Multi-objective optimization of double suction centrifugal pump using Kriging metamodels

This paper proposes a new multi-objective optimization method for a family of double suction centrifugal pumps with various blade shapes, using a Simulation-Kriging model-Experiment (SKE) approach. The Kriging metamodel is established to approximate the characteristic performance functions of a pump, namely, the efficiency and required net positive suction head (NPSHr). Hence, the two objectives are to maximize the efficiency and simultaneously to minimize NPSHr. The Non-dominated Sorting Genetic Algorithm II (NSGA II) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) have been applied to the multi-objective optimization problem, respectively. The Pareto solution set is obtained by a more effective and efficient manner of the two multi-objective optimization algorithms. A tradeoff optimal design point is selected from the Pareto solution set by means of a robust design based on Monte Carlo simulations, and the optimal solution is further compared with the value of the physical prototype test. The results show that the solution of the proposed multi-objective optimization method is in line with the experiment test.     

A robust fuzzy multi-objective location-routing problem for hazardous waste under uncertain conditions

Industrialization and population growth have been accompanied by many problems such as waste management worldwide. Waste management and reduction have a vital role in national management. The presents study represents a multi-objective location-routing problem for hazardous wastes. The model was solved using Non dominated Sorting Genetic Algorithm-II, Multi-Objective Particle Swarm Optimization, Multi-Objective Invasive Weed Optimization, Pareto Envelope-based Selection Algorithm, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer algorithms. The findings revealed that the Multi-Objective Invasive Weed Optimization algorithm was the best and the most efficient among the algorithms used in this study. Obtaining income from the incineration of the wastes and reducing the risk of COVID-19 infection are the first innovation of the present study, which considered in the presented model. The second innovation is that uncertainty was considered for some of the crucial parameters of the model while the robust fuzzy optimization model was applied. Besides, the model was solved using several meta-heuristic algorithms such as Multi-Objective Invasive Weed Optimization, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer, which were rarely used in literature. Eventually, the most efficient algorithm was identified by comparing the considered algorithms.

     

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.     

自适应邻域的多目标网格任务调度算法研究

针对网格计算中的多目标网格任务调度问题,提出了一种基于自适应邻域的多目标网格任务调度算法。该算法通过求解多个网格任务调度目标函数的非劣解集,采用自适应邻域的方法来保持网格任务调度多目标解集的分布性,尝试解决网格任务调度中多目标协同优化问题。实验结果证明,该算法能够有效地平衡时间维度和费用维度目标,提高了资源的利用率和任务的执行效率,与Min-min和Max-min算法相比具有较好的性能。     

基于多策略融合的混合多目标蝗虫优化算法

为提高蝗虫优化算法（GOA）求解多目标问题的性能,提出一种基于多策略融合的混合多目标蝗虫优化算法（HMOGOA）。首先,利用Halton序列建立初始种群,保证种群在初始阶段具有均匀分布和较高多样性;然后,通过差分变异算子引导种群变异,促进种群向优势个体移动同时进行更大范围寻优;最后,利用自适应权重因子根据种群优化情况动态调整算法全局搜索和局部寻优能力,提高优化效率及解集质量。选取7个典型函数进行实验测试,并将HMOGOA与多目标蝗虫优化、多目标粒子群（MOPSO）、基于分解的多目标进化（MOEA/D）及非支配排序遗传算法（NSGA Ⅱ）对比分析。实验结果表明,该算法避免了其他四种算法的局部最优问题,明显提高了解集分布均匀性和分布广度,具有更好的收敛精度和稳定性。     

基于多策略融合的混合多目标蝗虫优化算法

为提高蝗虫优化算法（GOA）求解多目标问题的性能，提出一种基于多策略融合的混合多目标蝗虫优化算法（HMOGOA）。首先，利用Halton序列建立初始种群，保证种群在初始阶段具有均匀分布和较高多样性；然后，通过差分变异算子引导种群变异，促进种群向优势个体移动同时进行更大范围寻优；最后，利用自适应权重因子根据种群优化情况动态调整算法全局搜索和局部寻优能力，提高优化效率及解集质量。选取7个典型函数进行实验测试，并将HMOGOA与多目标蝗虫优化、多目标粒子群（MOPSO）、基于分解的多目标进化（MOEA/D）及非支配排序遗传算法（NSGA Ⅱ）对比分析。实验结果表明，该算法避免了其他四种算法的局部最优问题，明显提高了解集分布均匀性和分布广度，具有更好的收敛精度和稳定性。     

Multidisciplinary design of a guided flying vehicle using simplex nondominated sorting genetic algorithm II

This paper presents design of a typical Guided Flying Vehicle (GFV) using the multidisciplinary design optimization (MDO). The main objectives of this multi-disciplinary design are maximizing the payload’s weight as well as minimizing the miss distance. The main disciplines considered for this design include aerodynamics, dynamic, guidance, control, structure, weight and balance. This design of GFV is applied to three and six Degree of Freedom (DOF) to show comparison of simulation results. The hybrid scheme of optimization algorithm is based on Nelder-Mead Simplex optimization algorithm and Nondominated Sorting Genetic Algorithm II (NSGA II), called Simplex-NSGA II. This scheme is implemented for finding an optimal solution through the MDO. The Simplex-NSGA II method is a heuristic optimization algorithm that applies to multi-objective functions and the results are then compared with the most famous algorithms, like Nondominated Sorting Genetic Algorithm II (NSGA II) and Multi-Objective Particle Swarm Optimization (MOPSO). Simulation results demonstrate the superior performance of the Simplex-NSGA II over NSGA II and MOPSO. Also, it is used in this study in order to achieve an optimal solution using MDO in both 3DOF and 6DOF simulations of GFV to reach desirable performance index.     

Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization

Due to the novelty of the Grey Wolf Optimizer (GWO), there is no study in the literature to design a multi-objective version of this algorithm. This paper proposes a Multi-Objective Grey Wolf Optimizer (MOGWO) in order to optimize problems with multiple objectives for the first time. A fixed-sized external archive is integrated to the GWO for saving and retrieving the Pareto optimal solutions. This archive is then employed to define the social hierarchy and simulate the hunting behavior of grey wolves in multi-objective search spaces. The proposed method is tested on 10 multi-objective benchmark problems and compared with two well-known meta-heuristics: Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) and Multi-Objective Particle Swarm Optimization (MOPSO). The qualitative and quantitative results show that the proposed algorithm is able to provide very competitive results and outperforms other algorithms. Note that the source codes of MOGWO are publicly available at http://www.alimirjalili.com/GWO.html.     

救灾物资高维多目标自适应分配问题建模与求解

针对救灾物资分配中效率和公平性的均衡问题,提出一种基于二维整数编码的高维多目标自适应分配算法。首先构建了一个综合考虑应急响应总时间、灾民恐慌度、救灾物资未满足度、物资分配公平性、灾民损失、应急响应总成本的高维多目标优化模型,然后采用二维整数编码和自适应个体修正（AIR）解决潜在的应急资源冲突,最后引入移位密度估计和第二代强度帕累托进化算法（SPEA2）设计了一个救灾物资高维多目标分配算法。在仿真实验中,与带有编码修正机制的非支配排序差异演化算法（ERNS-DE）和基于贪心搜索的多目标遗传算法（GSMOGA）相比,所提算法在两种应急环境中的覆盖值分别提高了34.87%、100%和23.59%、100%,同时所提算法的超体积值也远远高于两种对比算法。实验结果表明,所提模型和算法可以让决策者根据实际应急需求选择应急方案,具有更好的灵活性和求解效率。     

改进的排序变异多目标差分进化算法

针对多目标差分进化算法在求解问题时收敛速度慢和均匀性欠佳的问题,提出了一种改进的排序变异多目标差分进化算法（MODE-IRM）。该算法将参与变异的三个父代个体中的最优个体作为基向量,提高了排序变异算子的求解速度;另外,算法采用反向参数控制方法在不同的优化阶段动态调整参数值,进一步提高了算法的收敛速度;最后,引入了改进的拥挤距离计算公式进行排序操作,提高了解的均匀性。采用标准多目标优化问题ZDTl~ZDT4,ZDT6和DTLZ6~DTLZ7进行仿真实验:MODE-IRM在总体性能上均优于MODE-RMO和PlatEMO平台上的MOEA/D-DE、RM-MEDA以及IM-MOEA;在世代距离（GD）、反向世代距离（IGD）和间隔指标（SP）性能度量指标方面,MODE-IRM在所有优化问题上的均值和方差均明显小于MODE-RMO。实验结果表明MODE-IRM在收敛性和均匀性指标上明显优于对比算法。     

Near optimal process plan selection for multiple jobs in networked based manufacturing using multi-objective evolutionary algorithms

The networked manufacturing offers several advantages in current competitive atmosphere by way of reducing the manufacturing cycle time and maintenance of the production flexibility, thereby achieving several feasible process plans. In this paper, we have addressed a Multi Objective Problem (MOP) which covers-minimize the makespan and to maximize the machine utilization while generating the feasible process plans for multiple jobs in the context of network based manufacturing system. A new multi-objective based Territory Defining Evolutionary Algorithm (TDEA) to resolve the above computationally challenge problem have been developed. In particular, with two powerful Multi-Objective Evolutionary Algorithms (MOEAs), viz. Non-dominated Sorting Genetic Algorithm (NSGA-II) and Controlled Elitist-NSGA-II (CE-NSGA-II) the performance of the proposed TDEA has been compared. An illustrative example along with three complex scenarios is presented to demonstrate the feasibility of the approach. The proposed algorithm is validated and the results are analyzed and compared.     

Case-base maintenance with multi-objective evolutionary algorithms

Case-Base Reasoning is a problem-solving methodology that uses old solved problems, called cases, to solve new problems. The case-base is the knowledge source where the cases are stored, and the amount of stored cases is critical to the problem-solving ability of the Case-Base Reasoning system. However, when the case-base has many cases, then performance problems arise due to the time needed to find those similar cases to the input problem. At this point, Case-Base Maintenance algorithms can be used to reduce the number of cases and maintain the accuracy of the Case-Base Reasoning system at the same time. Whereas Case-Base Maintenance algorithms typically use a particular heuristic to remove (or select) cases from the case-base, the resulting maintained case-base relies on the proportion of redundant and noisy cases that are present in the case-base, among other factors. That is, a particular Case-Base Maintenance algorithm is suitable for certain types of case-bases that share some indicators, such as redundancy and noise levels. In the present work, we consider Case-Base Maintenance as a multi-objective optimization problem, which is solved with a Multi-Objective Evolutionary Algorithm. To this end, a fitness function is introduced to measure three different objectives based on the Complexity Profile model. Our hypothesis is that the Multi-Objective Evolutionary Algorithm performing Case-Base Maintenance may be used in a wider set of case-bases, achieving a good balance between the reduction of cases and the problem-solving ability of the Case-Based Reasoning system. Finally, from a set of the experiments, our proposed Multi-Objective Evolutionary Algorithm performing Case-Base Maintenance shows regularly good results with different sets of case-bases with different proportion of redundant and noisy cases.     

教与同伴学习粒子群算法求解多目标柔性作业车间调度问题

针对多目标柔性作业车间调度问题,提出了带Pareto非支配解集的教与同伴学习粒子群算法。首先,以工件的最大完工时间、最大机器负荷和所有机器总负荷为优化目标建立了多目标柔性作业车间调度模型。然后,该算法结合多目标Pareto方法和教与同伴学习粒子群算法,采用快速非支配排序算法产生初始Pareto非支配解集,用提取Pareto支配层程序更新Pareto非支配解集,同时采用混合分派规则产生初始种群,采用开口向上抛物线递减的惯性权重选择策略提高算法的收敛速度。最后,对3个Benchmark算例进行仿真实验。理论分析和仿真表明,与带向导性局部搜索的多目标进化算法(MOEA-GLS)和带局部搜索的控制遗传算法(AL-CGA)相比,对于相同的测试实例,该算法能产生更多更好的Pareto非支配解;在计算时间方面,该算法要小于带向导性局部搜索的多目标进化算法。实验结果表明该算法可以有效解决多目标柔性作业车间调度问题。     

Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville–Thermalito complex

This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville–Thermalito Complex (OTC) – a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation–storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California.     

树型网格计算环境下的自适应任务调度算法

提出一种基于树型计算网格的自适应调度算法,实现对小粒度独立任务和用户大作业的自适应最优调度。通过对网格环境的实时检测,给出了基于节点负载状况、节点任务执行时间、任务传输时间和任务特性的自适应调度算法,即基于最优任务分配方案的启发式任务调度算法。通过实验与其他调度算法的比较,证明了所提出的任务调度算法在负载平衡和最优跨度方面具有明显的优越性。     

Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution

This article introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations or islands, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study how the performance of the cooperative coevolutionary multi-objective approaches can be drastically increased with respect to their corresponding original versions. This is specially interesting for solving complex problems involving a large number of variables, since the problem decomposition performed by the model at the island level allows for much faster executions (the number of variables to handle in every island is divided by the number of islands). We conduct a study on a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We propose a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine.     

基于knee points的改进多目标人工蜂群算法

传统的人工蜂群算法（Artificial Bee Colony algorithm,ABC）及其在多目标上的扩展（Multi Objective Artificial Bee Colony algorithm,MOABC）存在着在高维、多峰函数情况下收敛速度变慢、后期容易陷入局部最优以及寻优精度丢失等问题。基于knee points提高收敛性和分布性的特点,设计了一种快速识别knee point的算法并将其应用到多目标人工蜂群算法中,提出了一种基于knee points的改进多目标人工蜂群算法（KnMOABC）。算法在迭代过程中考虑pareto支配关系的同时,优先选择knee point作为下一代个体,极大地增强了算法的收敛速度,同时,在knee point识别算法中加入自适应的策略以保持良好的分布性。实验结果表明,KnMOABC的性能优于三个最新的多目标人工蜂群对比算法。     

Conception of a dominance-based multi-objective local search in the context of classification rule mining in large and imbalanced data sets

Classification on medical data raises several problems such as class imbalance, double meaning of missing data, volumetry or need of highly interpretable results. In this paper a new algorithm is proposed: MOCA-I (Multi-Objective Classification Algorithm for Imbalanced data), a multi-objective local search algorithm that is conceived to deal with these issues all together. It is based on a new modelization as a Pittsburgh multi-objective partial classification rule mining problem, which is described in the first part of this paper. An existing dominance-based multi-objective local search (DMLS) is modified to deal with this modelization. After experimentally tuning the parameters of MOCA-I and determining which version of DMLS algorithm is the most effective, the obtained MOCA-I version is compared to several state-of-the-art classification algorithms. This comparison is realized on 10 small and middle-sized data sets of literature and 2 real data sets; MOCA-I obtains the best results on the 10 data sets and is statistically better than other approaches on the real data sets.     

混合分散搜索的进化多目标优化算法

在进化多目标优化算法中,种群的多样性、对目标空间的搜索能力及算法的鲁棒性直接影响算法的收敛能力和解集的分散性。针对这些问题,提出了一种混合分散搜索的进化多目标优化算法(SSMOEA)。SSMOEA在混合分散搜索算法架构的同时,重新设计其多样性的选取策略,并引入协同进化机制。此外,为了提高算法的自适应性和鲁棒性,采用了一种新颖的自适应多交叉算子选择方法。SSMOEA与经典的多目标进化算法SPEA2、NSGA-Ⅱ和MOEA/D在12个基准测试函数上的对比结果表明,SSMOEA不仅在求得的Pareto最优解集的宽广性、均匀性和逼近性上有明显优势,而且算法的鲁棒性也有明显的提高。     

Identifying key players in large social networks by using a multi-objective artificial bee colony optimization approach

Identifying a set of individuals that have an influential relevance and act as key players is a matter of interest in many real world situations, especially in those related to the Internet. Although several approaches have been proposed in order to identify key players sets, they mainly focus just on the optimization of a single objective. This may lead to a poor performance since the sets identified are not usually able to perform well in real life applications where more objectives of interest are taken into account. Multi-objective optimization seems the natural extension for this task, but there is a lack of this type of methodologies in the scientific literature. An efficient Multi-Objective Artificial Bee Colony (MOABC) algorithm is proposed to address the key players identification problem and is applied in the context of six networks of different dimensions and characteristics. The proposed approach is able to best identify the key players than the ones previously proposed, especially in the context of large social networks. The model performance of the proposed approach has been evaluated according to different quality metrics. The results from the MOABC execution show important improvements with respect to the best multi-objective results in the scientific literature, specifically, in average, 13.20% of improvement in Hypervolume, 120.39% in Coverage Relation and 125.52% in number of non-dominated solutions. Even more, the proposed algorithm is also more robust when repeating executions.