An improved ?-PSO algorithm with mutation

Aiming at the shortcoming of basic PSO algorithm, that is, easily plunging into the local minimum, we propose an advanced PSO algorithm with mutation operator. By adding the mutation operator to the algorithm, the advanced algorithm can not only escape from the local minimum's basin of attraction of the later phase, but also maintain the characteristic of fast speed in the early convergence phase. By the contrast experiments of three multimodal test functions and an example whose problem space is non-convex set, it has been proved that the advanced PSO algorithm can improve the global convergence ability, greatly enhance the rate of convergence and overcome the shortcoming of basic PSO algorithm.

In order to overcome the drawbacks of falling into local extremum and lower optimization precision of standard particle swarm optimization (PSO) algorithm, multipopulation strategy, adaptive dynamic adjustment strategy and co-evolution mode are introduced into the standard PSO algorithm in order to propose an improved coevolutionary PSO(MPACEPSO) algorithm based on multi-strategy evolution mode and multi-population co-evolutionary mechanism. In the evolutionary process of MPACEPSO algorithm, the multi-population strategy is used to divide the population into several subpopulations, which use different co-evolutionary model to evolve. These sub-populations are influenced and promoted each other in order to realize the exchange of information and co-evolution among the sub-populations, improve the convergence speed and search precision of MPACEPSO algorithm, and effectively suppress the appearance of the local optimum. The adaptive dynamic adjustment strategy of inertia weight is used to keep the diversity of population, reduce the probability of falling into the local extremum. Finally, the ZDT functions are selected to test the optimization performance of proposed MPACEPSO algorithm. The experimental results show that the proposed MPACEPSO algorithm has faster convergence speed, stronger global search ability, higher solving precision and better dynamic optimization performance. The experimental result analysis shows that the proposed MPACEPSO algorithm is insensitive to parameters and easy to be used in solving the complex optimization problems.

The standard particle swarm optimization algorithm (simply called PSO) has many advantages such as rapid convergence. However, a major disadvantage confronting the PSO algorithm is that they often converge to some local optimization. In order to avoid the occurrence of premature convergence and local optimization of the PSO algorithm, a particle swarm optimization algorithm based on genetic selection stra-tegy, simply called GSS-PSO, is singled out in this paper. GSS-PSO not only retains the rapid convergence charactering of the standard PSO algorithms, but also scales up their global search ability. At last, we experimentally tested the efficiency of our new GSS-PSO algorithm using eight classical functions. The experimental results show that our new GSS-PSO algorithm is generally better than the PSO algorithm.KeywordsPSOConvergenceFunction optimizationGSS

A novel orthogonal PSO algorithm based on orthogonal diagonalization

Particle Swarm Optimization (PSO) algorithm has recently gained more attention in the global optimization research due to its simplicity and global search ability. This paper proposes a hybrid of PSO and Generalized Generation Gap model with Parent- Centric Recombination operator (G3PCX) [25], a well-known real-coded genetic algorithm. The proposed hybrid algorithm, namely PSPG, combines fast convergence and rotational invariance of G3PCX as well as global search ability of PSO. The performance of PSPG algorithm is evaluated using 8 widely-used nonlinear benchmark functions of 30 and 200 decision variables having different properties. The experiments study the effects of its new probability parameter Px and swarm size for optimizing those functions. The results are analyzed and compared with those from the Standard PSO [14] and G3PCX algorithms. The proposed PSPG with Px = 0.10 and 0.15 can outperform both algorithms with a statistical significance for most functions. In addition, the PSPG is not much sensitive to its swarm size as most PSO algorithms are. The best swarm sizes are 40 and 50 for unimodal and multimodal functions, respectively, of 30 decision variables.

In recent years a number of works have been done to extend Particle Swarm Optimization (PSO) to solve multi-objective optimization problems, but a few of them can be used to tackle binary-coded problems. In this paper, a novel modified multi-objective binary PSO (MMBPSO) algorithm is proposed for the better multi-objective optimization performance. A modified updating strategy is developed which is simpler and easier to implement compared with standard discrete binary PSO. The mutation operator and dissipation operator are introduced to improve the search ability and keep the diversity of algorithm. The experimental results on a set of multi-objective benchmark functions demonstrate that the proposed MBBPSO is a competitive multi-objective optimizer and outperforms the standard binary PSO algorithm in terms of convergence and diversity.

In order to improve the stability and sensitivity of particle swarm optimization (PSO) algorithm and to solve the problem of premature convergence, in this re-search, a computer PSO algorithm based on thermodynamic motion mechanism is proposed based on the principle of thermodynamic motion mechanism. Firstly, the thermodynamic motion phenomenon, the diffusion law in kinematics and the standard PSO algorithm are introduced. Then, according to the basic idea of thermodynamic motion mechanism, the standardized PSO algorithm is optimized and its optimization process is introduced. Finally, the experimental results are analysed by setting the test function. The results show that among the five test functions, the computer PSO algorithm based on thermodynamic motion mechanism has a higher probability of jumping out of the local optimal solution. Its robustness and stability are much better than standard PSO algorithms. The evolution ability of the computer PSO algorithm based on thermodynamic motion mechanism is better than that of the standard PSO algorithm. The standard PSO algorithm is superior because it is based on thermodynamic motion mechanism. The research in this paper can provide good guidance for improving the performance of PSO algorithm.

Particle swarm optimisation PSO is a population-based stochastic search algorithm, which simulates the social behaviour of bird flocking or fish schooling. Many previous studies have shown that PSO is an effective optimisation technique in evolutionary optimisation community. However, the standard PSO still suffers from premature convergence when solving complex multimodal problems. In this paper, we propose a new PSO algorithm called multi-strategy based bare bones PSO MPSO. The MPSO introduces generalised opposition-based learning GOBL and two neighbourhood search strategies into the original bare bones PSO. Simulation study is conducted on 13 well-known benchmark functions. The results show that MPSO achieves better results than the standard PSO and two other PSO algorithms.

An improved Chaotic Particle Swarm Optimization (CPSO) algorithm for a jobshop scheduling problem, with minimization of makespan as the criterion, is proposed in this research. A real-valued encoding scheme based on a matrix representation is developed, which converts the continuous position value of particles in PSO to the processing order of job operation. A compound chaotic search strategy that integrates both Tent and Logistic chaotic search process is employed to the global best particle to enhance the local searching ability of PSO. In addition, a gaussian disturbance technology is embedded in the CPSO algorithm to improve the diversity of the particles in the swarm. The performance of CPSO is compared with the standard PSO algorithm on a benchmark instance of jobshop scheduling problems. The results show that the proposed CPSO algorithm has a superior performance to the PSO algorithm.

In this paper, a novel method for robotic belt grinding based on support vector machine and particle swarm optimization algorithm is presented. Firstly, the dynamic model of the robotic belt grinding process is built using support vector machine method. This is the basis of our work because the dynamic model shows the relation between the removal and control parameters (contact force and robot's speed) of robot. Secondly, the method of reverse solution of the dynamic model is introduced. According to this method, control parameters of robot can be accurately calculated by the given value of removal. Thirdly, the standard PSO algorithm is introduced to get smooth and stable trajectories of the control parameters, because the trajectory jitter of the control parameters has a great influence on the grinding accuracy. Finally, a variation on the traditional PSO algorithm is presented, which is called the cooperative particle swarm optimizer, or CPSO, employing cooperative behavior to significantly improve the performance of the original algorithm. The experiment results show that the novel method for robotic belt grinding performs well in the control of the robot parameters and the grinding accuracy and efficiency is improved.

In this paper, we discuss the implementation of Evolutionary Programming (EP) using a mutation operator based on Levy probability distribution and investigate its performance in optimization of selected antenna problems. Since the shape-parameter, alpha, in the Levy distribution results in Cauchy and Gaussian distributions for values of 1 and 2, respectively, one can design adaptive schemes that dynamically change the shape of Levy distribution in generation of offsprings during the evolutionary process in order to exploit the desirable properties of these two distributions. In particular, we introduce a simple adaptive scheme and compare its performance in antenna optimization to adaptive and non-adaptive schemes, previously reported in the literature.

Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [−1, 1], and Gauss distribution with mean 0 and variance 1 ( U [ 0 , 1 ] , U [ − 1 , 1 ] and G ( 0 , 1 ) ), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles.

Due to its complexity and non-deterministic polynomial-time hard characteristic, multirobot task allocation problem remains a challenging issue in the field of cooperative robotics. Thanks to its easy implementation and promising convergence speed, the particle swarm optimization method has recently aroused increasing research interest in the area of multirobot task allocation problem. However, the efficiency of the standard particle swarm optimization is hindered by several deficiencies such as the inefficient capabilities in balancing exploration and exploitation, as well as the high likelihood of plunging into stagnation. Aiming at enhancing the performance of particle swarm optimization via remedying these two drawbacks, this paper proposes an improved particle swarm optimization method, which integrates standard particle swarm optimization 2011 with evolutionary game theory. To prevent particles being locked into stagnation, particles in the proposed particle swarm optimization first adopt the updating rules of standard particle swarm optimization 2011 to undertake their movements. Subsequently, attempting to well trade off the exploration and exploitation capabilities of particles, a novel self-adaptive strategy, which is determined by the evolutionary stable strategies of evolutionary game theory and the iteration number of particle swarm optimization, is presented to adaptively adjust the main control parameters of particles in the proposed particle swarm optimization. Since the convergence of particle swarm optimization remains paramount and dramatically affects the performance of particle swarm optimization, this paper also analytically investigates the convergence of the proposed particle swarm optimization and provides a convergence-guaranteed parameter selection principle for the proposed method. Finally, leveraging the development of the proposed particle swarm optimization, this paper completes the design of a new particle swarm optimization–based multirobot task allocation method. The performance of the new particle swarm optimization–based multirobot task allocation method is tested through three different allocation cases against four well-known evolutionary methods. Experimental results confirm that the proposed method generally outperforms its contenders in terms of the solution quality. Moreover, the proposed method performs slightly better than the majority of its peers as far as the computation time is concerned.

To deal with non-paper test composition algorithm impact on exam quality, we proposed the test-sheet composition algorithms. By comparing a variety of existing intelligent algorithms in the application of test-sheet composition, we identify the shortcomings of existing algorithms, such as the "premature" of algorithm due to the poor local search ability and the low convergence rate, etc. PSO algorithm has no crossover, mutation operators. It directly provides the speed, position update formula, and completes the assessment with the help of the fitness function of iterations. The principles and mechanisms of algorithm are simpler. On the basis of standard PSO algorithm, we proposed a Binary Particle Swarm Optimize (BPSO) algorithm based on probability. Bayes formula was used to overcome the human factors impacting on algorithm convergence speed. The algorithm validity has been shown in the simulation experiment with Java.

This article presents a novel parallel multi-swarm optimization (PMSO) algorithm with the aim of enhancing the search ability of standard single-swarm PSOs for global optimization of very large-scale multimodal functions. Different from the existing multi-swarm structures, the multiple swarms work in parallel, and the search space is partitioned evenly and dynamically assigned in a weighted manner via the roulette wheel selection (RWS) mechanism. This parallel, distributed framework of the PMSO algorithm is developed based on a master–slave paradigm, which is implemented on a cluster of PCs using message passing interface (MPI) for information interchange among swarms. The PMSO algorithm handles multiple swarms simultaneously and each swarm performs PSO operations of its own independently. In particular, one swarm is designated for global search and the others are for local search. The first part of the experimental comparison is made among the PMSO, standard PSO, and two state-of-the-art algorithms (CTSS and CLPSO) in terms of various un-rotated and rotated benchmark functions taken from the literature. In the second part, the proposed multi-swarm algorithm is tested on large-scale multimodal benchmark functions up to 300 dimensions. The results of the PMSO algorithm show great promise in solving high-dimensional problems.