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.     

A ranking selection-based particle swarm optimizer for engineering design optimization problems

Particle swarm optimization (PSO) algorithms have been proposed to solve optimization problems in engineering design, which are usually constrained (possibly highly constrained) and may require the use of mixed variables such as continuous, integer, and discrete variables. In this paper, a new algorithm called the ranking selection-based PSO (RSPSO) is developed. In RSPSO, the objective function and constraints are handled separately. For discrete variables, they are partitioned into ordinary discrete and categorical ones, and the latter is managed and searched directly without the concept of velocity in the standard PSO. In addition, a new ranking selection scheme is incorporated into PSO to elaborately control the search behavior of a swarm in different search phases and on categorical variables. RSPSO is relatively simple and easy to implement. Experiments on five engineering problems and a benchmark function with equality constraints were conducted. The results indicate that RSPSO is an effective and widely applicable optimizer for optimization problems in engineering design in comparison with the state-of-the-art algorithms in the area.     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

带自适应感知能力的粒子群优化算法

提出一种求解约束优化问题的改进粒子群优化算法。它利用可行性判断规则处理约束条件,更新个体最优解和全局最优解。通过为粒子赋予自适应感知能力,算法能较好地平衡全局和局部搜索,且有能力跳出局部极值,防止早熟。边界附近粒子的感知结果被用来修正其飞行速度以加强算法对约束边界的搜索。实验结果表明,新算法收敛速度快,寻优能力强,能很好地求解约束优化问题。     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems.

In this correspondence, an approach based on coevolutionary particle swarm optimization to solve constrained optimization problems formulated as min-max problems is presented. In standard or canonical particle swarm optimization (PSO), a uniform probability distribution is used to generate random numbers for the accelerating coefficients of the local and global terms. We propose a Gaussian probability distribution to generate the accelerating coefficients of PSO. Two populations of PSO using Gaussian distribution are used on the optimization algorithm that is tested on a suite of well-known benchmark constrained optimization problems. Results have been compared with the canonical PSO (constriction factor) and with a coevolutionary genetic algorithm. Simulation results show the suitability of the proposed algorithm in terms of effectiveness and robustness.     

求解均值-CVaR投资组合模型的改进粒子群算法

针对粒子群算法易跳过全局极值,且只能求解连续性问题的缺点,提出离散复形法局部搜索的思想,来有效提高粒子群算法在离散型问题中的搜索性能。针对粒子群算法易陷入局部极小的缺点,引入自适应粒子迁徙操作保证粒子的多样性,有效避免陷入局部收敛。对采用CVaR度量风险、构建有交易费用和限制证券比例的均值-CVaR投资组合模型进行仿真实验,实验结果验证了算法的有效性。将改进的粒子群算法应用到求解均值-CVaR模型的投资组合问题,与其他算法相比,该方法精度更高、性能更稳定。     

Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach

This paper presents an extension to the basic particle swarm optimization approach for the solution of constrained engineering design optimization problems. The approach takes advantage of the PSO ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using an augmented Lagrange multiplier method. Details in the algorithm implementation and properties are presented and the effectiveness of the approach is illustrated in different benchmark structural optimization test cases. Results show the ability of the proposed methodology to find better solutions for structural optimization tasks as compared to other optimization algorithms.     

一种动态分级的混合粒子群优化算法

针对粒子群算法早熟收敛和搜索精度不高的问题,提出一种动态分级的混合粒子群优化算法．该算法采取３种级别的并行粒子群算法,分别用于全局搜索和局部搜索及二者的结合,并根据搜索阶段动态调整各种级别中并行变量的数目．在全局搜索中,将混沌机制引入算法中以增强算法的全局搜索能力;在局部搜索中,采用单纯形法对适应度最优解进行局部寻优．仿真实验表明,该算法比其他优化算法具有更好的性能．     

A particle swarm optimization based memetic algorithm for dynamic optimization problems

Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic optimization problems. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments.     

A hybrid cooperative search algorithm for constrained optimization

Many engineering design problems can be formulated as constrained optimization problems which often consist of many mixed equality and inequality constraints. In this article, a hybrid coevolutionary method is developed to solve constrained optimization problems formulated as min–max problems. The new method is fast and capable of global search because of combining particle swarm optimization and gradient search to balance exploration and exploitation. It starts by transforming the problem into unconstrained one using an augmented Lagrangian function, then using two groups to optimize different components of the solution vector in a cooperative procedure. In each group, the final stage of the search procedure is accelerated by via a simple local search method on the best point reached by the preceding exploration based search. We validated the effectiveness and robustness of the proposed algorithm using several engineering problems taken from the specialised literature.     

An improved vector particle swarm optimization for constrained optimization problems

Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm [30], which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable.     

复形法粒子群优化算法研究

针对基本粒子群优化算法对复杂函数优化时难以获得最优解的缺陷,提出了一种复形粒子群优化算法。该算法采用复形法来提高粒子的局部搜索能力,从而保证了算法能够跳出局部最优,获得全局最优解。实验结果表明,与文献算法相比,该算法在基准函数优化时具有更强的寻优能力和更高的搜索精度。     

改进约束鸡群算法在神经网络的应用

针对基本鸡群优化算法CSO存在收敛速度慢、易陷入局部最优等问题,提出一种改进约束鸡群算法ICCSO,改进了基本鸡群算法的边界约束处理机制,提高了算法的收敛速度和全局搜索能力。以标准测试函数和BP神经网络为例进行数值仿真,仿真结果表明了所提出的改进约束鸡群优化算法的合理性及有效性。     

一种高效粒子群优化算法

针对标准粒子群算法收敛速度慢和易出现早熟收敛等问题,提出一种高效粒子群优化算法．首先利用局部搜索算法的局部快速收敛性,对整个粒子群目前找到的最优位置进行局部搜索;然后,为了跳出局部最优,保持粒子的多样性,给出一个学习算子．该算法能增强算法的全局探索和局部开发能力．通过对10个标准测试函数的仿真实验并与其他算法相比较,结果表明了所提出的算法具有较快的收敛速度和很强的跳出局部最优的能力,优化性能得到显著提高．     

A novel particle swarm optimization algorithm with Levy flight

Particle swarm optimization (PSO) is one of the well-known population-based techniques used in global optimization and many engineering problems. Despite its simplicity and efficiency, the PSO has problems as being trapped in local minima due to premature convergence and weakness of global search capability. To overcome these disadvantages, the PSO is combined with Levy flight in this study. Levy flight is a random walk determining stepsize using Levy distribution. Being used Levy flight, a more efficient search takes place in the search space thanks to the long jumps to be made by the particles. In the proposed method, a limit value is defined for each particle, and if the particles could not improve self-solutions at the end of current iteration, this limit is increased. If the limit value determined is exceeded by a particle, the particle is redistributed in the search space with Levy flight method. To get rid of local minima and improve global search capability are ensured via this distribution in the basic PSO. The performance and accuracy of the proposed method called as Levy flight particle swarm optimization (LFPSO) are examined on well-known unimodal and multimodal benchmark functions. Experimental results show that the LFPSO is clearly seen to be more successful than one of the state-of-the-art PSO (SPSO) and the other PSO variants in terms of solution quality and robustness. The results are also statistically compared, and a significant difference is observed between the SPSO and the LFPSO methods. Furthermore, the results of proposed method are also compared with the results of well-known and recent population-based optimization methods.     

一种基于Cauchy变异的量子粒子群算法

和其他优化算法相比,粒子群算法有着简单易实现以及寻优结果快的优点,但研究结果表明标准粒子群算法在优化过程中存在着易于陷入最小的缺陷。文章提出了一种基于Cauchy策略的量子-粒子群算法。标准测试函数的仿真结果表明,新的算法不仅能够提高算法的全局搜索能力,而且能够加快算法的寻优速度,能够应用在实际工程中的函数优化问题。     

一种基于教与学的混合灰狼优化算法

针对灰狼优化算法(GWO)存在收敛精度不高、易陷入局部最优的不足,提出一种基于教与学的混合灰狼优化算法(HGWO).首先,采用佳点集理论进行种群初始化,提高初始种群的遍历性;其次,提出一种非线性控制参数策略,在迭代前期增加全局搜索能力,避免算法陷入局部最优,在迭代后期增加局部开发能力,提高收敛精度;最后,结合教与学算法(TLBO)和粒子群优化算法,修改原位置更新公式以优化算法搜索方式,从而提升算法的收敛性能.为验证HGWO算法的有效性,选取9种标准测试函数,将HGWO算法、GWO算法以及其他群体智能优化算法和其他改进GWO算法进行仿真实验.实验结果表明,所提出的HGWO算法性能优于GWO算法和其他群体智能优化算法,且在改进算法中具有一定优势.     

求解约束优化问题的动态邻域粒子群算法*

粒子群算法(PSO)求解约束优化问题存在较严重的早熟收敛现象,为了有效抑制早熟收敛,提出了基于改进的约束自适应方法的动态邻域粒子群算法(IPSO)。算法采用动态邻域策略提高算法的全局搜索能力,设计了一种改进的自适应约束处理方法,根据迭代代数线性增加搜索偏向系数,在早期偏向于搜索可行解,在后期偏向于搜索最优解,并引入序列二次规划增强算法的局部搜索能力。通过基准测试函数实验对比分析,表明该算法对于约束优化问题具有较好的全局收敛性。