by considering human error and preventive maintenance. The proposed mathematical model takes into account conflicting objective functions including makespan, human error and machine availability. In order to find the optimum scheduling, human error, maintenance and production factors are considered, simultaneously. Human error is measured by Human Error Assessment and Reduction Technique (HEART). Three metaheuristic methods including non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) are developed to find near-optimal solution. The Taguchi method is applied by adjusting parameters of metaheuristic algorithms. Several illustrative examples and a real case study (auto spare parts manufacturer) are applied to show the applicability of the multi-objective mixed integer nonlinear programming model. The proposed approach of this study may be used for similar open shop problems with minor modifications.     

Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance

The receiver operating characteristics (ROC) analysis has gained increasing popularity for analyzing the performance of classifiers. In particular, maximizing the convex hull of a set of classifiers in the ROC space, namely ROCCH maximization, is becoming an increasingly important problem. In this work, a new convex hull-based evolutionary multi-objective algorithm named ETriCM is proposed for evolving neural networks with respect to ROCCH maximization. Specially, convex hull-based sorting with convex hull of individual minima (CH-CHIM-sorting) and extreme area extraction selection (EAE-selection) are proposed as a novel selection operator. Empirical studies on 7 high-dimensional and imbalanced datasets show that ETriCM outperforms various state-of-the-art algorithms including convex hull-based evolutionary multi-objective algorithm (CH-EMOA) and non-dominated sorting genetic algorithm II (NSGA-II).     

A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

This paper presents a novel method of multi-objective optimization by learning automata (MOLA) to solve complex multi-objective optimization problems. MOLA consists of multiple automata which perform sequential search in the solution domain. Each automaton undertakes dimensional search in the selected dimension of the solution domain, and each dimension is divided into a certain number of cells. Each automaton performs a continuous search action, instead of discrete actions, within cells. The merits of MOLA have been demonstrated, in comparison with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and non-dominated sorting genetic algorithm II (NSGA-II), on eleven multi-objective benchmark functions and an optimal problem in the midwestern American electric power system which is integrated with wind power, respectively. The simulation results have shown that MOLA can obtain more accurate and evenly distributed Pareto fronts, in comparison with MOEA/D and NSGA-II.     

Solving multi-objective multicast routing problems by evolutionary multi-objective simulated annealing algorithms with variable neighbourhoods

This paper presents the investigation of an evolutionary multi-objective simulated annealing (EMOSA) algorithm with variable neighbourhoods to solve the multi-objective multicast routing problems in telecommunications. The hybrid algorithm aims to carry out a more flexible and adaptive exploration in the complex search space by using features of the variable neighbourhood search to find more non-dominated solutions in the Pareto front. Different neighbourhood strictures have been designed with regard to the set of objectives, aiming to drive the search towards optimising all objectives simultaneously. A large number of simulations have been carried out on benchmark instances and random networks with real world features including cost, delay and link utilisations. Experimental results demonstrate that the proposed EMOSA algorithm with variable neighbourhoods is able to find high-quality non-dominated solutions for the problems tested. In particular, the neighbourhood structures that are specifically designed for each objective significantly improved the performance of the proposed algorithm compared with variants of the algorithm with a single neighbourhood.     

公交网络时刻表再协同设计的多目标优化模型

为了改善公交服务质量,公交运营者试图调整现有时刻表的发车时间,使不同线路的车次协同到达换乘站点以方便乘客换乘。针对此场景,研究了公交时刻表重新协同设计问题,提出了求解该问题的多目标模型。模型考虑了对发车间隔灵敏的乘客需求、灵活的车次协同到站方式和发车时间的规则性,分析了该多目标模型的特征和计算复杂性,表明本文研究的问题是NP-hard问题,且它的帕累托最优前沿是非凸的,设计了基于非支配排序的遗传算法求解模型。算例表明,与枚举算法相比,提出的求解算法在较短的时间内可获得高质量的帕累托解。     

随机混流U型拆卸线平衡排序问题多目标进化算法优化

针对混流U型拆卸线平衡排序问题,考虑拆卸时间不确定,建立了该问题最小拆卸线平均闲置率、尽早拆卸危害和高需求零部件、最小化平均方向改变次数的多目标优化模型,并提出一种基于分解和动态邻域搜索的混合多目标进化算法(Hybrid Multi-objective Evolutionary Algorithm Based on Decomposition, HMOEA/D)。该算法通过采用弹性任务分配策略、动态邻域结构和动态调整权重以保证解的可行性并搜索得到分布较好的非劣解集。最后,仿真求解实验设计技术(DOE)生成的测试算例,结果表明HMOEA/D较其它算法能得到更接近Pareto最优、分布更好的近似解集。     

Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm

In this paper, we develop a novel stochastic multi-objective multi-mode transportation model for hub covering location problem under uncertainty. The transportation time between each pair of nodes is an uncertain parameter and also is influenced by a risk factor in the network. We extend the traditional comprehensive hub location problem by considering two new objective functions. So, our multi-objective model includes (i) minimization of total current investment costs and (ii) minimization of maximum transportation time between each origin–destination pair in the network. Besides, a novel multi-objective imperialist competitive algorithm (MOICA) is proposed to obtain the Pareto-optimal solutions of the problem. The performance of the proposed solution algorithm is compared with two well-known meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES). Computational results show that MOICA outperforms the other meta-heuristics.     

考虑序列设置时间的混合流水车间多目标调度研究

基于混合流水车间多品种的特性,序列设置时间和工序跳跃是很多车间在调度时需要考虑的两个重要问题,论文充分考虑这两种生产约束,建立了以最大完工时间和负荷均衡指标为双目标的混合流水车间多目标调度数学模型,并运用改进的NSGA-II算法对基于实际企业生产数据假设的算例进行仿真求解,结果表明求解的调度方案符合实际需求,能够为企业的实际调度提供有效的方案。     

An improved NSGA-III algorithm based on elimination operator for many-objective optimization

Due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance schemes in the environmental selection, the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to handle many-objective optimization problems. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the uniformly distributed reference points to significantly promote population diversity, but the convergence based on the Pareto-dominance relation could still be enhanced. For this purpose, an improved NSGA-III algorithm based on elimination operator (NSGA-III-EO) is proposed. In the proposed algorithm, the elimination operator first identifies the reference point with maximum niche count and then employs the penalty-based boundary intersection distance to rank the individuals associated with it. To this end, the selection scheme is used to remove the worse individuals rather than to select the superior individuals. The proposed NSGA-III-EO is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art MOEAs. Additionally, it is also tested on constrained problems having a large number of objectives and shows good performance.     

A multi-objective hot-rolling scheduling problem in the compact strip production

This paper addresses a hot-rolling scheduling problem from compact strip production processes. At first, a mathematical model that consists of two coupled sub-problems is presented. The first sub-problem is the sheet-strip assignment problem that is about how to assign sheet-strips to rolling-turns with the objective of minimizing virtual sheet-strips. The second is the sheet-strip sequencing problem that is about how to sort the sheet-strips in each rolling-turn with the objective of minimizing the maximal changes in thickness between adjacent sheet-strips and the change times of the thickness so as to ensure high quality sheet-strips to be produced. And then, an improved hot-rolling scheduling heuristic is proposed to solve the sheet-strip assignment problem. A multi-objective evolutionary algorithm is developed to find the Pareto optimal or near-optimal solutions for the sheet-strip sequencing problem. Besides, the problem-specific knowledge is explored. The key operators including crossover operator, mutation operator and repair operator are designed for the multi-objective evolutionary algorithm. At last, extensive experiments based on real-world instances from a compact strip production process are carried out. The results demonstrate the effectiveness of the proposed algorithms for solving the hot-rolling scheduling problem under consideration.     

Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

A parallel competitive colonial algorithm for JIT flowshop scheduling

This paper proposes two parallel algorithms which are improved by heuristics for a bi-objective flowshop scheduling problem with sequence-dependent setup times in a just-in-time environment. In the proposed algorithms, the population will be decomposed into the several sub-populations in parallel. Multiple objectives are combined with min–max method then each sub-population evolves separately in order to obtain a good approximation of the Pareto-front. After unifying the obtained results, we propose a variable neighborhood algorithm and a hybrid variable neighborhood search/tabu search algorithm to improve the Pareto-front. The non-dominated sets obtained from our proposed algorithms, a genetic local search and restarted iterated Pareto greedy algorithm are compared. It is found that most of the solutions in the net non-dominated front are yielded by our proposed algorithms.     

Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.     

On the computation of all supported efficient solutions in multi-objective integer network flow problems

This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets.     

Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm

In today’s manufacturing industry more than one performance criteria are considered for optimization to various degrees simultaneously. To deal with such hard competitive environments it is essential to develop appropriate multicriteria scheduling approaches. In this paper consideration is given to the problem of scheduling n independent jobs on a single machine with due dates and objective to simultaneously minimize three performance criteria namely, total weighted tardiness (TWT), maximum tardiness and maximum earliness. In the single machine scheduling literature no previous studies have been performed on test problems examining these criteria simultaneously. After positioning the problem within the relevant research field, we present a new heuristic algorithm for its solution. The developed algorithm termed the hybrid non-dominated sorting differential evolution (h-NSDE) is an extension of the author’s previous algorithm for the single-machine mono-criterion TWT problem. h-NSDE is devoted to the search for Pareto-optimal solutions. To enable the decision maker for evaluating a greater number of alternative non-dominated solutions, three multiobjective optimization approaches have been implemented and tested within the context of h-NSDE: including a weighted-sum based approach, a fuzzy-measures based approach which takes into account the interaction among the criteria as well as a Pareto-based approach. Experiments conducted on existing data set benchmarks problems show the effect of these approaches on the performance of the h-NSDE algorithm. Moreover, comparative results between h-NSDE and some of the most popular multiobjective metaheuristics including SPEA2 and NSGA-II show clear superiority for h-NSDE in terms of both solution quality and solution diversity.     

不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化

项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。     

An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results.