Self-organization of Decentralized Swarm Agents Based on Modified Particle Swarm Algorithm

In this paper, an attempt has been made by incorporating some special features in the conventional particle swarm optimization (PSO) technique for decentralized swarm agents. The modified particle swarm algorithm (MPSA) for the self-organization of decentralized swarm agents is proposed and studied. In the MPSA, the update rule of the best agent in swarm is based on a proportional control concept and the objective value of each agent is evaluated on-line. In this scheme, each agent self-organizes to flock to the best agent in swarm and migrate to a moving target while avoiding collision between the agent and the nearest obstacle/agent. To analyze the dynamics of the MPSA, stability analysis is carried out on the basis of the eigenvalue analysis for the time-varying discrete system. Moreover, a guideline about how to tune the MPSA's parameters is proposed. The simulation results have shown that the proposed scheme effectively constructs a self-organized swarm system in the capability of flocking and migration.Category (5) – Intelligent Systems / Intelligent Control / Fuzzy Control / Prosthetics / Robot Motion Planning     

Ensemble particle swarm optimizer

According to the “No Free Lunch (NFL)” theorem, there is no single optimization algorithm to solve every problem effectively and efficiently. Different algorithms possess capabilities for solving different types of optimization problems. It is difficult to predict the best algorithm for every optimization problem. However, the ensemble of different optimization algorithms could be a potential solution and more efficient than using one single algorithm for solving complex problems. Inspired by this, we propose an ensemble of different particle swarm optimization algorithms called the ensemble particle swarm optimizer (EPSO) to solve real-parameter optimization problems. In each generation, a self-adaptive scheme is employed to identify the top algorithms by learning from their previous experiences in generating promising solutions. Consequently, the best-performing algorithm can be determined adaptively for each generation and assigned to individuals in the population. The performance of the proposed ensemble particle swarm optimization algorithm is evaluated using the CEC2005 real-parameter optimization benchmark problems and compared with each individual algorithm and other state-of-the-art optimization algorithms to show the superiority of the proposed ensemble particle swarm optimization (EPSO) algorithm.     

Self-organization of unicycle swarm robots based on a modified particle swarm framework

In this paper, an attempt has been made to incorporate some special features in the conventional particle swarm optimization (PSO) technique for unicycle robots with line of sight. The modified particle swarm framework (MPSF) for the self-organization of unicycle swarm robots is proposed and studied. The framework explores the benefits by dynamic associations with the proposed MPSF to realize complex swarming behaviors. In this scheme, out of sights by obstacles or neighbor robots are considered when a robot moves to a target. Each robot self-organizes to flock to the best robot in the swarm seen in its sight and migrates to a moving target while avoiding collision with obstacles and neighboring robots through the interaction of robots with line of sight. The resulting MPSF is advantageous for practical implementations since it is used for robots, even in cases where a target is blocked by obstacles or robots. Extensive simulation is presented to illustrate the viability and effectiveness of the proposed framework.     

Two-layer particle swarm optimization for unconstrained optimization problems

In this article, a two-layer particle swarm optimization (TLPSO) is proposed to increase the diversity of the particles so that the drawback of trapping in a local optimum is avoided. In order to design the TLPSO, a structure with two layers (top layer and bottom layer) is proposed so that M swarms of particles and one swarm of particles are generated in the bottom layer and the top layer, respectively. Each global best position in each swarm of the bottom layer is set to be the position of the particle in the swarm of the top layer. Therefore, the global best position in the swarm of the top layer influences indirectly the particles of each swarm in the bottom layer so that the diversity of the particles increases to avoid trapping into a local optimum. Besides, a mutation operation is added into the particles of each swarm in the bottom layer so that the particles leap the local optimum to find the global optimum. Finally, some optimization problems of different types of high dimensional functions are used to illustrate the efficiency of the proposed method.     

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.     

Particle swarm optimization with justification and designed mechanisms for resource-constrained project scheduling problem

The studied resource-constrained project scheduling problem (RCPSP) is a classical well-known problem which involves resource, precedence, and temporal constraints and has been applied to many applications. However, the RCPSP is confirmed to be an NP-hard combinatorial problem. Restated, it is hard to be solved in a reasonable time. Therefore, there are many metaheuristics-based schemes for finding near optima of RCPSP were proposed. The particle swarm optimization (PSO) is one of the metaheuristics, and has been verified being an efficient nature-inspired algorithm for many optimization problems. For enhancing the PSO efficiency in solving RCPSP, an effective scheme is suggested. The justification technique is combined with PSO as the proposed justification particle swarm optimization (JPSO), which includes other designed mechanisms. The justification technique adjusts the start time of each activity of the yielded schedule to further shorten the makespan. Moreover, schedules are generated by both forward scheduling particle swarm and backward scheduling particle swarm in this work. Additionally, a mapping scheme and a modified communication mechanism among particles with a designed gbest ratio (GR) are also proposed to further improve the efficiency of the proposed JPSO. Simulation results demonstrate that the proposed JPSO provides an effective and efficient approach for solving RCPSP.     

解决约束优化问题的改进粒子群算法

针对约束优化问题的求解,提出一种改进的粒子群算法（CMPSO）。在CMPSO算法中,为了增加种群多样性,提升种群跳出局部最优解的能力,引入种群多样性阈值,当种群多样性低于给定阈值时,对全局最优粒子位置和粒子自身最优位置进行多项式变异;并根据粒子违背约束条件的程度,提出一种新的粒子间比较准则来比较粒子间的优劣,该准则可以保留一部分性能较优的不可行解;为提升种群向全局最优解飞行的概率,采取一种广义学习策略。对经典测试函数的仿真结果表明,所提出的算法是一种可行的约束优化问题的求解方法。     

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。     

层次学习骨干粒子群优化算法

对骨干粒子群优化(BPSO) 种群多样性迅速丧失的原因进行分析, 提出层次学习骨干粒子群优化算法以克 服早熟现象. 该算法中粒子依不同的学习概率向粒子自身的最优粒子、优胜粒子和群体最优粒子学习, 该机制使群 体实现不同层次的搜索并有效维持群体的多样性. 此外, 群体最优粒子依概率采用跳跃策略以增强逃逸能力或采用 扰动策略以提高解的质量. 将所提出的算法与多种改进的粒子群优化算法进行对比, 仿真结果表明, 所提出算法的综 合表现优于其他算法.     

Visual cooperation based on LOS for self-organization of swarm robots

In this study, an attempt has been made to incorporate visual cooperation among decentralized swarm robots for self-organization. Self-organization based on color recognition is presented to overcome the constraints faced in conventional self-organization based on centralized control, in which an external ceiling camera or beacon systems are used. In the proposed scheme, a singular association rule is introduced: a swarm robot considers line-of-sight (LOS) visual information only about its reference robot or a moving target. In particular, this paper presents the following set of cases pertaining to self-organization of swarm robots: 1) a case in which a robot loses a moving target from its LOS, 2) a case in which a robot loses a reference robot from its LOS, 3) a case in which a robot is lost, and 4) a case in which all robots lose the target from their LOS. Results of a simulation and an experiment on prey pursuit show that the proposed self-organization method can be effectively used for multiple mobile robots, despite the use of a simple association rule.     

Cultural quantum-behaved particle swarm optimization for environmental/economic dispatch

In this paper, a novel CMOQPSO algorithm is proposed, in which cultural evolution mechanism is introduced into quantum-behaved particle swarm optimization (QPSO) to solve multiobjective environmental/economic dispatch (EED) problems. There are growing concerns about the ability of QPSO to handle multiobjective optimization problems. Two important issues in extending QPSO to multiobjective context are the construction of exemplar positions for each particle and the maintenance of population diversity. In the proposed CMOQPSO, one particle is measured for multiple times at each iteration in order to enhance its global searching ability. Belief space, which is based on cultural evolution mechanism and contains different types of knowledge extracted from the particle swarm, is adopted to generate global best positions for the multiple measurements of each particle. Moreover, to maintain population diversity and avoid premature, a novel local search operator, which is based on the knowledge in belief space, is proposed in this paper. CMOQPSO is compared with several state-of-art algorithms and tested on EED systems with 6 and 40 generators respectively. The comparative results demonstrate the effectiveness of the proposed algorithm.     

Potential-function-based shape formation in swarm simulation

This paper presents a potential-function-based formation shape control scheme for swarm simulation. The potential function is designed to avoid collision among agents, approach a destination, and achieve a certain shape formation around the destination. The agents move in a swarm to the formation position, which is generated from a reference point and the neighboring agents. In the framework, a local minimum case created by combining the potential repulsed from neighboring robots and that attracted from a reference point is presented; herein, a robot escapes from a local minimum using a virtual escape point after recognizing the trapped situation. Similarly, in the proposed framework, for a well-equipped formation shape, potential functions are designed to maintain the same relative distance between neighboring robots on a formation line, which also satisfies scalability for the number of agents. The simulation results show that the proposed approach can effectively construct elliptical, diamond, and heart-shaped formations for swarm agents.     

粒子带质量的粒子群算法

针对粒子群算法在陷入局部最优时难于跳出的缺陷提出了一种带有质量的粒子群算法。该算法受运动学原理启发,粒子位置的更新不仅受自身最优和种群最优的影响,还受到由粒子质量引起的梯度场的影响。当粒子群出现早熟现象时,用电磁学原理与动量守恒定理更新种群的最优位置,使群体能及时摆脱局部最优区域。仿真结果表明,该算法优化4种具有代表性的基准函数,无论是在优化精度方面还是在优化效率方面,均较以往提出的改进粒子群算法在性能上有所改进。     

Pseudo-decentralized switching control

The decentralized control of plants with uncertain mathematical models is studied in this paper. In particular, it is assumed that the plant is described by a continuous LTI model, which is contained in a specified family P? of plant models, and in this case it is assumed that a family of decentralized controllers has been found to satisfactorily control the models contained in P?. A switching control scheme is then proposed that uses the input-output information of each agent to switch between the local candidate controllers in each corresponding agent. A binary communication link is assumed to exist between the local control agents to assure that all agents switch to the next candidate controller, simultaneously. Simulation results, using the proposed decentralized scheme, are given and compared with the centralized scheme.     

A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.     

Multi swarm bare bones particle swarm optimization with distribution adaption

Bare bones PSO is a simple swarm optimization approach that uses a probability distribution like Gaussian distribution in the position update rules. However, due to its nature, Bare bones PSO is highly prone to premature convergence and stagnation. The characteristics of the probability distribution functions used in the update rule have a tense impact on the performance of the bare bones PSO. As a result, this paper investigates the use of different methods for estimating the probability distributions used in the update rule. Four methods or strategies are developed that are using Gaussian or multivariate Gaussian distributions. The choice of an appropriate updating strategy for each particle greatly depends on the characteristics of the fitness landscape that surrounds the swarm. To deal with issue, the cellular learning automata model is incorporated with the proposed bare bones PSO, which is able to adaptively learn suitable updating strategies for the particles. Through the interactions among its elements and the learning capabilities of its learning automata, cellular learning automata gradually learns to select the best updating rules for the particles based on their surrounding fitness landscape. This paper also, investigates a new and simple method for adaptively refining the covariance matrices of multivariate Gaussian distributions used in the proposed updating strategies. The proposed method is compared with some other well-known particle swarm approaches. The results indicate the superiority of the proposed approach in terms of the accuracy of the achieved results and the speed in finding appropriate solutions.     

新型多群体协同进化粒子群优化算法

在基本的MCPSO算法中除了主群与从群的信息交流,从群之间没有信息交流。为了解决这一问题,提出了一种具有中心交流机制的改进MCPSO算法,该策略可以实现各个从群之间的信息交流,从而加快算法收敛。仿真实验结果表明改进后的算法具有较好的求解精度和较快的收敛速度。     

Sequential approximation optimization assisted particle swarm optimization for expensive problems

In this paper, an efficient sequential approximation optimization assisted particle swarm optimization algorithm is proposed for optimization of expensive problems. This algorithm makes a good balance between the search ability of particle swarm optimization and sequential approximation optimization. Specifically, the proposed algorithm uses the optima obtained by sequential approximation optimization in local regions to replace the personal historical best particles and then runs the basic particle swarm optimization procedures. Compared with particle swarm optimization, the proposed algorithm is more efficient because the optima provided by sequential approximation optimization can direct swarm particles to search in a more accurate way. In addition, a space partition strategy is proposed to constraint sequential approximation optimization in local regions. This strategy can enhance the swarm diversity and prevent the preconvergence of the proposed algorithm. In order to validate the proposed algorithm, a lot of numerical benchmark problems are tested. An overall comparison between the proposed algorithm and several other optimization algorithms has been made. Finally, the proposed algorithm is applied to an optimal design of bearings in an all-direction propeller. The results show that the proposed algorithm is efficient and promising for optimization of the expensive problems.     

带偏向性轮盘赌的多算子协同粒子群优化算法

针对粒子群优化算法在处理高维、大规模、多变量耦合、多模态、多极值属性优化问题时易早熟收敛等性能和技术瓶颈,基于粒子群优化算法行为学习算子和3种不同学习偏好的差分变异算子,建立带偏向性轮盘赌的多算子选择与融合机制,提出一种带偏向性轮盘赌的多算子协同粒子群优化算法MOCPSO.MOCPSO针对迭代粒子群榜样粒子集,首先通过对迭代种群及其榜样粒子集优劣分组,同时采用轮盘赌分别为每组榜样粒子集选配不同学习偏好的变异算子,并为每组榜样粒子适配差分基向量和最优基向量,预学习并优化迭代种群及其榜样粒子,以权衡算法的全局探索和局部开发;然后通过合并所有子种群,并结合粒子群优化算法行为学习算子,指导迭代种群状态更新,以提高算法的全局收敛性;最后结合精英学习策略,对群体历史最优进行高斯扰动,以提高算法的局部逃生能力,保障算法收敛的多样性.实验结果表明,MOCPSO算法与5种先进的同类型群智能算法在求解CEC2014基准测试问题上具备竞争力,且有更强的优化特性.     

Coordinating metaheuristic agents with swarm intelligence

Coordination of multi agent systems remains as a problem since there is no prominent method suggests any universal solution. Metaheuristic agents are specific implementations of multi-agent systems, which imposes working together to solve optimisation problems using metaheuristic algorithms. An idea for coordinating metaheuristic agents borrowed from swarm intelligence is introduced in this paper. This swarm intelligence-based coordination framework has been implemented as swarms of simulated annealing agents collaborated with particle swarm optimization for multidimensional knapsack problem. A comparative performance analysis is also reported highlighting that the implementation has produced much better results than the previous works.