Bi-objective partial flexible job shop scheduling problem: NSGA-II,NRGA, MOGA and PAES approaches

This paper deals with a problem of partial flexible job shop with the objective of minimising makespan and minimising total operation costs. This problem is a kind of flexible job shop problem that is known to be NP-hard. Hence four multi-objective, Pareto-based, meta-heuristic optimisation methods, namely non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) and Pareto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal Pareto front. A new solution representation is introduced with the aim of solving the addressed problem. For the purpose of performance evaluation of our proposed algorithms, we generate some instances and use some benchmarks which have been applied in the literature. Also a comprehensive computational and statistical analysis is conducted in order to analyse the performance of the applied algorithms in five metrics including non-dominated solution, diversification, mean ideal distance, quality metric and data envelopment analysis are presented. Data envelopment analysis is a well-known method for efficiently evaluating the effectiveness of multi-criteria decision making. In this study we proposed this method of assessment of the non-dominated solutions. The results indicate that in general NRGA and PAES have had a better performance in comparison with the other two algorithms.     

Research on Cell Manufacturing Facility Layout Problem Based on Improved NSGA-II

With the rapid development of the individualized demand market, the demand for manufacturing flexibility has increased over time. As a result, a cell manufacturing system suitable for many varieties and small batches has been produced. With the goal of minimizing the area and logistics handling volume, and considering the arrangement order of facilities and channel constraints, a mathematical model was established, and the problem was solved by improved NSGA-II. After non-dominated sorting, traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals. Such a selection strategy is extremely easy to fall into the local optimal solution. The improved NSGA-II is to improve the original selection operation, which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation, and then select the last sorted ones of the remaining individuals into the cross operation, and combine the best and the worst ones into the cross operation. Finally, an example is given to simulate and improve the solution of NSGA-II and NSGA-II. The simulation results indicate that the improved NSGA-II population shows more obvious diversity, it is easier to jump out of the local optimal solution than NSGA-II, and the satisfactory layout scheme of manufacturing cells is obtained. Therefore, it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.     

Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm

The integration of process planning and scheduling is considered as a critical component in manufacturing systems. In this paper, a multi-objective approach is used to solve the planning and scheduling problem. Three different objectives considered in this work are minimisation of makespan, machining cost and idle time of machines. To solve this integration problem, we propose an improved controlled elitist non-dominated sorting genetic algorithm (NSGA) to take into account the computational intractability of the problem. An illustrative example and five test cases have been taken to demonstrate the capability of the proposed model. The results confirm that the proposed multi-objective optimisation model gives optimal and robust solutions. A comparative study between proposed algorithm, controlled elitist NSGA and NSGA-II show that proposed algorithm significantly reduces scheduling objectives like makespan, cost and idle time, and is computationally more efficient.     

Cross-trained workers scheduling for field service using improved NSGA-II

The proper balancing of geographically distributed task schedules and the associated workforce distributions are critical determinants of productivity in any people-centric production environment. The paper has investigated the cross-trained workers scheduling problem considering the qualified personal allocation and temporally cooperation of engineers simultaneously. A 0–1 programming model is developed and the non-dominated sorting genetic algorithm-II (NSGA-II) is adopted to deal with the NP-hard problem. In order to enforce the NSGA-II, significant improvements are made to function the approach in a more efficient way. It is observed that the improved NSGA-II outperforms the original NSGA-II in the experimental test. The promising outcomes of the formulation in the experiment make its implementation easily customisable and transferable for solving other intricate problems in the context of skilled workforce scheduling. Furthermore, the modified NSGA II can be used as an efficient and effective tool for other multiobjective optimisation problems.     

An improved NSGA-II algorithm for multi-objective lot-streaming flow shop scheduling problem

Crossover and mutation operators in NSGA-II are random and aimless, and encounter difficulties in generating offspring with high quality. Aiming to overcoming these drawbacks, we proposed an improved NSGA-II algorithm (INSGA-II) and applied it to solve the lot-streaming flow shop scheduling problem with four criteria. We first presented four variants of NEH heuristic to generate the initial population, and then incorporated the estimation of distribution algorithm and a mutation operator based on insertion and swap into NSGA-II to replace traditional crossover and mutation operators. Last but not least, we performed a simple and efficient restarting strategy on the population when the diversity of the population is smaller than a given threshold. We conducted a serial of experiments, and the experimental results demonstrate that the proposed algorithm outperforms the comparative algorithms.     

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.     

Hybrid genetic algorithm for bi-objective resource-constrained project scheduling

In this study, we considered a bi-objective, multi-project, multi-mode resource-constrained project scheduling problem. We adopted three objective pairs as combinations of the net present value (NPV) as a financial performance measure with one of the time-based performance measures, namely, makespan (C_max), mean completion time (MCT), and mean flow time (MFT) (i.e., minC_max/maxNPV, minMCT/maxNPV, and minMFT/maxNPV). We developed a hybrid non-dominated sorting genetic algorithm II (hybrid-NSGA-II) as a solution method by introducing a backward–forward pass (BFP) procedure and an injection procedure into NSGA-II. The BFP was proposed for new population generation and post-processing. Then, an injection procedure was introduced to increase diversity. The BFP and injection procedures led to improved objective functional values. The injection procedure generated a significantly high number of non-dominated solutions, thereby resulting in great diversity. An extensive computational study was performed. Results showed that hybrid-NSGA-II surpassed NSGA-II in terms of the performance metrics hypervolume, maximum spread, and the number of non-dominated solutions. Solutions were obtained for the objective pairs using hybrid-NSGA-II and three different test problem sets with specific properties. Further analysis was performed by employing cash balance, which was another financial performance measure of practical importance. Several managerial insights and extensions for further research were presented.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

Operational strategies for seru production system: a bi-objective optimisation model and solution methods

In recent years, the interest in seru production system (SPS) has increased to enhance the flexibility of production systems. Because the worker resource in an SPS is critical for adapting to changes in demand, this study focuses on workforce-related operational strategies rarely considered for SPS. To this end, for the first time in the literature, a bi-objective workforce scheduling problem is addressed by considering the interseru worker transfer in SPS. A novel optimisation model is proposed to achieve two objectives, that of minimising makespan and reducing workload imbalance among workers. Because it is proved that the problem falls within a non-deterministic polynomial-time hardness (NP-hard) class, non-dominated sorting genetic algorithm-II (NSGA-II) is employed to solve large-sized problems. For small-sized problems, the second version of the augmented ε-constrained (AUGMECON2) method is implemented and Pareto-optimal solutions are obtained. A set of evaluation metrics is considered to compare two different operational strategies in terms of the desired objectives. The computational results indicate that allowing worker transfer leads to better results for all metrics. The main contribution of the present study is to provide a novel optimisation model for the addressed problem to compare two operational strategies by considering the heterogeneity inherent of workers.     

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。     

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance     

Multi-objective imperfect preventive maintenance optimisation with NSGA-II

Maintenance optimisation is a multi-objective problem in nature, and it usually needs to achieve a trade-off among the conflicting objectives. In this study, a multi-objective maintenance optimisation (MOMO) model is proposed for electromechanical products, where both the soft failure and hard failure are considered, and minimal repair is performed accordingly. Imperfect preventive maintenance (IPM) is carried out during the preplanned periods, and modelled with a hybrid failure rate model and quasi-renewal coefficient. The initial IPM period and the total number of IPM periods are set as the decision variables, and a MOMO model is developed to optimise the availability and cost rate concurrently. The fast elitist non-dominated sorting genetic algorithm (NSGA-II) is applied to solve the model. A case study of wind turbine’s gearbox is provided. The results show that there are 30 optimal solutions in the MOMO’s Pareto frontier that can maximise the availability and minimise the cost rate simultaneously. Compared with the single-objective maintenance optimisation, it can provide more choices for maintenance decision, and better satisfy the resource constraints and the customer’s preference. The results of the sensitivity analysis show that the effect of age reduction factor on optimisation results is greater than that of failure rate increase factor.     

Optimal platform design using non-dominated sorting genetic algorithm II and technique for order of preference by similarity to ideal solution; application to automotive suspension system

Unlike conventional approaches where optimization is performed on a unique component of a specific product, optimum design of a set of components for employing in a product family can cause significant reduction in costs. Increasing commonality and performance of the product platform simultaneously is a multi-objective optimization problem (MOP). Several optimization methods are reported to solve these MOPs. However, what is less discussed is how to find the trade-off points among the obtained non-dominated optimum points. This article investigates the optimal design of a product family using non-dominated sorting genetic algorithm II (NSGA-II) and proposes the employment of technique for order of preference by similarity to ideal solution (TOPSIS) method to find the trade-off points among the obtained non-dominated results while compromising all objective functions together. A case study for a family of suspension systems is presented, considering performance and commonality. The results indicate the effectiveness of the proposed method to obtain the trade-off points with the best possible performance while maximizing the common parts.     

Permutation flow shop scheduling with earliness and tardiness penalties

We consider the permutation flow shop scheduling problem with earliness and tardiness penalties (E/T) and common due date for jobs. We show that the problem can be sub-divided into three cases: (i) the due date is such that all jobs are necessarily tardy; (ii) the due date is unrestricted; and (iii) the due date is between the two. Based on analytical results we provide partial characterisation of the optimal solution and develop a comprehensive approach for solving the problem over the entire range of due dates. Our approach, which draws upon the existing literature and results for the single machine problem, successfully exploits the properties of the optimal solution. Limited computational results indicate that the performance of the heuristic is reasonable and has the potential to significantly improve performance. This approach has been incorporated as part of the scheduling module of the production planning and scheduling system we developed for a medium-sized bulk drug manufacturer.     

Job shop scheduling with a non-regular objective: A comparison of neighbourhood structures based on a sequencing/timing decomposition

Commercial software packages for production management are characterized by a gap between MRP logic, based on a backward scheduling approach, and finite capacity scheduling, usually based on forward scheduling. In order to partially bridge that gap, we need scheduling algorithms able to meet due dates while keeping WIP and inventory costs low. This leads us to consider job shop scheduling problems characterized by non-regular objective functions; such problems are even more difficult than classical job shop scheduling, and suitable heuristics are needed. One possibility is to consider local search strategies based on the decomposition of the overall problem into sequencing and timing sub-problems. For given job sequences, the optimal timing problem can be solved as a node potential problem on a graph. Since solving the timing problem is a relatively time-consuming task, we need to define a suitable neighbourhood structure to explore the space of job sequences; this can be done by generalizing well-known results for the minimum makespan problem. A related issue is if solving timing problems exactly is really necessary, or if an approximate solution is sufficient; hence, we also consider solving the timing problem approximately by a fast heuristic. We compare different neighbourhood structures, by embedding them within a pure local improvement strategy. Computational experiments show that the overall approach performs better than release/dispatch rules, although the performance improvement depends on the problem characteristics, and that the fast heuristic is quite competitive with the optimal timing approach. On the one hand, these results pave the way to the development of better local search algorithms (based e.g. on tabu search); on the other hand, it is worth noting that the heuristic timing approach, unlike the optimal one, can be extended to cope with the complicating features typical of practical scheduling problems.     

Optimization of aluminium sheet hot stamping process using a multi-objective stochastic approach

This article aims to investigate the means to obtain optimal hot stamping process parameters and the influence of the stochastic variability of these parameters on forming quality. A multi-objective stochastic approach, integrating response surface methodology (RSM), multi-objective genetic algorithm optimization non-dominated sorting genetic algorithm II (NSGA-II) and the Monte Carlo simulation (MCS) method is proposed in this article to achieve this goal. RSM was used to establish the relationship between the process parameters and forming quality indices. NSGA-II was utilized to obtain a Pareto frontier, which consists of a series of optimal process parameters. The MCS method was employed to study and reduce the influence of a stochastic property of these process parameters on forming quality. The results confirmed the efficiency of the proposed multi-objective stochastic approach during optimization of the hot stamping process. Robust optimal process parameters guaranteeing good forming quality were also obtained using this approach.     

基于文化基因算法的开放车间调度问题研究

针对开放车间调度问题,运用了文化基因算法进行优化求解。在文化基因算法的框架中,既有种群中的全局搜索,又包含针对问题自身特点的局部搜索,为解决开放车间调度问题提供了一种新的算法。按照文化基因算法的思想和特点,将爬山法作为局部搜索策略加入到全局搜索策略所用到的遗传算法中,通过对开放车间调度问题的邻域结构进行研究,加入爬山搜索法进行优化求解。基于40个标准算例,通过与下界值的比较,验证了所提算法在解决具有较大搜索空间的调度问题时,其拥有更出色的算法性能。     

Altitude and roll control of a hovering quad-rotor air vehicle using the multi-objective approximate optimization of proportional–integral–differential control

This study explores the optimal proportional–integral–differential (PID) gains of a hovering quad-copter to allow recovery from disturbed altitude and roll positions. Computational fluid dynamics was used to determine the rotor distance and the blade shape parameters for maximizing the hovering thrust. Using a six-degree-of-freedom quad-copter dynamics model, a control algorithm was then used to obtain PID gains. The PID control was approximated using back-propagation neural networks (BPNs). Position control of the quad-copter model was performed by determining the optimal PID gains required to minimize the control duration for altitude and roll. The non-dominated sorting genetic algorithm (NSGA-II) was used for multi-objective optimization and a BPN was used for meta-modelling the PID control. The PID gains generated from bi-objective optimal designs were compared with the initial design. The results confirmed that the recovery time from an unbalanced position was reduced and that the motion of the quad-copter was better stabilized.     

Satisfying due-dates in a job shop with sequence-dependent family set-ups

This paper addresses job shop scheduling with sequence dependent family set-ups. Based on a simple, single-machine dynamic scheduling problem, state dependent scheduling rules for the single machine problem are developed and tested using Markov Decision Processes. Then, a generalized scheduling policy for the job shop problem is established based on a characterization of the optimal policy. The policy is combined with a 'forecasting' mechanism to utilize global shop floor information for local dispatching decisions. Computational results show that performance is significantly better than that of existing alternative policies.     

A blockchain-based approach for a multi-echelon sustainable supply chain

Blockchain technology is destined to revolutionise supply chain processes. At the same time, governmental and regulatory policies are forcing firms to adjust their supply chains in response to environmental concerns. The objective of this study is therefore to develop a distributed ledger-based blockchain approach for monitoring supply chain performance and optimising both emission levels and operational costs in a synchronised fashion, producing a better outcome for the supply chain. We propose the blockchain approach for different production allocation problems within a multi-echelon supply chain (MESC) under a carbon taxation policy. As such, we couple recent advances in digitalisation of operations with increasingly stringent regulatory environmental policies. Specifically, with lead time considerations under emission rate constraints (imposed by a carbon taxation policy), we simultaneously consider the production, distribution and inventory control decisions in a production allocation-based MESC problem. The problem is then formulated as a Mixed Integer Non-Linear Programming (MINLP) model. We show that the distributed ledger-based blockchain approach minimises both total cost and carbon emissions. We then validate the feasibility of the proposed approach by comparing the results with a non-dominated sorting genetic algorithm (NSGA-II). The findings provide support for policymakers and supply chain executives alike.