Simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection

Tolerance specification is an important part of mechanical design. Design tolerances strongly influence the functional performance and manufacturing cost of a mechanical product. Tighter tolerances normally produce superior components, better performing mechanical systems and good assemblability with assured exchangeability at the assembly line. However, unnecessarily tight tolerances lead to excessive manufacturing costs for a given application. The balancing of performance and manufacturing cost through identification of optimal design tolerances is a major concern in modern design. Traditionally, design tolerances are specified based on the designer’s experience. Computer-aided (or software-based) tolerance synthesis and alternative manufacturing process selection programs allow a designer to verify the relations between all design tolerances to produce a consistent and feasible design. In this paper, a general new methodology using intelligent algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Particle Swarm Optimization (MOPSO) for simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection is presented. The problem has a multi-criterion character in which 3 objective functions, 3 constraints and 5 variables are considered. The average fitness factor method and normalized weighted objective functions method are separately 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 Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

Particle swarm optimization with preference order ranking for multi-objective optimization

A new optimality criterion based on preference order (PO) scheme is used to identify the best compromise in multi-objective particle swarm optimization (MOPSO). This scheme is more efficient than Pareto ranking scheme, especially when the number of objectives is very large. Meanwhile, a novel updating formula for the particle’s velocity is introduced to improve the search ability of the algorithm. The proposed algorithm has been compared with NSGA-II and other two MOPSO algorithms. The experimental results indicate that the proposed approach is effective on the highly complex multi-objective optimization problems.     

A realistic variant of bi-objective unrelated parallel machine scheduling problem: NSGA-II and MOACO approaches

The problem investigated in this study involves an unrelated parallel machine scheduling problem with sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from a realistic scheduling problem in the shipyard. The optimization criteria are to simultaneously minimize mean weighted flow time and mean weighted tardiness. To formulate this complicated problem, a new mixed-integer programming model is presented. Considering the NP-complete characteristic of this problem, two famous meta-heuristics including a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective ant colony optimization (MOACO) which is a modified and adaptive version of BicriterionAnt algorithm are developed. Obviously, the precedence constraints increase the complexity of the scheduling problem in strong sense in order to generate feasible solutions, especially in parallel machine environment. Therefore a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. Due to the fact that appropriate design of parameter has a significant effect on the performance of algorithms, we calibrate the parameters of these algorithms by using new approach of Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The results indicated that the suggested MOACO statistically outperformed the proposed NSGA-II in solving the test problems. In addition, the application of the proposed algorithms is justified by a real block erection scheduling problem in the shipyard.     

A novel multi-objective meta-heuristic model for solving cross-docking scheduling problems

Cross-docking is a material handling and distribution technique in which products are transferred directly from the receiving dock to the shipping dock, reducing the need for a warehouse or distribution center. This process minimizes the storage and order-picking functions in a warehouse. In this paper, we consider cross-docking in a supply chain and propose a multi-objective mathematical model for minimizing the make-span, transportation cost and the number of truck trips in the supply chain. The proposed model allows a truck to travel from a supplier to the cross-dock facility and from the supplier directly to the customers. We propose two meta-heuristic algorithms, the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective particle swarm optimization (MOPSO), to solve the multi-objective mathematical model. We demonstrate the applicability of the proposed method and exhibit the efficacy of the procedure with a numerical example. The numerical results show the relative superiority of the NSGA-II method over the MOPSO method.     

A soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem

In this paper, a novel multi-objective location model within multi-server queuing framework is proposed, in which facilities behave as M/M/m queues. In the developed model of the problem, the constraints of selecting the nearest-facility along with the service level restriction are considered to bring the model closer to reality. Three objective functions are also considered including minimizing (I) sum of the aggregate travel and waiting times, (II) maximum idle time of all facilities, and (III) the budget required to cover the costs of establishing the selected facilities plus server staffing costs. Since the developed model of the problem is of an NP-hard type and inexact solutions are more probable to be obtained, soft computing techniques, specifically evolutionary computations, are generally used to cope with the lack of precision. From different terms of evolutionary computations, this paper proposes a Pareto-based meta-heuristic algorithm called multi-objective harmony search (MOHS) to solve the problem. To validate the results obtained, two popular algorithms including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are utilized as well. In order to demonstrate the proposed methodology and to compare the performances in terms of Pareto-based solution measures, the Taguchi approach is first utilized to tune the parameters of the proposed algorithms, where a new response metric named multi-objective coefficient of variation (MOCV) is introduced. Then, the results of implementing the algorithms on some test problems show that the proposed MOHS outperforms the other two algorithms in terms of computational time.     

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms.

     

A New Multi-objective Competitive Open Vehicle Routing Problem Solved by Particle Swarm Optimization

This paper presents a new variant of an open vehicle routing problem (OVRP), in which competition exists between distributors. In the OVRP with competitive time windows (OVRPCTW), the reaching time to customers affects the sales amount. Therefore, distributors intend to service customers earlier than rivals, to obtain the maximum sales. Moreover, a part of a driver??s benefit is related to the amount of sales; thus, the balance of goods carried in each vehicle is important in view of the limited vehicle capacities. In this paper, a new, multi-objective mathematical model of the homogeneous and competitive OVRP is presented, to minimize the travel cost of routes and to maximize the obtained sales while concurrently balancing the goods distributed among vehicles. This model is solved by the use of a multi-objective particle swarm optimization (MOPSO) algorithm, and the related results are compared with the results of NSGA-II, which is a well-known multi-objective evolutionary algorithm. A comparison of our results with three performance metrics confirms that the proposed MOPSO is an efficient algorithm for solving the competitive OVRP with a reasonable computational time and cost.     

基于Pareto邻域交叉算子的多目标粒子群优化算法

针对粒子群优化（PSO）算法局部搜索能力不足的问题,提出一种基于Pareto邻域交叉算子的多目标粒子群优化算法(MPSOP)。该算法利用粒子群优化算法和Pareto邻域交叉算子相结合的策略产生新种群,并利用尺度因子在线调节粒子群优化算法和Pareto邻域交叉算子的贡献量。数值实验选取6个常用测试函数并对NSGA-Ⅱ、SPEA2、MOPSO三个多目标算法进行比较,数值实验结果表明MPSOP算法的有效性。     

基于分解和差分进化的多目标粒子群优化算法

为了提高多目标优化算法解集的分布性和收敛性,提出一种基于分解和差分进化的多目标粒子群优化算法(dMOPSO-DE).该算法通过提出方向角产生一组均匀的方向向量,确保粒子分布的均匀性;引入隐式精英保持策略和差分进化修正机制选择全局最优粒子,避免种群陷入局部最优Pareto前沿;采用粒子重置策略保证群体的多样性.与非支配排序(NSGA-II)算法、多目标粒子群优化(MOPSO)算法、分解多目标粒子群优化(dMOPSO)算法和分解多目标进化-差分进化(MOEA/D-DE)算法进行比较,实验结果表明,所提出算法在求解多目标优化问题时具有良好的收敛性和多样性.     

批量生产柔性作业车间多目标精细化调度方法

提出了一种批量生产柔性作业车间多目标精细化调度方法。针对批量生产柔性作业车间多目标调度问题特点,建立了一类以完工时间最短和制造成本最低为优化目标的等量分批柔性作业车间调度多目标优化模型。提出了5种批量生产柔性作业车间精细化调度技术;设计了一种改进的NSGA II算法对模型进行求解。算法中引入面向对象技术处理复杂的实体逻辑关系,使用矩阵编码技术进行编码,采用分段交叉和分段变异的遗传算子实现遗传进化,应用上述5种精细化调度技术于解码过程以提高设备利用率。通过案例分析验证了该方法的有效性。     

基于多目标飞蛾算法的电力系统无功优化研究

鉴于电力需求的日益增长与传统无功优化方法的桎梏,如何更加合理有效地解决电力系统的无功优化问题逐渐成为了研究的热点。提出一种多目标飞蛾扑火算法来解决电力系统多目标无功优化的问题,算法引入固定大小的外部储存机制、自适应的网格和筛选机制来有效存储和提升无功优化问题的帕累托最优解集,算法采用CEC2009标准多目标测试函数来进行仿真实验,并与两种经典算法进行性能的对比分析。此外,在电力系统IEEE 30节点上将该算法与MOPSO,NGSGA-II算法的求解结果进行比较分析的结果表明,多目标飞蛾算法具有良好的性能,并在解决电力系统多目标无功优化问题上具有良好的潜力。     

A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms

In this paper, a bi-objective multi-product (r,Q) inventory model in which the inventory level is reviewed continuously is proposed. The aim of this work is to find the optimal value for both order quantity and reorder point through minimizing the total cost and maximizing the service level of the proposed model simultaneously. It is assumed that shortage could occur and unsatisfied demand could be backordered, too. There is a budget limitation and storage space constraint in the model. With regard to complexity of the proposed model, several Pareto-based meta-heuristic approaches such as multi-objective vibration damping optimization (MOVDO), multi-objective imperialist competitive algorithm (MOICA), multi-objective particle swarm optimization (MOPSO), non-dominated ranked genetic algorithm (NRGA), and non-dominated sorting genetic algorithm (NSGA-II) are applied to solve the model. In order to compare the results, several numerical examples are generated and then the algorithms were analyzed statistically and graphically.     

A multi-objective model for discovering high-quality knowledge based on data quality and prior knowledge

Discovering knowledge from data means finding useful patterns in data, this process has increased the opportunity and challenge for businesses in the big data era. Meanwhile, improving the quality of the discovered knowledge is important for making correct decisions in an unpredictable environment. Various models have been developed in the past; however, few used both data quality and prior knowledge to control the quality of the discovery processes and results. In this paper, a multi-objective model of knowledge discovery in databases is developed, which aids the discovery process by utilizing prior process knowledge and different measures of data quality. To illustrate the model, association rule mining is considered and formulated as a multi-objective problem that takes into account data quality measures and prior process knowledge instead of a single objective problem. Measures such as confidence, support, comprehensibility and interestingness are used. A Pareto-based integrated multi-objective Artificial Bee Colony (IMOABC) algorithm is developed to solve the problem. Using well-known and publicly available databases, experiments are carried out to compare the performance of IMOABC with NSGA-II, MOPSO and Apriori algorithms, respectively. The computational results show that IMOABC outperforms NSGA-II, MOPSO and Apriori on different measures and it could be easily customized or tailored to be in line with user requirements and still generates high-quality association rules.     

基于多层次信息交互的多目标粒子群优化算法

为提高多目标优化算法的收敛性和多样性,提出一种基于多层次信息交互的多目标粒子群优化算法.在该算法中,整个优化过程可分为标准粒子群优化层、粒子进化与学习层和档案信息交换层3个层次.粒子进化与学习层保证了每次迭代都能得到更好的粒子位置;档案信息交换层可以提供更好的全局最优.优化算法各个层次之间通过信息交互,共同提高算法的收敛性和多样性.与NSGA-Ⅱ和MOPSO算法的对比分析表明,所提出算法具有良好的性能,能够有效解决多目标优化问题.     

A particle swarm approach for optimizing a multi-stage closed loop supply chain for the solar cell industry

In order to implement sustainable strategies in a supply chain, enterprises should provide highly favorable and effective solutions for reducing carbon dioxide emissions, which brings out the issues of designing and managing a closed-loop supply chain (CLSC). This paper studies an integrated CLSC network design problem with cost and environmental concerns in the solar energy industry from sustainability perspectives. A multi-objective closed-loop supply chain design (MCSCD) model has been proposed, in consideration of many practical characteristics including flow conservation at each production/recycling unit of forward/reverse logistics (FL/RL), capacity expansion, and recycled components. A deterministic multi-objective mixed integer linear programming (MILP) model capturing the tradeoffs between the total cost and total CO₂ emissions was developed to address the multistage CSLC design problem. Subsequently, a multi-objective PSO (MOPSO) algorithm with crowding distance-based nondominated sorting approach is developed to search the near-optimal solution of the MCSCD model. The computational study shows that the proposed MOPSO algorithm is suitable and effective for solving large-scale complicated CLSC structure than the conventional branch-and-bound optimization approach. Analysis results show that an enterprise needs to apply an adequate recycling strategy or energy saving technology to achieve a better economic effectiveness if the carbon emission regulation is applied. Consequently, the Pareto optimal solution obtained from MOPSO algorithm may give the superior suggestions of CLSC design, such as factory location options, capacity expansion, technology selection, purchasing, and order fulfillment decisions in practice.     

求解差异机器平行批调度的双目标协同蚁群算法

利用用户的偏好信息, 提出一种基于蚁群的双目标协同优化算法(Bi-objective synergy ant colony optimization algorithm based on Pareto domination, PDACO)并用于求解平行批处理机调度问题. 考虑在一组差异容量并带有不同加工功率的平行批处理机器上, 加工带有不同到达时间、尺寸和加工时间的一组工件, 以同时最小化最大完工时间和总能耗. 偏好向量的引入虽然可以提高算法的收敛性, 但会降低解的多样性. 为了弥补这一缺陷, 在本文所提算法中, 利用两个子蚁群分别沿着不同方向, 迭代地进行独立和联合搜索. 最后, 通过大量的仿真实验验证了本文提出算法的有效性.     

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.

     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.