A hybrid project scheduling and material ordering problem: Modeling and solution algorithms

A novel combination of a multimode project scheduling problem with material ordering, in which material procurements are exposed to the total quantity discount policy is investigated in this paper. The study aims at finding an optimal Pareto frontier for a triple objective model derived for the problem. While the first objective minimizes the makespan of the project, the second objective maximizes the robustness of the project schedule and finally the third objective minimizes the total costs pertaining to renewable and nonrenewable resources involved in a project. Four well-known multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm II (SPEAII), multi objective particle swarm optimization (MOPSO), and multi objective evolutionary algorithm based on decomposition (MOEAD) solve the developed triple-objective problem. The parameters of algorithms are tuned by the response surface methodology. The algorithms are carried out on a set of benchmarks and are compared based on five performance metrics evaluating their efficiencies in terms of closeness to the optimal frontier, diversity, and variance of results. Finally, a statistical assessment is conducted to analyze the results obtained by the algorithms. Results show that the NSGAII considerably outperforms others in 4 out of 5 metrics and the MOPSO performs better in terms of the remaining metric.     

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.     

Multi-objective genetic algorithm and its applications to flowshop scheduling

In this paper, we propose a multi-objective genetic algorithm and apply it to flowshop scheduling. The characteristic features of our algorithm are its selection procedure and elite preserve strategy. The selection procedure in our multi-objective genetic algorithm selects individuals for a crossover operation based on a weighted sum of multiple objective functions with variable weights. The elite preserve strategy in our algorithm uses multiple elite solutions instead of a single elite solution. That is, a certain number of individuals are selected from a tentative set of Pareto optimal solutions and inherited to the next generation as elite individuals. In order to show that our approach can handle multi-objective optimization problems with concave Pareto fronts, we apply the proposed genetic algorithm to a two-objective function optimization problem with a concave Pareto front. Last, the performance of our multi-objective genetic algorithm is examined by applying it to the flowshop scheduling problem with two objectives: to minimize the makespan and to minimize the total tardiness. We also apply our algorithm to the flowshop scheduling problem with three objectives: to minimize the makespan, to minimize the total tardiness, and to minimize the total flowtime.     

Multiobjective model for solving resource‐leveling problem with discounted cash flows

Nowadays, executers are struggling to improve the economic and scheduling situation of projects. Construction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are inefficient and costly to implement on site. The objective of the resource‐leveling problem is to reduce resource fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, minimizing the discounted costs of resource fluctuations and minimizing the project makespan are considered in a multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the optimization problem is NP‐hard, we propose multiobjective evolutionary algorithms, namely nondominated sorting genetic algorithm‐II (NSGA‐II), strength Pareto evolutionary algorithm‐II (SPEA‐II), and multiobjective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order to study the performance of these algorithms, three criteria are proposed and compared with each other to demonstrate the strengths of each applied algorithm. To validate the results obtained for the suggested model, we compared the results of the first objective function with a well‐tuned genetic algorithm and differential algorithm, and we also compared the makespan results with one of the popular algorithms for the resource constraints project scheduling problem. Finally, we can observe that the NSGA‐II algorithm presents better solutions than the other two algorithms on average.     

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., C_max), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.     

多QoS约束的双目标最优的网格工作流调度研究*

针对当前网格工作流调度算法中大多只考虑DAG结构的网格工作流,涉及QoS参数较少或将多QoS参数聚合成一个单目标函数进行优化调度,提出了一种多QoS约束的双目标最优的网格工作流调度算法。该算法是基于AGWL网格工作流模型和改进的MOPSO算法,其目标是在满足可靠性、可利用性和声誉这三维QoS参数约束下,同时最小化两个冲突目标,即响应时间和服务费用。通过与原MOPSO所设计的网格工作流调度算法比较,该算法能获得更优的优化解。     

局部搜索与改进MOPSO的混合优化算法及其应用

为弥补粒子群后期收敛缓慢与早熟的不足,提出了一种局部搜索与改进MOPSO的混合优化算法(H-MOP- SO)。该算法首先采用非均匀变异算子和自适应惯性权重,强化全局搜索能力;继而建立混合算法模型,并利用侧步 爬山搜索算法对粒子群作周期性优化,使远离前沿的粒子朝下降方向搜索,而靠近前沿的粒子朝非支配方向搜索,加 快粒子群的收敛并改善解集多样性。对标准测试函数的求解表明,该算法比MOPSO, NSGA-II和MOEA/D具有更 好的多样性和收敛性。供应商优选问题的求解进一步验证了H-MOPSO的有效性。     

Robust RST control design based on Multi-Objective Particle Swarm Optimization approach

In this paper, a novel method for the digital two-Degrees-Of-Freedom (2DOF) controller design, called canonical RST structure, is proposed and successfully implemented based on a Multi-Objective Particle Swarm Optimization (MOPSO) approach. This is a polynomial control structure allowing independently the regulation and the tracking of discrete-time systems. An application to the variable speed control of an electrical DC Drive is investigated. The RST design and tuning problem is formulated as a multi-objective optimization problem. The proposed MOPSO algorithm which is based on the Pareto dominance is used to identify the non-dominated solutions. This approach used the leader selection strategy that is called a geographically-based system. In addition, the adaptive grid method is used to produce well-distributed Pareto fronts in the multi-objective formalism. The well known NSGA-II and the proposed MOPSO algorithms are evaluated and compared with each other in terms of several performance metrics in order to show the superiority and the effectiveness of the proposed method. Simulation results demonstrate the advantages of the MOPSO-tuned RST control structure in terms of performance and robustness.

     

云环境中基于分解的多目标工作流调度算法

云服务提供商在给用户提供海量虚拟资源的同时,也面临着一个现实的问题,即怎样调度这些资源,以最小的代价(完工时间、执行费用、资源利用率等)完成工作流的执行。针对IaaS环境下的工作流调度问题,以完工时间和执行费用作为目标,提出了一种基于分解的多目标工作流调度算法。该算法结合了基于列表的启发式算法和多目标进化算法的选择过程,采用一种分解方法,将多目标优化问题分解为一组单目标优化子问题,然后同时求解这些单目标子问题,使得调度过程更为简单有效。算法利用天马项目发布的现实世界中的工作流进行实验,结果表明,和MOHEFT算法以及NSGA-II*算法相比较,所提出的算法能得到更优的Pareto解集,同时具有更低的时间复杂度。     

A bi-objective integrated procurement,production, and distribution problem of a multi-echelon supply chain network design: A new tuned MOEA

Efficient management of supply chain (SC) requires systematic considerations of miscellaneous issues in its comprehensive version. In this paper, a multi-periodic structure is developed for a supply chain network design (SCND) involving suppliers, factories, distribution centers (DCs), and retailers. The nature of the logistic decisions is tactical that encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to retailers via DCs, and the storage of raw materials and end product at factories and DCs. Besides, to make the structure more comprehensive, a flow-shop scheduling model in manufacturing part of the SC is integrated in order to obtain optimal delivery time of the product that consists of the makespan and the ship time of the product to DCs via factories. Moreover, to make the model more realistic, shortage in the form of backorder can occur in each period. The two objectives are minimizing the total SC costs as well as minimizing the average tardiness of product to DCs. The obtained model is a bi-objective mixed-integer non-linear programming (MINLP) model that is shown to belong to NP-Hard class of the optimization problems. Thus, a novel algorithm, called multi-objective biogeography based optimization (MOBBO) with tuned parameters is presented to find a near-optimum solution. As there is no benchmark available in the literature, the parameter-tuned multi-objective simulated annealing algorithm (MOSA) and the popular non-dominated sorting genetic algorithm (NSGA-II) are developed to validate the results obtained and to evaluate the performance of MOBBO using randomly generated test instances.     

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.     

求解不相关并行机调度问题的十进制多目标灰狼算法

针对不相关并行机调度问题,面向降低能源消耗和减少完工时间的目标,提出一种更高效的基于十进制整数编码的多目标灰狼算法.求解时,采用将资源配置与作业排序相结合的十进制整数编码方式,设计了针对多目标离散调度问题的两阶段位置更新机制.同时引入了N S GA-Ⅱ的精英保留策略,提高了算法的寻优能力,应用最大迭代次数停止准则结束循环并保留最优解.最后,通过数值实验与有代表性的前沿算法进行仿真对比,以验证所提算法的可行性与有效性.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

多目标优化在特征选择子集评价中的应用

特征选择是处理高维大数据常用的降维手段,但其中牵涉到的多个彼此冲突的特征子集评价目标难以平衡。为综合考虑特征选择中多种子集评价方式间的折中,优化子集性能,提出一种基于子集评价多目标优化的特征选择框架,并重点对多目标粒子群优化（MOPSO）在特征子集评价中的应用进行了研究。该框架分别根据子集的稀疏度、分类能力和信息损失度设计多目标优化函数,继而基于多目标优化算法进行特征权值向量寻优,并通过权值向量Pareto解集膝点选取确定最优向量,最终实现基于权值向量排序的特征选择。设计实验对比了基于多目标粒子群优化算法的特征选择（FS_MOPSO）与四种经典方法的性能,多个数据集上的结果表明,FS_MOPSO在低维空间表现出更高的分类精度,并保证了更少的信息损失。     

Genetic algorithms in integrated process planning and scheduling

Process planning and scheduling are actually interrelated and should be solved simultaneously. Most integrated process planning and scheduling methods only consider the time aspects of the alternative machines when constructing schedules. The initial part of this paper describes a genetic algorithm (GA) based algorithm that only considers the time aspect of the alternative machines. The scope of consideration is then further extended to include the processing capabilities of alternative machines, with different tolerance limits and processing costs. In the proposed method based on GAs, the processing capabilities of the machines, including processing costs as well as number of rejects produced in alternative machine are considered simultaneously with the scheduling of jobs. The formulation is based on multi-objective weighted-sums optimization, which are to minimize makespan, to minimize total rejects produced and to minimize the total cost of production. A comparison is done w ith the traditional sequential method and the multi-objective genetic algorithm (MOGA) approach, based on the Pareto optimal concept.     

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.     

变邻域遗传算法在车间物流调度中的应用

针对含有自动引导小车(Automated Guided Vehicle,AGV)的离散化车间物流调度问题,以最小化物流任务时间惩罚成本和最小化运载小车的总行驶距离为优化目标,构建离散化车间多目标物流调度优化模型,设计一种基于Pareto寻优的多目标混合变邻域搜索遗传算法(VNSGA-II).以遗传算法为基础,通过使用NSGA-II的Pareto分层和拥挤度计算方法评估种群优劣实现多目标优化,为了提高算法的寻优能力,避免算法陷入局部最优,通过添加保优记忆库对精英个体进行保护,并利用变邻域搜索算法在搜索过程中的局部寻优能力,针对本文模型特点,设计6个随机邻域结构,来达到算法求解最优值的目标.并提出了基于关键AGV小车的插入邻域和基于关键物流任务的交换邻域调整策略以进一步降低成本.最后,以某离散车间物流调度为实例,分别使用VNSGA-II、带精英策略的快速非支配排序遗传算法Ⅱ(Nondominated Sorting Genetic AlgorithmⅡ,NSGA-II)和强Pareto进化算法(Strong Pareto Evolutionary Algorithm 2,SPEA2)对问题进行求解,计算结果表明,VNSGA-II能得到更好的Pareto解集,验证了算法的有效性和可行性.     

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.     

Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment

In this study, an integrated multi-objective production-distribution flow-shop scheduling problem will be taken into consideration with respect to two objective functions. The first objective function aims to minimize total weighted tardiness and make-span and the second objective function aims to minimize the summation of total weighted earliness, total weighted number of tardy jobs, inventory costs and total delivery costs. Firstly, a mathematical model is proposed for this problem. After that, two new meta-heuristic algorithms are developed in order to solve the problem. The first algorithm (HCMOPSO), is a multi-objective particle swarm optimization combined with a heuristic mutation operator, Gaussian membership function and a chaotic sequence and the second algorithm (HBNSGA-II), is a non-dominated sorting genetic algorithm II with a heuristic criterion for generation of initial population and a heuristic crossover operator. The proposed HCMOPSO and HBNSGA-II are tested and compared with a Non-dominated Sorting Genetic Algorithm II (NSGA-II), a Multi-Objective Particle Swarm Optimization (MOPSO) and two state-of-the-art algorithms from recent researches, by means of several comparing criteria. The computational experiments demonstrate the outperformance of the proposed HCMOPSO and HBNSGA-II.     

A dynamic closed-loop location-inventory problem under disruption risk

In this paper, a dynamic closed-loop location-inventory problem is addressed that optimizes strategic decisions (i.e., facility location in terms of contracting/selection of distribution centers and reworking centers) along with tactical ones (i.e., allocation of centers, inventory management) under facility disruption risks. The presented model seeks to minimize total cost as the first objective function, and time as the second one in the considered network. Due to the NP-Hard nature of the model, a hybrid meta-heuristic algorithm based on Multi-Objective Particle Swarm Optimization (MOPSO) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is presented to solve the problem in large scales. Finally, applicability of the proposed model is tested via a real case study and the results are analyzed in depth.