A new evolutionary search strategy for global optimization of high-dimensional problems

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population’s capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones.     

高维化工数据共轭粒子群算法处理

针对化工数据多为高维数据,而粒子群算法对求解高维优化问题易陷局部极值,提出将共轭方向法与粒子群算法相结合处理高维数据.当粒子群算法迭代了一定步数而陷入局部极值并得局部最优解χ*时,以χ*为初值,用共轭方向法对其求解,利用粒子群算法对低维优化问题的有效性,将得新的更优的当前最优解χ**,从而使算法跳出局部极值;在新极值的条件下,又用粒子群算法对原问题求解,如此反复直至结束.通过经典的测试函数对其测试,结果表明这一尝试是有效的.最后将算法用于SO2催化氧化反应动力学模型的非线性参数估计,获得满意效果.     

A new gradient based particle swarm optimization algorithm for accurate computation of global minimum

Stochastic optimization algorithms like genetic algorithms (GAs) and particle swarm optimization (PSO) algorithms perform global optimization but waste computational effort by doing a random search. On the other hand deterministic algorithms like gradient descent converge rapidly but may get stuck in local minima of multimodal functions. Thus, an approach that combines the strengths of stochastic and deterministic optimization schemes but avoids their weaknesses is of interest. This paper presents a new hybrid optimization algorithm that combines the PSO algorithm and gradient-based local search algorithms to achieve faster convergence and better accuracy of final solution without getting trapped in local minima. In the new gradient-based PSO algorithm, referred to as the GPSO algorithm, the PSO algorithm is used for global exploration and a gradient based scheme is used for accurate local exploration. The global minimum is located by a process of finding progressively better local minima. The GPSO algorithm avoids the use of inertial weights and constriction coefficients which can cause the PSO algorithm to converge to a local minimum if improperly chosen. The De Jong test suite of benchmark optimization problems was used to test the new algorithm and facilitate comparison with the classical PSO algorithm. The GPSO algorithm is compared to four different refinements of the PSO algorithm from the literature and shown to converge faster to a significantly more accurate final solution for a variety of benchmark test functions.     

A two-stage quantum-behaved particle swarm optimization with skipping search rule and weight to solve continuous optimization problem

Quantum-behaved particle swarm optimization (QPSO) is a recently developed heuristic method by particle swarm optimization (PSO) algorithm based on quantum mechanics, which outperforms the search ability of original PSO. But as many other PSOs, it is easy to fall into the local optima for the complex optimization problems. Therefore, we propose a two-stage quantum-behaved particle swarm optimization with a skipping search rule and a mean attractor with weight. The first stage uses quantum mechanism, and the second stage uses the particle swarm evolution method. It is shown that the improved QPSO has better performance, because of discarding the worst particles and enhancing the diversity of the population. The proposed algorithm (called ‘TSQPSO’) is tested on several benchmark functions and some real-world optimization problems and then compared with the PSO, SFLA, RQPSO and WQPSO and many other heuristic algorithms. The experiment results show that our algorithm has better performance than others.     

基于动态行为选择的和声搜索算法

和声搜索算法是一种模拟音乐即兴创作过程的元启发式搜索,已成功应用于解决许多实际问题.针对高维函数优化问题,提出一种基于动态行为选择的和声搜索算法.在算法中新和声的即兴创作有3种策略,迭代过程中通过计算每个策略的即时价值和综合价值选择和声的即兴创作策略,并通过个体即兴创作策略选择方法提升寻优速度或避免陷入局部最优解.将所提出算法与9个改进和声搜索算法在22个基准函数上进行对比.实验结果表明,所提出算法具有较好的求解精度、稳定性和收敛速度,擅长于解决复杂的高维问题.     

Gradient-based adaptive particle swarm optimizer with improved extremal optimization

Most real-world applications can be formulated as optimization problems, which commonly suffer from being trapped into the local optima. In this paper, we make full use of the global search capability of particle swarm optimization (PSO) and local search ability of extremal optimization (EO), and propose a gradient-based adaptive PSO with improved EO (called GAPSO-IEO) to overcome the issue of local optima deficiency of optimization in high-dimensional search and reduce the time complexity of the algorithm. In the proposed algorithm, the improved EO (IEO) is adaptively incorporated into PSO to avoid the particles being trapped into the local optima according to the evolutional states of the swarm, which are estimated based on the gradients of the fitness functions of the particles. We also improve the mutation strategy of EO by performing polynomial mutation (PLM) on each particle, instead of on each component of the particle, therefore, the algorithm is not sensitive to the dimension of the swarm. The proposed algorithm is tested on several unimodal/multimodal benchmark functions and Berkeley Segmentation Dataset and Benchmark (BSDS300). The results of experiments have shown the superiority and efficiency of the proposed approach compared with those of the state-of-the-art algorithms, and can achieve better performance in high-dimensional tasks.     

一种基于粒子群算法求解约束优化问题的混合算法

通过将粒子群算法(PSO)与差别进化算法(DE)相结合，提出一种混合算法PSODE，用于求解约束优化问题．PSODE是在PSO算法中适当引入不可行解，将粒子群拉向约束边界，加强对约束边界的搜索，同时与DE算法结合以加强搜索能力．基于典型高维复杂函数的仿真表明，该算法简单高效，鲁棒性强．     

Particle swarm optimization with adaptive time-varying topology connectivity

Particle swarm optimization (PSO) has shown its competitive performance for solving benchmark and real-world optimization problems. Nevertheless, it requires better control of exploration/exploitation searches to prevent the premature convergence of swarms. Thus, this paper proposes a new PSO variant called PSO with adaptive time-varying topology connectivity (PSO-ATVTC) that employs an ATVTC module and a new learning framework. The proposed ATVTC module specifically aims to balance the algorithm's exploration/exploitation searches by varying the particle's topology connectivity with time according to its searching performance. The proposed learning framework consists of a new velocity update mechanism and a new neighborhood search operator to improve the algorithm's performance. A comprehensive study was conducted on 24 benchmark functions and one real-world problem. Compared with nine well-established PSO variants and six other cutting-edge metaheuristic search algorithms, the searching performance of PSO-ATVTC was proven to be more prominent in majority of the tested 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。     

粒子群优化算法的性能分析和参数选择

惯性权重和加速因子是影响粒子群算法优化性能的重要参数.基于常用的12个测试函数,本文通过实验研究了不同参数组合下粒子的探索能力和算法的优化性能,在此基础上推荐了一组固定的参数组合.通过惯性权重和加速因子的不同变化策略组合对算法性能影响的实验分析,推荐了一种变化的参数设置方法.基于CEC2015发布的15个基准函数进一步验证了本文推荐的参数选取方法的有效性.最后讨论了粒子群优化（Particle swarm optimization,PSO）算法在连续优化和离散优化方面的应用问题.