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.     

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.     

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.     

The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms

This paper compares the effectiveness of five state-of-the-art multiobjective evolutionary algorithms (MOEAs) together with a steady state evolutionary algorithm on the mean–variance cardinality constrained portfolio optimization problem (MVCCPO). The main computational challenges of the model are due to the presence of a nonlinear objective function and the discrete constraints. The MOEAs considered are the Niched Pareto genetic algorithm 2 (NPGA2), non-dominated sorting genetic algorithm II (NSGA-II), Pareto envelope-based selection algorithm (PESA), strength Pareto evolutionary algorithm 2 (SPEA2), and e-multiobjective evolutionary algorithm (e-MOEA). The computational comparison was performed using formal metrics proposed by the evolutionary multiobjective optimization community on publicly available data sets which contain up to 2196 assets.     

Extraction of decision alternatives in construction management projects: Application and adaptation of NSGA-II and MOPSO

The time-cost trade-off problem is a known bi-objective problem in the field of project management. Recently, a new parameter, the quality of the project has been added to previously considered time and cost parameters. The main specification of the time-cost trade-off problem is discretization of the decision space to limited and accountable decision variables. In this situation the efficiency of the traditional methods decrease and applying of the evolutionary algorithms is necessary. In this paper, two evolutionary algorithms that originally search the decision space in a continuous manner including: (1) multi-objective particle swarm optimization (MOPSO) and (2) nondominated sorting genetic algorithm (NSGA)-II, are considered as the optimization tools to solve two construction project management problems. These problems are both in discrete domain including two or tree objectives, separately. In this regard, some procedures has been suggested and then applied to adopt both algorithms capable in solving the problems in a discrete domain. Results show the advantages and effectiveness of the used procedures in reporting the optimal Pareto for the optimization problems. Moreover, the NSGA-II is more successful in determining optimal alternatives in both time-cost trade-off (TCTO) and time-cost-quality trade-off (TCQTO) problems than the MOPSO algorithm.     

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.     

基于Pareto最优解集的多目标粒子群优化算法

本文结合Pareto支配思想、精英保留策略、锦标赛和排挤距离选择技术,对传统的粒子更新策略进行改进,给出了一种新的粒子淘汰准则,提出了一种基于Pareto最优解集的多目标粒子群优化算法。最后,通过7个多目标标准测试函数进行测试。测试结果表明,该方法有效可行,其性能优于如NSGAII、SPEA2等多目标优化算法。     

Automatic clustering algorithm based on multi-objective Immunized PSO to classify actions of 3D human models

Multi-objective clustering algorithms are preferred over its conventional single objective counterparts as they incorporate additional knowledge on properties of data in the from of objectives to extract the underlying clusters present in many datasets. Researchers have recently proposed some standardized multi-objective evolutionary clustering algorithms based on genetic operations, particle swarm optimization, clonal selection principles, differential evolution and simulated annealing, etc. In many cases it is observed that hybrid evolutionary algorithms provide improved performance compared to that of individual algorithm. In this paper an automatic clustering algorithm MOIMPSO (Multi-objective Immunized Particle Swarm Optimization) is proposed, which is based on a recently developed hybrid evolutionary algorithm Immunized PSO. The proposed algorithm provides suitable Pareto optimal archive for unsupervised problems by automatically evolving the cluster centers and simultaneously optimizing two objective functions. In addition the algorithm provides a single best solution from the Pareto optimal archive which mostly satisfy the users' requirement. Rigorous simulation studies on 11 benchmark datasets demonstrate the superior performance of the proposed algorithm compared to that of the standardized automatic clustering algorithms such as MOCK, MOPSO and MOCLONAL. An interesting application of the proposed algorithm has also been demonstrated to classify the normal and aggressive actions of 3D human models.     

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.

     

基于海明差异评价的多目标进化算法

为提高多目标进化算法的分布性和收敛性,提出一种基于海明距离差异的多目标进化算法。在非支配前沿的基础上定义海明等级,依据海明距离的大小对个体进行选择操作。同时结合海明差异和Pareto评价方法,对外部存储器中最优解进行更新和维护,通过结构相似度构建小生境空间,并引导算法趋向Pareto最优前沿面。对6个典型函数的测试结果表明,较其他对比算法,该算法在具备收敛性的同时能够保持较好的均匀性分布。     

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.     

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.     

基于动态调整的多目标粒子群优化算法

为了改善多目标粒子群优化算法生成的最终Pareto前端的多样性和收敛性,提出了一种针对多目标粒子群算法进化状态的检测机制.通过对外部Pareto解集的更新情况进行检测,进而评估算法的进化状态,获取反馈信息来动态调整进化策略,使得算法在进化过程中兼顾近似Pareto前端的多样性和收敛性.最后,在ZDT系列测试函数中,将本文算法与其他4种对等算法比较,证明了本文算法生成的最终Pareto前端在多样性和收敛性上均有显著的优势.     

基于网格排序的多目标粒子群优化算法

在多目标进化算法中,近年的研究倾向于基于Pareto支配的最优化方法.针对传统的基于Pareto支配在排序效率上过低的问题,提出了一种基于网格排序的框架,利用网格同时表征收敛性与分布性的特性,结合粒子群算法,提出了一种基于网格排序的多目标粒子群优化算法.与个体两两进行比较的基于Pareto支配的策略不同,基于网格排序的机制融合了整个解空间中个体的占优信息,并利用占优信息进行排序,从而高效地得到个体在种群中的优劣关系;结合粒子到近似最优边界的距离,进一步加强了粒子在解空间中优劣关系的判别.对比实验分析表明：所提算法不论是在收敛性还是分布性上都具有较好的优势.在此基础上,讨论了网格划分数对算法效率的影响,从另一方面验证了算法的效率.     

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.     

Pareto optimal sensor locations for structural identification

Theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed. The objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling. For a single model class, the information entropy is used as the optimality criterion for selecting the best sensor configuration. For multiple model classes, the problem is formulated as a multi-objective optimization problem of finding the Pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices. A heuristic algorithm is proposed for constructing effective Pareto optimal sensor configurations that are superior, in terms of computational efficiency and accuracy, to the Pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi-objective optimisation problems. The theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10-DOF chain-like spring mass model and a 32-DOF truss structure.     

The assessment of evolutionary algorithms for analyzing the positional accuracy and uncertainty of maps

Pre-geodetic maps are an important part of our cultural heritage and a potential source of information for historical studies. Historical cartography should be evaluated in terms of precision and uncertainty prior to their use in any application. In the last decade, the majority of papers that address multi-objective optimization employed the concept of Pareto optimality. The goal of Pareto-based multi-objective strategies is to generate a front (set) of nondominated solutions as an approximation to the true Pareto-optimal front. This article proposes a solution for the problems of multi-objective accuracy and uncertainty analysis of pre-geodetic maps using four Pareto-based multi-objective evolutionary algorithms: HVSEA, NSGAII, SPEAII and msPESA. “The Geographic Atlas of Spain (AGE)” by Tomas Lopez in 1804 provides the cartography for this study. The results obtained from the data collected from the kingdoms of Extremadura and Aragon, sheets of maps (54-55-56-57) and (70-71-72-73), respectively, demonstrate the advantages of these multi-objective approaches compared with classical methods. The results show that the removal of 8% of the towns it is possible to obtain improvements of approximately 30% for HVSEA, msPESA and NSGAII. The comparison of these algorithms indicates that the majority of nondominated solutions obtained by NSGAII dominate the solutions obtained by msPESA and HVSEA; however, msPESA and HVSEA obtain acceptable extreme solutions in some instances. The Pareto fronts based on multi-objective evolutionary algorithms (MOEAs) are a better alternative when the uncertainty of map analyzed is high or unknown. Consequently, Pareto-based multi-objective evolutionary algorithms establish new perspectives for analyzing the positional accuracy and uncertainty of maps.     

基于平衡搜索策略的多目标粒子群优化算法*

鉴于平衡全局和局部搜索在多目标粒子群优化算法获取完整均匀Pareto最优前沿方面的重要性,设计平衡全局和局部搜索策略,进而提出改进的多目标粒子群优化算法(bsMOPSO).文中策略在局部搜索方面设计归档集自挖掘子策略,通过对归档集中均匀分布的部分粒子进行柯西扰动,使归档集涵盖整个前沿面的局部搜索.在全局搜索方面设计边界最优粒子引导搜索子策略,以边界最优粒子替换部分粒子的全局最优解,引导粒子向各维目标的边界区域搜索.选取4种对比算法在ZDT和DTLZ系列的部分测试函数上进行实验,结果表明bsMOPSO具有更快的Pareto最优前沿收敛效率和更好的分布性.     

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。     

A multi-objective artificial physics optimization algorithm based on ranks of individuals

This paper proposes a multi-objective artificial physics optimization algorithm based on individuals’ ranks. Using a Pareto sorting based technique and incorporating the concept of neighborhood crowding degree, evolutionary individuals in the search space are evaluated at first. Then each individual is assigned a unique serial number in terms of its performance, which affects the mass of the individual. Thereby, the population evolves towards the direction of the Pareto-optimal front. Synchronously, the presented approach has good diversity, such that the population is spread evenly on the Pareto front. Results of simulation on a number of difficult test problems show that the proposed algorithm, with less evolutionary generations, is able to find a better spread of solutions and better convergence near the true Pareto-optimal front compared to classical multi-objective evolutionary algorithms (NSGA, SPEA, MOPSO) and to simple multi-objective artificial physics optimization algorithm.