The Particle Swarm Optimization (PSO) algorithm is a flexible heuristic optimizer that can be used for solving cardinality constrained binary optimization problems. In such problems, only K elements of the N-dimensional solution vector can be non-zero. The typical solution is to use a mapping function to enforce the cardinality constraint on the trial PSO solution. In this paper, we show that when K is small compared to N, the use of the mapped solution in the velocity vector tends to lead to early stagnation. As a solution, we recommend to use the untransformed solution as a direction in the velocity vector. We use numerical experiments to document the gains in performance when K is small compared to N.

中文翻译：

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速度稀疏度对基数约束粒子群算法性能的影响

粒子群优化（PSO）算法是一种灵活的启发式优化器，可用于解决基数受限的二进制优化问题。在这样的问题中，仅N维解向量的K个元素可以为非零。典型的解决方案是使用映射功能对试用PSO解决方案实施基数约束。在本文中，我们表明，当K小于N时，速度矢量中的映射解的使用往往会导致早期停滞。作为解决方案，我们建议使用未变换的解决方案作为速度矢量的方向。我们使用数值实验来证明当K小于ñ。