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.     

求解多目标最小生成树的一种新的遗传算法

在改进的非支配排序遗传算法（NSGA-II）的基础上,提出了一种新的基于生成树边集合编码的繁殖算子求解多目标最小生成树问题的遗传算法。通过快速非支配排序法,降低了算法的计算复杂度,引入保存精英策略,扩大采样空间。实验结果表明：对于多目标最小生成树问题,边集合编码具有较好的遗传性和局部性,而且基于此繁殖算子的遗传算法在求解效率和解的质量方面都优于基于PrimRST的遗传算法。     

基于二进制交叉和变异的粒子群算法及应用

粒子群算法在求解多峰问题时极易陷入局部最优解,提出了基于模拟二进制交叉和多项式变异的粒子群算法(sPDPSO>。在该算法中,为了更好地利用每个粒子的历史信息,引入了外部存档存储每个粒子的最优位置( pbest) ;同时,对外部存档中的pbest进行二进制交叉,而对新产生的全局最优粒子进行多项式变异。基准函数的测试结果显示,SPDPS()算法在求解多峰问题上有一定的优势。在实际应用中,以TSP为研究对象,结果显示SPDPSO算法获得了比其它算法更好的解。     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

基于遗传交叉和多混沌策略改进的粒子群优化算法

为有效改进基本PSO算法的搜索能力,提出了一种基于遗传交叉和多混沌方式改进的粒子群算法。该算法为获得比当前群体更优的最优解,采用了以下四种措施：其一,对当前群体中的最优解和每个粒子最优解进行遗传交叉操作;其二,用混沌系统动态地调整PSO算法的惯性权重;其三,对整个解空间进行混沌全局搜索;最后,对当前群体中最优解进行多维和单维的混沌局部搜索。仿真实验结果表明：与其它三种算法相比,提出的算法在解决8个整数和混合整数非线性规划问题时不仅收敛速度最快,而且具有100%的成功率。     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

一种催化粒子群算法及其性能分析

针对粒子群算法（PSO）在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种新颖的混合算法—催化粒子群算法（CPSO）。在CPSO优化过程中,种群中的粒子始终保持其个体历史最优值pbests。CPSO种群更新由改造PSO、横向交叉以及垂直交叉三个搜索算子交替进行,其中,每个算子产生的中庸解均通过贪婪思想产生占优解pbests,并作为下一个算子的父代种群。在CPSO中,纵横交叉算法（CSO）作为PSO的加速催化剂,一方面通过横向交叉改善PSO的全局收敛性能,另一方面通过纵向交叉维持种群的多样性。对6个典型benchmark函数的仿真结果表明,相比其它主流PSO变体,CPSO在全局收敛能力和收敛速率方面具有明显优势。     

基于交叉和变异的多目标粒子群算法

为了保证粒子群算法求得的非劣解尽可能接近真实的Pareto前沿并保持多样性分布. 提出一种基于交叉和变异的多目标粒子群算法(CMMOPSO). 在CMMOPSO算法中, 首先, 识别Pareto前沿的稀疏部分包含的粒子, 并对这些粒子进行交叉操作以增加多样性分布; 其次, 对于远离Pareto前沿的粒子进行变异操作, 以提升粒子向真实的Pareto前沿飞行的概率. 在基准函数的测试中, 结果显示CMMOPSO算法比其它算法有更好的运行效果. 因此, CMMOPSO算法可以作为求解多目标问题的一种有效算法.     

一种改进的鲁棒多目标优化方法

针对在解决某些复杂多目标优化问题过程中,所得到的Pareto最优解易受设计参数或环境参数扰动的影响,引入了鲁棒的概念并提出一种改进的鲁棒多目标优化方法,它利用了经典的基于适应度函数期望和方差方法各自的优势,有效地将两种方法结合在一起。为了实现该方法,给出一种基于粒子群优化算法的多目标优化算法。仿真实例结果表明,所给出的方法能够得到更为鲁棒的Pareto最优解。     

求解整数非线性规划结合正交杂交的离散PSO 算法

针对整数非线性规划问题,提出一种结合正交杂交的离散粒子群优化(PSO)算法.首先采用舍入取整方法,为了减少舍入误差,对PSO中的每个粒子到目前为止的最好位置进行随机修正,将基于正交实验设计的正交杂交算子引入离散PSO算法,以增强搜索性能;然后对PSO算法中的惯性权重和收缩因子采用动态调整策略,以提高算法的搜索效率;最后对一些不同维数的整数非线性规划问题进行数值仿真实验,实验结果表明了所提出算法的有效性.     

A fuzzy particle swarm optimization algorithm for computer communication network topology design

Particle swarm optimization (PSO) is a powerful optimization technique that has been applied to solve a number of complex optimization problems. One such optimization problem is topology design of distributed local area networks (DLANs). The problem is defined as a multi-objective optimization problem requiring simultaneous optimization of monetary cost, average network delay, hop count between communicating nodes, and reliability under a set of constraints. This paper presents a multi-objective particle swarm optimization algorithm to efficiently solve the DLAN topology design problem. Fuzzy logic is incorporated in the PSO algorithm to handle the multi-objective nature of the problem. Specifically, a recently proposed fuzzy aggregation operator, namely the unified And-Or operator (Khan and Engelbrecht in Inf. Sci. 177: 2692–2711, 2007), is used to aggregate the objectives. The proposed fuzzy PSO (FPSO) algorithm is empirically evaluated through a preliminary sensitivity analysis of the PSO parameters. FPSO is also compared with fuzzy simulated annealing and fuzzy ant colony optimization algorithms. Results suggest that the fuzzy PSO is a suitable algorithm for solving the DLAN topology design problem.     

A novel intelligent particle swarm optimization algorithm for solving cell formation problem

The formation of manufacturing cells forms the backbone of designing a cellular manufacturing system. In this paper, we present a novel intelligent particle swarm optimization algorithm for the cell formation problem. The proposed solution method benefits from the advantages of particle swarm optimization algorithm (PSO) and self-organization map neural networks by combining artificial individual intelligence and swarm intelligence. Numerical examples demonstrate that the proposed intelligent particle swarm optimization algorithm significantly outperforms PSO and yields better solutions than the best solutions existed in the literature of cell formation. The application of the proposed approach is examined in a case problem where real data is utilized for cell reconfiguration of an actual company involved in agricultural manufacturing sector.

     

基于正交设计的多目标粒子群算法*

为了提升粒子群算法求解多目标问题的能力,通过分析初始种群的方法对算法的影响,提出一种基于正交设计的多目标粒子群算法(ODMOPSO)。在算法运行过程中,通过正交设计来产生初始种群,使得种群均匀分布在可行区域,进而使得算法能够在整个可行解空间上进行均匀搜索;同时,引入广义学习策略提升粒子向Pareto前沿飞行的概率。在基准函数的测试中,结果显示ODMOPSO算法获得了质量更高的解。     

An exploratory research of elitist probability schema and its applications in evolutionary algorithms

An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0–1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.     

A multi-objective mixed-discrete particle swarm optimization with multi-domain diversity preservation

Among population-based optimization algorithms guided by meta-heuristics, Particle Swarm Optimization (PSO) has gained significant popularity in the past two decades, particularly due to its ease of implementation and fast convergence capabilities. This paper seeks to translate the beneficial features of PSO from solving typical continuous single-objective problems to solving multi-objective mixed-discrete problems, which is relatively a new ground for PSO application. The original Mixed-Discrete PSO (MDPSO) algorithm, which included an exclusive diversity preservation technique to significantly mitigate premature particle clustering, has been shown to be a powerful single-objective solver for highly constrained MINLP problems. This papers makes fundamental advancements to MDPSO, enabling it to solve complex multi-objective problems with mixed-discrete design variables. Specifically, in the velocity update equation for any particle, the explorative term is modified to point towards a stochastically selected non-dominated solution at that iteration ? thereby adopting the concept of multi-leader swarms. The fractional domain in the diversity preservation technique, which was previously defined in terms of the best global particle, is now formulated as a function of the extreme members in the set of intermediate Pareto optimal solutions. With this advancement, diversity preservation not only mitigates premature particle stagnation, but also promotes more uniform coverage of the Pareto frontier. The multi-objective MDPSO algorithm is tested using a set of benchmark problems and a wind farm layout optimization problem. To illustrate the competitive benefits of the new MO-MDPSO algorithm, the results are compared with those given by other popular multi-objective solvers such as NSGA-II and SPEA.     

A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem

To better reflect the uncertainty existing in the actual disassembly environment, the multi-objective disassembly line balancing problem with fuzzy disassembly times is investigated in this paper. First, a mathematical model of the multi-objective fuzzy disassembly line balancing problem (MFDLBP) is presented, in which task disassembly times are assumed as triangular fuzzy numbers (TFNs). Then a Pareto improved artificial fish swarm algorithm (IAFSA) is proposed to solve the problem. The proposed algorithm is inspired from the food searching behaviors of fish including prey, swarm and follow behaviors. An order crossover operator of the traditional genetic algorithm is employed in the prey stage. The Pareto optimal solutions filter mechanism is adopted to filter non-inferior solutions. The proposed model after the defuzzification is validated by the LINGO solver. And the validity and the superiority of the proposed algorithm are proved by comparing with a kind of hybrid discrete artificial bee colony (HDABC) algorithm using two test problems. Finally, the proposed algorithm is applied to a printer disassembly instance including 55 disassembly tasks, for which the computational results containing 12 non-inferior solutions further confirm the practicality of the proposed Pareto IAFSA in solving the MFDLBP.     

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.     

聚酯工业生产缩聚过程的多目标优化

介绍一种聚酯(PET)生产缩聚过程的多目标优化技术,以最终产品的产量最大和质量最佳为优化目标,以第三和第四缩聚釜为优化对象,运用复合神经网络技术及相关机理知识建立优化模型。借鉴非劣分层方法、精英策略和群智思想,建立混合优化算法,通过该算法及惩罚函数寻优,设定生产过程中操作变量的最优参数,采用实际工业生产数据仿真和验证,建立周期性的两级优化结构来实现优化控制。     

Indicator-based set evolution particle swarm optimization for many-objective problems

Multi-objective particle swarm optimization (MOPSO) has been well studied in recent years. However, existing MOPSO methods are not powerful enough when tackling optimization problems with more than three objectives, termed as many-objective optimization problems (MaOPs). In this study, an improved set evolution multi-objective particle swarm optimization (S-MOPSO, for short) is proposed for solving many-objective problems. According to the proposed framework of set evolution MOPSO (S-MOPSO), including quality indicators-based objective transformation, the Pareto dominance on sets, and the particle swarm operators for set evolution, an enhanced S-MOPSO method is developed by updating particles hierarchically, i.e., a set of solutions is first regarded as a particle to be updated and then the solutions in a selected set are further evolved by a modified PSO. In the set evolutionary stage, the strategy for efficiently updating the set particle is proposed. When further evolving a single solution in the initial decision space of the optimized MaOP, the global and local best particles are dynamically determined based on those ideal reference points. The performance of the proposed algorithm is empirically demonstrated by applying it to several scalable benchmark many-objective problems.     

A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

This paper proposes a formulation of the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) and a particle swarm optimization (PSO) algorithm for solving it. The formulation is a generalization of three existing VRPSPD formulations. The main PSO algorithm is developed based on GLNPSO, a PSO algorithm with multiple social structures. A random key-based solution representation and decoding method is proposed for implementing PSO for VRPSPD. The solution representation for VRPSPD with n customers and m   vehicles is a (n+2m)$(n+2m)$-dimensional particle. The decoding method starts by transforming the particle to a priority list of customers to enter the route and a priority matrix of vehicles to serve each customer. The vehicle routes are constructed based on the customer priority list and vehicle priority matrix. The proposed algorithm is tested using three benchmark data sets available from the literature. The computational result shows that the proposed method is competitive with other published results for solving VRPSPD. Some new best known solutions of the benchmark problem are also found by the proposed method.