A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.     

Simultaneous scheduling of production and maintenance tasks in the job shop

This paper deals with the job shop problem of simultaneous scheduling of production operations and preventive maintenance tasks. To solve this problem, we develop an elitist multi-objective genetic algorithm that provides a set of Pareto optimal solutions minimising the makespan and the total maintenance cost. A deep study was made to choose the best encoding, operators, and the different probabilities. Some lower bounds of the adopted criteria are developed. The computational experiments carried out on a set of published instances validate the efficiency of the proposed algorithm.     

Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.     

Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

A multi-point simulated annealing heuristic for solving multiple objective unrelated parallel machine scheduling problems

This study considers the problem of job scheduling on unrelated parallel machines. A multi-objective multi-point simulated annealing (MOMSA) algorithm was proposed for solving this problem by simultaneously minimising makespan, total weighted completion time and total weighted tardiness. To assess the performance of the proposed heuristic and compare it with that of several benchmark heuristics, the obtained sets of non-dominated solutions were assessed using four multi-objective performance indicators. The computational results demonstrated that the proposed heuristic markedly outperformed the benchmark heuristics in terms of the four performance indicators. The proposed MOMSA algorithm can provide a new benchmark for future research related to the unrelated parallel machine scheduling problem addressed in this study.     

Pareto optimization using the struggle genetic crowding algorithm

Many real-world engineering design problems involve the simultaneous optimization of several conflicting objectives. In this paper, a method combining the struggle genetic crowding algorithm with Pareto-based population ranking is proposed to elicit trade-off frontiers. The new method has been tested on a variety of published problems, reliably locating both discontinuous Pareto frontiers as well as multiple Pareto frontiers in multi-modal search spaces. Other published multi-objective genetic algorithms are less robust in locating both global and local Pareto frontiers in a single optimization. For example, in a multi-modal test problem a previously published non-dominated sorting GA (NSGA) located the global Pareto frontier in 41% of the optimizations, while the proposed method located both global and local frontiers in all test runs. Additionally, the algorithm requires little problem specific tuning of parameters.     

Two efficient algorithms for constructing almost even approximations of the Pareto front in multi-objective optimization problems

In this article, two algorithms are proposed for constructing almost even approximations of the Pareto front of multi-objective optimization problems. The first algorithm is a hybrid of the ε-constraint and Pascoletti–Serafini scalarization methods for solving bi-objective problems. The second is a modification of the successive Pareto optimization (SPO) algorithm for solving three-objective problems. In these algorithms, the MATLAB fmincon solver is used to solve single-objective optimization problems, which returns a local optimal solution. Some metrics are considered to evaluate the quality of approximations obtained by the suggested algorithms on six test problems, and their results are compared with other algorithms (normal constraint, weighted constraint, SPO, differential evolution, multi-objective evolutionary algorithm/decomposition–differential evolution, non-dominated sorting genetic algorithm-II and S-metric selection evolutionary multi-objective algorithm). Experimental results show that the proposed algorithms provide almost even approximations of the whole Pareto front, and better quality of approximation and CPU time compared with established algorithms.     

Migration NSGA: method to improve a non-elitist searching of Pareto front,with application in magnetics

The paper describes a migration strategy to improve classical non-dominated sorting genetic algorithm (NSGA) to find optimal solution of a multi-objective problem. Migration NSGA has been tested to assess its performance using analytical functions for which the Pareto front is known in analytical form, as well as two case studies in electromagnetics, for which the Pareto front is not known a priori. This strategy improves the approximation of the Pareto-optimal solutions of a multi-objective problem by introducing new individuals in the population miming the effect of migrations.     

Multi-objective unrelated parallel machine scheduling: a Tabu-enhanced iterated Pareto greedy algorithm

This work proposes a high-performance algorithm for solving the multi-objective unrelated parallel machine scheduling problem. The proposed approach is based on the iterated Pareto greedy (IPG) algorithm but exploits the accessible Tabu list (TL) to enhance its performance. To demonstrate the superior performance of the proposed Tabu-enhanced iterated Pareto greedy (TIPG) algorithm, its computational results are compared with IPG and existing algorithms on the same benchmark problem set. Experimental results reveal that incorporating the accessible TL can eliminate ineffective job moves, causing the TIPG algorithm to outperform state-of-the-art approaches in the light of five multi-objective performance metrics. This work contributes a useful theoretical and practical optimisation method for solving this problem.     

Bi-objective reentrant hybrid flowshop scheduling: an iterated Pareto greedy algorithm

The multi-objective reentrant hybrid flowshop scheduling problem (RHFSP) exhibits significance in many industrial applications, but appears under-studied in the literature. In this study, an iterated Pareto greedy (IPG) algorithm is proposed to solve a RHFSP with the bi-objective of minimising makespan and total tardiness. The performance of the proposed IPG algorithm is evaluated by comparing its solutions to existing meta-heuristic algorithms on the same benchmark problem set. Experimental results show that the proposed IPG algorithm significantly outperforms the best available algorithms in terms of the convergence to optimal solutions, the diversity of solutions and the dominance of solutions. The statistical analysis manifestly shows that the proposed IPG algorithm can serve as a new benchmark approach for future research on this extremely challenging scheduling problem.     

混合工作日历下批量生产柔性作业车间多目标调度方法

提出了一种混合工作日历下批量生产柔性作业车间多目标调度方法。考虑设备的混合工作日历约束,构建了以生产周期最短、制造成本最低为优化目标的批量生产柔性作业车间多目标调度模型。设计了一种带精英策略的非支配排序遗传算法(NSGA II)求解该模型。算法中,采用“基于工序和设备的分段编码”方式分别对工序和设备进行编码;采用“基于工序和设备的分段交叉和变异方式”进行交叉和变异操作,采用“遗传算子改进策略”保证交叉、变异后子代个体的可行性;解码操作采用“基于平顺移动的原理”和“基于工作日历的时间推算技术”推算工序的调整开始、调整结束、加工开始和加工结束时刻。最后,通过案例分析验证了所提方法的有效性。     

A Pareto block-based estimation and distribution algorithm for multi-objective permutation flow shop scheduling problem

Multi-objective flow shop scheduling plays a key role in real-life scheduling problem which attract the researcher attention. The primary concern is to find the best sequence for flow shop scheduling problem. Estimation of Distribution Algorithms (EDAs) has gained sufficient attention from the researchers and it provides prominent results as an alternate of traditional evolutionary algorithms. In this paper, we propose the pareto optimal block-based EDA using bivariate model for multi-objective flow shop scheduling problem. We apply a bivariate probabilistic model to generate block which have the better diversity. We employ the non-dominated sorting technique to filter the solutions. To check the performance of proposed approach, we test it on the benchmark problems available in OR-library and then we compare it with non-dominated sorting genetic algorithm-II (NSGA-II). Computational results show that pareto optimal BBEDA provides better result and better convergence than NSGA-II.     

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.     

A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling

This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-front. In the second phase, to improve the Pareto-front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over a genetic algorithm in the first phase and three hybrid metaheuristics in the second and third phases. Experiments on the test problems with different structures show that the multi-phase method is a better tool to approximate the efficient set than the global archive sub-population genetic algorithm presented previously.     

Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem

The increasing market demand for product variety forces manufacturers to design mixed-model assembly lines (MMAL) on which a variety of product models similar to product characteristics are assembled. This paper presents a method combining the new ranked based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named non-dominated ranking genetic algorithm (NRGA) to a just-in-time (JIT) sequencing problem when two objectives are considered simultaneously. The two objectives are minimisation the number of setups and variation of production rates. This type of problem is NP-hard. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. The solutions obtained via NRGA are compared against solutions obtained via total enumeration (TE) scheme in small problems and also against four other search heuristics in small, medium and large problems. Experimental results show that the proposed algorithm is competitive with these other algorithms in terms of quality and diversity of solutions.     

A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.     

带调整时间的多目标流水车间调度的优化算法

为高效地求解带调整时间的多目标流水车间调度问题,提出了一种多目标混合遗传算法,此算法依据基于Pareto优于关系的个体排序数和密度值计算适应度,保持解的多样性,并采用非劣解并行局部搜索策略,提高算法的搜索效率.此外,引入精英策略保证算法的收敛性,在进化过程中通过淘汰掉个别最差个体,进一步加快解的收敛速度.仿真结果表明,新算法能够有效地解决带调整时间的多目标流水车间调度问题.     

改进遗传算法求解多时间约束的柔性作业车间调度问题

将加工时间、调整时间和移动时间分别作为独立时间因素考虑到柔性作业车间调度模型中,建立以最大完工时间最小、总调整时间最小、总移动时间最小为目标的考虑多时间约束的柔性作业车间调度模型,并提出改进的遗传算法求解该模型。通过测试标准数据集,并对比其他文献算法,验证了改进的遗传算法的可行性和有效性。     

Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.     

Multi-objective meta-heuristics to solve three-stage assembly flow shop scheduling problem with machine availability constraints

In this paper, a three-stage assembly flow shop scheduling problem with machine availability constraints is taken into account. Two objectives of minimising total weighted completion times (flow time) and minimising sum of weighted tardiness and earliness are simultaneously considered. To describe this problem, a mathematical model is presented. The problem is generalisation of three-machine flow shop scheduling problem and two-stage assembly flow shop scheduling problem. Since these problems are known to be NP-hard, the considered problem is also strongly NP-hard. Therefore, two multi-objective meta-heuristics are presented to efficiently solve this problem in a reasonable amount of time. Comprehensive computational experiments are performed to illustrate the performance of the presented algorithms.