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.     

Co-evolutionary particle swarm optimization to solve constrained optimization problems

This paper presents a co-evolutionary particle swarm optimization (CPSO) algorithm to solve global nonlinear optimization problems. A new co-evolutionary PSO (CPSO) is constructed. In the algorithm, a deterministic selection strategy is proposed to ensure the diversity of population. Meanwhile, based on the theory of extrapolation, the induction of evolving direction is enhanced by adding a co-evolutionary strategy, in which the particles make full use of the information each other by using gene-adjusting and adaptive focus-varied tuning operator. Infeasible degree selection mechanism is used to handle the constraints. A new selection criterion is adopted as tournament rules to select individuals. Also, the infeasible solution is properly accepted as the feasible solution based on a defined threshold of the infeasible degree. This diversity mechanism is helpful to guide the search direction towards the feasible region. Our approach was tested on six problems commonly used in the literature. The results obtained are repeatedly closer to the true optimum solution than the other techniques.     

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.     

A discrete version of particle swarm optimization for flowshop scheduling problems

Particle swarm optimization (PSO) is a novel metaheuristic inspired by the flocking behavior of birds. The applications of PSO to scheduling problems are extremely few. In this paper, we present a PSO algorithm, extended from discrete PSO, for flowshop scheduling. In the proposed algorithm, the particle and the velocity are redefined, and an efficient approach is developed to move a particle to the new sequence. To verify the proposed PSO algorithm, comparisons with a continuous PSO algorithm and two genetic algorithms are made. Computational results show that the proposed PSO algorithm is very competitive. Furthermore, we incorporate a local search scheme into the proposed algorithm, called PSO-LS. Computational results show that the local search can be really guided by PSO in our approach. Also, PSO-LS performs well in flowshop scheduling with total flow time criterion, but it requires more computation times.     

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.     

定位-运输路线安排问题的改进离散粒子群优化算法

定位-运输路线安排问题(LRP)是集成物流中的一个NP-hard难题,为求解一类特殊的LRP问题,提出改进的离散粒子群优化算法.该方法采用整体优化的思想,将LAP和VRP集成在一起.通过合适的粒子编码方式,并改进粒子的运动方程,引入相应的变异算子和趋同扰动算子等,使得算法的适用性和性能获得了改善.通过仿真实验及与另2个典型算法的比较分析,证明了该算法的有效性.     

A revised particle swarm optimization based discrete Lagrange multipliers method for nonlinear programming problems

In this paper, a new algorithm for solving constrained nonlinear programming problems is presented. The basis of our proposed algorithm is none other than the necessary and sufficient conditions that one deals within a discrete constrained local optimum in the context of the discrete Lagrange multipliers theory. We adopt a revised particle swarm optimization algorithm and extend it toward solving nonlinear programming problems with continuous decision variables. To measure the merits of our algorithm, we provide numerical experiments for several renowned benchmark problems and compare the outcome against the best results reported in the literature. The empirical assessments demonstrate that our algorithm is efficient and robust.     

改进的粒子群算法求解非线性约束优化问题

提出了一种改进的粒子群算法（Improved Particle Swarm Optimization,IPSO）,使用了一种新型的变异策略,并在搜索过程中将部分邻近的个体聚集成核,从而形成多子群引导粒子探测新的搜索区域,采用了简单易行的罚函数约束处理机制,使算法在求解较难的非线性约束优化问题时具有很强的全局搜索能力与效率。对比数值实验结果表明,该算法能够有效、稳定地求解非线性约束优化问题。     

Improved global-best-guided particle swarm optimization with learning operation for global optimization problems

In this paper, an improved global-best-guided particle swarm optimization with learning operation (IGPSO) is proposed for solving global optimization problems. The particle population is divided into current population, historical best population and global best population, and each population is assigned a corresponding searching strategy. For the current population, the global neighborhood exploration strategy is employed to enhance the global exploration capability. A local learning mechanism is used to improve local exploitation ability in the historical best population. Furthermore, stochastic learning and opposition based learning operations are employed to the global best population for accelerating convergence speed and improving optimization accuracy. The effects of the relevant parameters on the performance of IGPSO are assessed. Numerical experiments on some well-known benchmark test functions reveal that IGPSO algorithm outperforms other state-of-the-art intelligent algorithms in terms of accuracy, convergence speed, and nonparametric statistical significance. Moreover, IGPSO performs better for engineering design optimization problems.     

An improved quantum-behaved particle swarm optimization for multi-peak optimization problems

In this paper, we propose an improved quantum-behaved particle swarm optimization (QPSO), namely species-based QPSO (SQPSO), using the notion of species for solving multi-peak optimization problems. In the proposed SQPSO, the population is divided into subpopulations (species) based on their similarities. Each species is grouped around a dominating particle called the species seed. During the process of iterations, species are able to simultaneously optimize towards multiple optima by using QPSO, so each peak will definitely be searched in parallel, regardless of whether it is global or local optima. Further, SQPSO is applied to solve systems of nonlinear equations describing certain fitness functions, which are multi-peak functions. Our experiments demonstrate that SQPSO is able to search multiple peaks of a given function as accurate and efficient as possible. Finally the experiments for the solutions of systems of nonlinear equations show that the algorithm is successful in locating multiple solutions with better accuracy.     

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.     

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.     

一类非线性极小极大问题的改进粒子群算法

针对一类非线性极小极大问题目标函数非光滑的特点给求解带来的困难,利用改进的粒子群算法并结合极大熵函数法给出了此类问题的一种新的有效算法。首先利用极大熵函数将无约束和有约束极小极大问题转化为一个光滑函数的无约束最优化问题,将此光滑函数作为粒子群算法的适应值函数;然后用数学中的外推方法给出一个新的粒子位置更新公式,并应用这个改进的粒子群算法来优化此问题。数值结果表明,该算法收敛快﹑数值稳定性好,是求解非线性极小极大问题的一种有效算法。     

一种弹性粒子群优化算法

当某个粒子与最优粒子很接近时,其飞行速度将趋于零,这是粒子群优化算法容易陷入局部极小的主要原因.为此,提出一种弹性粒子群优化算法.算法中,粒子速度不依赖其与最优粒子之间距离的大小,而仅依赖于其方向信息,并采用一种自适应策略弹性地修正粒子速度的幅值.将弹性粒子群优化算法应用于几种典型测试函数的优化,数值仿真结果表明,弹性粒子群优化算法能有效地找出全局最优点.     

Conjugate direction particle swarm optimization solving systems of nonlinear equations

Solving systems of nonlinear equations is a difficult problem in numerical computation. For most numerical methods such as the Newton’s method for solving systems of nonlinear equations, their convergence and performance characteristics can be highly sensitive to the initial guess of the solution supplied to the methods. However, it is difficult to select a good initial guess for most systems of nonlinear equations. Aiming to solve these problems, Conjugate Direction Particle Swarm Optimization (CDPSO) was put forward, which introduced conjugate direction method into Particle Swarm Optimization (PSO)in order to improve PSO, and enable PSO to effectively optimize high-dimensional optimization problem. In one optimization problem, when after some iterations PSO got trapped in local minima with local optimal solution , conjugate direction method was applied with as a initial guess to optimize the problem to help PSO overcome local minima by changing high-dimension function optimization problem into low-dimensional function optimization problem. Because PSO is efficient in solving the low-dimension function optimization problem, PSO can efficiently optimize high-dimensional function optimization problem by this tactic. Since CDPSO has the advantages of Method of Conjugate Direction (CD) and Particle Swarm Optimization (PSO), it overcomes the inaccuracy of CD and PSO for solving systems of nonlinear equations. The numerical results showed that the approach was successful for solving systems of nonlinear equations.     

Neutrino-like particle for particle swarm optimization

The real-world optimal problems frequently encountered by various industries are the nonlinear constrained optimization problems (NCOPs), where the constraints represent the limitations of practical resources. Many researchers have attempted to improve particle swarm optimization (PSO) in the past decades; however, in solving the NCOPs, the PSO-based approaches often cause premature convergences. The problem-specific constraints frequently generate many infeasible regions that block the movements of particles. The particles' behavior causes the exploration abilities of particles that tend to weaken along with time. The decreasing of exploration ability often comes from the particle becoming stagnant or moving unusefully. This study proposes a neutrino-like particle (NLP) with adaptive NLP hyperparameters that simulate the natural neutrino behavior. The proposed NLPs can be embedded in the PSO-based approaches for overcoming premature convergence. The experiment results demonstrate that all referenced PSO-based methods with the NLPs improved significantly compared with those without the NLPs to solve the NCOPs. All referenced PSO-based methods that embedded the NLPs also significantly outperform four recent strong algorithms in most IEEE CEC 2020 benchmark problems. Therefore, the proposed NLPs with adaptive NLP hyperparameters can effectively solve the premature convergences, reinforce the exploration ability, and maintain the exploitation capability for solving the NCOPs over the whole evolution process.     

Parameter selection in synchronous and asynchronous deterministic particle swarm optimization for ship hydrodynamics problems

Deterministic optimization algorithms are very attractive when the objective function is computationally expensive and therefore the statistical analysis of the optimization outcomes becomes too expensive. Among deterministic methods, deterministic particle swarm optimization (DPSO) has several attractive characteristics such as the simplicity of the heuristics, the ease of implementation, and its often fairly remarkable effectiveness. The performances of DPSO depend on four main setting parameters: the number of swarm particles, their initialization, the set of coefficients defining the swarm behavior, and (for box-constrained optimization) the method to handle the box constraints. Here, a parametric study of DPSO is presented, with application to simulation-based design in ship hydrodynamics. The objective is the identification of the most promising setup for both synchronous and asynchronous implementations of DPSO. The analysis is performed under the assumption of limited computational resources and large computational burden of the objective function evaluation. The analysis is conducted using 100 analytical test functions (with dimensionality from two to fifty) and three performance criteria, varying the swarm size, initialization, coefficients, and the method for the box constraints, resulting in more than 40,000 optimizations. The most promising setup is applied to the hull-form optimization of a high speed catamaran, for resistance reduction in calm water and at fixed speed, using a potential-flow solver.     

一种多样性控制的粒子群优化算法

针对粒子群优化(PSO)算法的早熟收敛问题,提出一种新的基于群体多样性控制的PSO算法(DCPSO).该方法使得粒子在收缩状态下充分搜索,在发散状态下能够飞离群体的聚集位置,不断的收缩-发散过程保证了群体能在较大的空间进行搜索,减少了粒子群算法的早熟收敛现象.通过对多个标准测试函数的实验结果表明,DCPSO算法在复杂优化问题中具有较强的全局搜索能力,而且比现有的多样性指导的PSO算法(ARPSO)具有更好的性能.     

一种基于粒子群优化的非线性系统辨识方法

针对单入单出离散时间非线性动态系统提出一种辨识方法.该方法采用带误差修正的改进泛模型作为非线性系统的结构模型,模型中的时变特征参量及误差修正系数采用粒子群（PSO）算法优化,优化后的模型可以逼近非线性系统.该方法简单、易于实现.通过对Box-Jenkins煤气炉数据等非线性被控对象的仿真研究及对模型的分析,表明了所提出算法的有效性.     

离散微粒群优化算法的研究进展

首先,介绍了近年来出现的５种较为典型的离散ＰＳＯ,并分析了它们与基本ＰＳＯ 之间的联系和区别;然后,归纳了提高离散ＰＳＯ 优化性能的若干途径,并总结了离散ＰＳＯ 的应用现状;最后,探讨了离散ＰＳＯ 有待进一步研究的若干方向和内容．