A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

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.     

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.     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

多目标粒子群算法在交叉培训规划中的应用

为了进一步提高人力资源交叉培训规划的实用性,增加了对于员工学习行为的考虑,提出了在保证任务覆盖水平的基础上,获得员工满意度最大和学习效率最高的多目标优化模型.本文针对问题的特征,采用多目标粒子群(MOPSO)算法对多目标优化模型进行了求解,并设计了多种算法策略,以适应不同的问题环境.通过数值实验,分析了不同问题规模下,针对不同性能指标算法参数和策略的适用性.最后,以柔性单元装配生产线为例,进行了数值实验,实验结果表明了模型的有效性和合理性.     

基于多目标粒子群算法的混合流水车间调度方法研究

混合流水车间调度问题HFSP是一种具有很强应用背景的生产调度问题。本文给出了一种HFSP多目标调度模型,提出了一种针对该类问题的多目标粒子群算法。该算法采用基于Pareto支配关系的极值更新策略;采取对自适应惯性权重递减和对种群变异的方法以保持种群多样性;设置Pareto解池保存计算中出现的Pareto最优解,并提出了一种基于适应度拥挤度的聚类算法优化解的分布特性。实验结果表明,本文算法是求解HFSP问题的一种有效方法。     

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.

     

Multi-Objective Optimization of Slow Moving Inventory System Using Cuckoo Search

This paper focuses on the development of a multi-objective lot size–reorder point backorder inventory model for a slow moving item. The three objectives are the minimization of (1) the total annual relevant cost, (2) the expected number of stocked out units incurred annually and (3) the expected frequency of stockout occasions annually. Laplace distribution is used to model the variability of lead time demand. The multi-objective Cuckoo Search (MOCS) algorithm is proposed to solve the model. Pareto curves are generated between cost and service levels for decision-makers. A numerical problem is considered on a slow moving item to illustrate the results. Furthermore, the performance of the MOCS algorithm is evaluated in comparison to multi-objective particle swarm optimization (MOPSO) using metrics, such as error ratio, maximum spread and spacing.     

寻求“理想” 解的改进多目标粒子群优化算法

如何在众多非劣解中为决策者推荐一个合理的方案是使用多目标粒子群算法(MOPSO) 所面临的问题. 为此, 将逼近理想解的排序方法(TOPSIS 策略) 引入到算法中. 为了提高求解精度和均匀性, 还提出了基于Pbest 的变异策略和改进的?? 邻近距离策略. 测试结论显示, 仅使用TOPSIS 策略确定Gbest 的算法, 求解精度虽好, 但均匀性较差, 而包含所有改进策略的算法在精度和均匀性方面都更优, 并且能够按照TOPSIS 方法在非劣解集中找到一个适合向决策者推荐的“理想” 方案.

     

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.     

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.     

Multi-objective optimization of hybrid backorder inventory model

This paper addresses inventory problem for the products that are sold in monopolistic and captive markets experiencing hybrid backorder (i.e., fixed backorder and time-weighted backorder). The problem with stochastic demand is studied first by developing single objective (cost) inventory model. Computational results of a numerical problem show the effectiveness of hybrid backorder inventory model over fixed backorder inventory model. The model is later extended to multi-objective inventory model. Three objectives of multi-objective inventory model are the minimization of total cost, minimization of stockout units and minimization of the frequency of stockout. A multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the inventory model and generate Pareto curves. The Pareto curves obtained for hybrid backorder inventory model are compared with the existing Pareto curves that are based on fixed backorder. The results show a substantial reduction in stockout units and frequency of stockout with a marginal rise in cost with proposed hybrid backorder inventory system in comparison to existing fixed backorder inventory system. Sensitivity analysis is done to study the robustness of total cost, order quantity, and safety stock factor with the change in holding cost. In the end, the performance of the MOPSO algorithm is compared with the multi-objective genetic algorithm (MOGA). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread.     

基于协作频谱感知的智能电网通信网性能研究

将认知无线电频谱感知技术应用于智能电网的通信网中,可以有效提高频谱资源的利用率。现有研究仅考虑单用户单供电商,但是对需求响应管理性能与感知能耗权衡问题却没有给出理想的解决方案。建立基于多节点协作频谱感知的多用户单供电商智能电网通信网模型。在此基础上,为求解该模型需求响应管理和能耗感知性能权衡问题,提出基于多目标粒子群(MOPSO)的求解方法。仿真结果表明,所提协作频谱感知模型可以显著提高系统需求响应管理性能;MOPSO算法可实现系统需求响应管理性能和感知能耗的最佳权衡,有利于决策者根据实际要求灵活选择最优方案。     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

Simple heuristics-based selection of guides for multi-objective PSO with an application to electrical distribution system planning

In multi-objective particle swarm optimization (MOPSO), a proper selection of local guides significantly influences detection of non-dominated solutions in the objective/solution space and, hence, the convergence characteristics towards the Pareto-optimal set. This paper presents an algorithm based on simple heuristics for selection of local guides in MOPSO, named as HSG-MOPSO (Heuristics-based-Selection-of-Guides in MOPSO). In the HSG-MOPSO, the set of potential guides (in a PSO iteration) consists of the non-dominated solutions (which are normally stored in an elite archive) and some specifically chosen dominated solutions. Thus, there are two types of local guides in the HSG-MOPSO, i.e., non-dominated and dominated guides; they are named so as to signify whether the chosen guide is a non-dominated or a dominated solution. In any iteration, a guide, from the set of available guides, is suitably selected for each population member. Some specified proportion of the current population members follow their respective nearest non-dominated guides and the rest follow their respective nearest dominated guides. The proposed HSG-MOPSO is firstly evaluated on a number of multi-objective benchmark problems along with investigations on the controlling parameters of the guide selection algorithm. The performance of the proposed method is compared with those of two well-known guide selection methods for evolutionary multi-objective optimization, namely the Sigma method and the Strength Pareto Evolutionary Algorithm-2 (SPEA2) implemented in PSO framework. Finally, the HSG-MOPSO is evaluated on a more involved real world problem, i.e., multi-objective planning of electrical distribution system. Simulation results are reported and analyzed to illustrate the viability of the proposed guide selection method for MOPSO.     

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.     

Comparisons of some improving strategies on MOPSO for multi-objective (r, Q) inventory system

This paper presents comparisons of some recent improving strategies on multi-objective particle swarm optimization (MOPSO) algorithm which is based on Pareto dominance for handling multiple objective in continuous review stochastic inventory control system. The complexity of considering conflict objectives such as cost minimization and service level maximization in the real-world inventory control problem needs to employ more exact optimizers generating more diverse and better non-dominated solutions of a reorder point and order size system. At first, we apply the original MOPSO employed for the multi-objective inventory control problem. Then we incorporate the mutation operator to maintain diversity in the swarm and explore all the search space into the MOPSO. Next we change the leader selection strategy used that called geographically-based system (Grids) and instead of that, crowding distance factor is also applied to select the global optimal particle as a leader. Also we use ε-dominance concept to bound archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. Finally, the MOPSO algorithms created using these strategies are evaluated and compared with each other in terms of some performance metrics taken from the literature. The results indicate that these strategies have significant influences on computational time, convergence, and diversity of generated Pareto optimal solutions.     

基于多目标粒子群–稀疏提升算法的电网频率反馈优化控制

频率反馈控制策略是维持电网频率稳定性的主要手段.本文建立了频率反馈控制系数和电网拓扑与电网频率稳定性的小信号分析模型,推导得出了能改善电网频率稳定性的频率反馈控制系数的参数范围.提出了基于多目标粒子群的稀疏提升算法(multi-objective particle swarm optimization sparse promoting algorithm, MOPSO–SPA),进行频率反馈控制系数矩阵的优化,提高了电网频率响应性能并降低了成本代价.用本文提出的算法设计了IEEE–39标准测试系统和陕北局部电网的频率反馈控制系数,并进行仿真对比,验证了算法的高效性和优越性.     

基于MOPSO与凸优化算法的稀布圆阵列方向图优化

为了降低稀布阵列的峰值旁瓣电平并抑制稀布阵列的栅瓣,提出了一种多目标粒子群与凸优化相结合的方向图综合算法。该算法将多目标粒子群优化(Multi-objective particles swarm optimization,MOPSO)作为全局搜索器,凸优化算法作为局部搜索器来搜索最优解,优化的变量不仅是阵元的权值,而且还加入了阵元位置这一参数,从而能够提供更多的自由度来控制稀布阵列的性能。基于30阵元的稀布圆形阵列的仿真结果表明：与单纯使用MOPSO算法相比,本文提出的用MOPSO算法优化阵元位置,凸优化算法优化阵元权值的联合优化算法,得到的栅瓣和峰值旁瓣电平都小于-19.3　dB。     

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.