一种均衡各速度项系数的多目标粒子群优化算法

粒子群优化算法已成为求解多目标优化问题的有效方法之一,而速度更新公式中的惯性、局部和全局3个速度项的系数的动态合理设置是算法优化效率的关键问题。为解决现有算法仅单独设置各速度项系数导致优化效率不高的问题,提出了一种均衡各速度项系数的多目标粒子群优化算法。该方法旨在通过粒子的局部最优和全局最优的信息来引导种群的进化方向,动态调整每一个粒子速度项系数来均衡惯性、局部和全局3个速度项在搜索中的作用,从而更为准确地刻画算法的搜索能力和搜索精度,更好地平衡算法的探究和探索能力,进一步提高粒子群优化算法解决复杂多目标优化问题的效率。在7个标准测试函数上进行实验,并与5种经典的进化算法进行对比,结果表明新算法在综合指标IGD以及多样性评估指标Δ评分上具有更好的收敛速度和分布性,验证了新算法的有效性。     

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.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

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.     

基于不可行度和内分泌原理的多目标粒子群方法

针对有约束条件的多目标优化问题,提出了一种求解带约束的基于内分泌思想的多目标粒子群算法。利用不可行度方法和约束主导原理指导进化过程中精英种群的选择操作和约束条件的处理,根据生物体激素调节机制中促激素和释放激素间的相互作用原理,考虑当前非劣解集中的个体对其最邻近的一类群体的监督控制,引入当前粒子的类全局最优位置来反映其所属类中最好位置粒子对当前粒子的影响。为验证多目标约束优化算法的有效性,对两个典型的多目标优化问题进行了仿真实验,仿真结果表明该算法能较大概率地获得多目标约束优化问题的可行Pareto最优解。     

A hybrid multi-objective PSO–EDA algorithm for reservoir flood control operation

Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO–EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO–EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO–EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO–EDA is suitable for solving MO-RFCO problems.     

多目标优化问题的粒子群算法仿真研究*

研究了一种用于求解多目标优化问题的粒子群算法(CMMOPSO)。该算法采用外部存档存储每一代产生的非劣解, 并且采用拥挤距离来维持外部存档规模, 同时提出一种新的全局最优粒子的选取策略(基于拥挤距离和收敛性距离)来提升粒子向Pareto前沿飞行的概率;为提升种群跳出局部最优解的能力, 以一定的概率对外部存档中粒子进行变异操作。通过典型的多目标测试函数对提出的算法进行检测, 结果表明,CMMOPSO算法在求解多目标问题上有一定的优势。因此, CMMOPSO可以作为求解多目标优化问题的有效算法。     

Multi-objective rule mining using a chaotic particle swarm optimization algorithm

In this paper, classification rule mining which is one of the most studied tasks in data mining community has been modeled as a multi-objective optimization problem with predictive accuracy and comprehensibility objectives. A multi-objective chaotic particle swarm optimization (PSO) method has been introduced as a search strategy to mine classification rules within datasets. The used extension to PSO uses similarity measure for neighborhood and far-neighborhood search to store the global best particles found in multi-objective manner. For the bi-objective problem of rule mining of high accuracy/comprehensibility, the multi-objective approach is intended to allow the PSO algorithm to return an approximation to the upper accuracy/comprehensibility border, containing solutions that are spread across the border. The experimental results show the efficiency of the algorithm.     

求解约束优化问题的多目标粒子群算法*

提出一种多目标粒子群算法处理约束优化问题(MOCPSO). 首先将约束优化问题转化为多目标问题, 然后给出一个不可行阈值来充分地利用不可行粒子的信息引导种群的飞行; 并提出一种粒子间的比较准则以比较它们的优劣; 最后, 为了增加种群的多样性, 提升种群跳出局部最优解的能力, 引入高斯白噪声扰动. 选取有代表性的标准测试函数对MOCPSO算法的性能进行仿真实验, 相比较其它算法, 结果显示MOCPSO算法是求解约束优化问题的有效算法.     

Particle swarm optimization with query-based learning for multi-objective power contract problem

Particle swarm optimization (PSO) is one of the most important research topics on swarm intelligence. Existing PSO techniques, however, still contain some significant disadvantages. In this paper, we present a new QBL-PSO algorithm that uses QBL (query-based learning) to improve both the exploratory and exploitable capabilities of PSO. Here, we apply a QBL method proposed in our previous research to PSO, and then test this new algorithm on a real case study on problems of power conservation. Our algorithm not only broadens the search diversity of PSO, but also improves its precision. Conventional PSO often snag on local solutions when performing queries, instead of finding better global solutions. To resolve this limitation, when particles converge in nature, we direct some of them into an “ambiguous solution space” defined by our algorithm. This paper introduces two ways to invoke this QBL algorithm. Our experimental results confirm that the proposed method attains better convergence to the global best solution. Finally, we present a new PSO model for solving multi-objective power conservation problems. Overall, this model successfully reduces power consumption, and to our knowledge, this paper represents the first attempt within the literature to apply the QBL concept to PSO.     

多子群协同进化的多目标微粒群优化算法

微粒群优化(PSO)算法是一种非常有竞争力的求解多目标优化问题的群智能算法,因其容易陷入局部极值,导致非劣解集的收敛性和正确性不理想。为此提出一种基于多目标分解进化策略的多子群协同进化的多目标微粒群优化算法(MOPSO_MC),算法中每个子群对应于一个多目标分解之后的子问题,并构造了一种新的速率更新策略,每个粒子跟踪自身历史最优值、子群最优值和子群邻域最优值,从而在增强算法的局部寻优能力的同时,也能从邻域子群获得进化信息,实现协同进化。最后通过仿真实验,与现在主流的多目标微粒群算法在ZDT基准测试函数上比较,验证了算法的收敛性,解分布的均匀性和正确性。     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm 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.     

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。     

改进粒子群优化算法在TDOA定位中的应用

针对TDOA定位估计中的非线性最优化问题,提出了一种基于改进粒子群优化的TDOA定位算法。该算法在自适应粒子群优化算法的基础上,引入禁忌搜索策略,有效地解决了粒子群优化算法容易陷入局部最优的问题,使算法快速收敛到全局最优解。仿真结果表明:该算法性能稳定,定位精度高。     

最佳维变异粒子群优化算法在传感器调度中应用

粒子群优化(PSO)算法的主要特点是能快速得到问题的解,缺点是容易陷入局部最优.提出了一种利用最佳维变异技术和量子理论方法改进的PSO算法,并应用于目标跟踪传感器调度问题.目标的动力学模型为线性高斯模型,传感器观测值被高斯噪声污染并与目标状态线性相关.对于多传感器单目标跟踪的数学问题,引入提出的最佳维变异PSO算法,在...     

Handling multi-objective optimization problems with a multi-swarm cooperative particle swarm optimizer

This paper presents a new multi-objective optimization algorithm in which multi-swarm cooperative strategy is incorporated into particle swarm optimization algorithm, called multi-swarm cooperative multi-objective particle swarm optimizer (MC-MOPSO). This algorithm consists of multiple slave swarms and one master swarm. Each slave swarm is designed to optimize one objective function of the multi-objective problem in order to find out all the non-dominated optima of this objective function. In order to produce a well distributed Pareto front, the master swarm is developed to cover gaps among non-dominated optima by using a local MOPSO algorithm. Moreover, in order to strengthen the capability locating multiple optima of the PSO, several improved techniques such as the Pareto dominance-based species technique and the escape strategy of mature species are introduced. The simulation results indicate that our algorithm is highly competitive to solving the multi-objective optimization problems.     

一种新的混合粒子群算法求解置换流水车间调度问题

针对粒子群算法易早熟的缺点,提出了一种结合迭代贪婪(IG)算法的混合粒子群算法。算法通过连续几代粒子个体极值和全局极值的变化判断粒子的状态,在发现粒子出现停滞或者粒子群出现早熟后,及时利用IG算法的毁坏操作和构造操作对停滞粒子和全局最优粒子进行变异,变异后利用模拟退火思想概率接收新值。全局最优粒子的改变会引导粒子跳出局部极值的约束,增加粒子的多样性,从而克服粒子群的早熟现象。同时,为了使算法能更快找到或逼近最优解,采用了循环迭代策略,在阶段优化结果的基础上,周而复始循环迭代进行求解。将提出的混合粒子群算法应用于置换流水车间调度问题,并在问题求解时与几个具有代表性的算法进行了比较。结果表明,提出的算法能够克服粒子群早熟,在求解质量方面优于其他算法。     

A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems

In this paper, a modified particle swarm optimization (PSO) algorithm is developed for solving multimodal function optimization problems. The difference between the proposed method and the general PSO is to split up the original single population into several subpopulations according to the order of particles. The best particle within each subpopulation is recorded and then applied into the velocity updating formula to replace the original global best particle in the whole population. To update all particles in each subpopulation, the modified velocity formula is utilized. Based on the idea of multiple subpopulations, for the multimodal function optimization the several optima including the global and local solutions may probably be found by these best particles separately. To show the efficiency of the proposed method, two kinds of function optimizations are provided, including a single modal function optimization and a complex multimodal function optimization. Simulation results will demonstrate the convergence behavior of particles by the number of iterations, and the global and local system solutions are solved by these best particles of subpopulations.     

A recombination-based hybridization of particle swarm optimization and artificial bee colony algorithm for continuous optimization problems

This paper presents a hybridization of particle swarm optimization (PSO) and artificial bee colony (ABC) approaches, based on recombination procedure. The PSO and ABC are population-based iterative methods. While the PSO directly uses the global best solution of the population to determine new positions for the particles at the each iteration, agents (employed, onlooker and scout bees) of the ABC do not directly use this information but the global best solution in the ABC is stored at the each iteration. The global best solutions obtained by the PSO and ABC are used for recombination, and the solution obtained from this recombination is given to the populations of the PSO and ABC as the global best and neighbor food source for onlooker bees, respectively. Information flow between particle swarm and bee colony helps increase global and local search abilities of the hybrid approach which is referred to as Hybrid approach based on Particle swarm optimization and Artificial bee colony algorithm, HPA for short. In order to test the performance of the HPA algorithm, this study utilizes twelve basic numerical benchmark functions in addition to CEC2005 composite functions and an energy demand estimation problem. The experimental results obtained by the HPA are compared with those of the PSO and ABC. The performance of the HPA is also compared with that of other hybrid methods based on the PSO and ABC. The experimental results show that the HPA algorithm is an alternative and competitive optimizer for continuous optimization problems.