A Survey of Swarm Intelligence Techniques in VLSI Routing Problems <s> 2) CPSO <s> The particle swarm optimizer (PSO) is a stochastic, population-based optimization technique that can be applied to a wide range of problems, including neural network training. This paper presents a variation on the traditional PSO algorithm, called the cooperative particle swarm optimizer, or CPSO, employing cooperative behavior to significantly improve the performance of the original algorithm. This is achieved by using multiple swarms to optimize different components of the solution vector cooperatively. Application of the new PSO algorithm on several benchmark optimization problems shows a marked improvement in performance over the traditional PSO. <s> BIB001 </s> A Survey of Swarm Intelligence Techniques in VLSI Routing Problems <s> 2) CPSO <s> Inspired by the phenomenon of symbiosis in natural ecosystem, a master-slave mode is incorporated into Particle Swarm Optimization (PSO), and a Multi-population Cooperative Optimization (MCPSO) is thus presented. In MCPSO, the population consists of one master swarm and several slave swarms. The slave swarms execute PSO (or its variants) independently to maintain the diversity of particles, while the master swarm enhances its particles based on its own knowledge and also the knowledge of the particles in the slave swarms. In the simulation part, several benchmark functions are performed, and the performance of the proposed algorithm is compared to the standard PSO (SPSO) to demonstrate its efficiency. <s> BIB002 </s> A Survey of Swarm Intelligence Techniques in VLSI Routing Problems <s> 2) CPSO <s> This paper attempts to address the question of scaling up Particle Swarm Optimization (PSO) algorithms to high dimensional optimization problems. We present a cooperative coevolving PSO (CCPSO) algorithm incorporating random grouping and adaptive weighting, two techniques that have been shown to be effective for handling high dimensional nonseparable problems. The proposed CCPSO algorithms out-performed a previously developed coevolving PSO algorithm on nonseparable functions of 30 dimensions. Furthermore, the scalability of the proposed algorithm to high dimensional nonseparable problems (of up to 1000 dimensions) is examined and compared with two existing coevolving Differential Evolution (DE) algorithms, and new insights are obtained. Our experimental results show the proposed CCPSO algorithms can perform reasonably well with only a small number of evaluations. The results also suggest that both the random grouping and adaptive weighting schemes are viable approaches that can be generalized to other evolutionary optimization methods. <s> BIB003 </s> A Survey of Swarm Intelligence Techniques in VLSI Routing Problems <s> 2) CPSO <s> This paper presents a new cooperative coevolving particle swarm optimization (CCPSO) algorithm in an attempt to address the issue of scaling up particle swarm optimization (PSO) algorithms in solving large-scale optimization problems (up to 2000 real-valued variables). The proposed CCPSO2 builds on the success of an early CCPSO that employs an effective variable grouping technique random grouping. CCPSO2 adopts a new PSO position update rule that relies on Cauchy and Gaussian distributions to sample new points in the search space, and a scheme to dynamically determine the coevolving subcomponent sizes of the variables. On high-dimensional problems (ranging from 100 to 2000 variables), the performance of CCPSO2 compared favorably against a state-of-the-art evolutionary algorithm sep-CMA-ES, two existing PSO algorithms, and a cooperative coevolving differential evolution algorithm. In particular, CCPSO2 performed significantly better than sep-CMA-ES and two existing PSO algorithms on more complex multimodal problems (which more closely resemble real-world problems), though not as well as the existing algorithms on unimodal functions. Our experimental results and analysis suggest that CCPSO2 is a highly competitive optimization algorithm for solving large-scale and complex multimodal optimization problems. <s> BIB004
The traditional PSO needs a mass of particles to deal with high-dimensional problems, so that the calculation is quite complicated and it is difficult to get a satisfactory solution. The general approach to solving high-dimensional problems is to adopt a divide-and-conquer strategy. Early CPSO algorithms are also based on this strategy. The CPSO proposed by Van den Bergh and Engelbrecht BIB001 decomposes the input vector into multiple sub-vectors and performs PSO for each sub-vector, and then integrates the search results into a global swarm. In 2005, Niu et al. BIB002 introduced the master-slave mode into PSO. A swarm is formed from one master swarm and multiple slave swarms. The slave swarms execute PSO (or its variants) independently to maintain the diversity of particles, while the master swarm enhances its particles based on its own knowledge and also the knowledge of the particles in the slave swarms. Reference BIB003 combines random grouping and adaptive weighting, and proposes Cooperatively Coevolving Particle Swarm Optimization (CCPSO), which can perform reasonably well with only a small number of evaluations. Later based on CCPSO, they adopted a new PSO position update rule that relies on Cauchy and Gaussian distributions to sample new points in the search space, and a scheme to dynamically determine the coevolving subcomponent sizes of the variables BIB004 . This method has become a very competitive method to solve complex multimodal optimization problems. PSO based on collaborative strategy is a powerful way to deal with high-dimensional problems. Parallel execution of multiple populations can speed up the efficiency. And information exchange in subgroups can balance exploration and exploitation, reducing the risk of premature convergence and local optimal. In dealing with complex VLSI routing issues, collaborative PSO has an opportunity to achieve better solutions.