This paper describes a class of novel initializations in Deterministic Particle Swarm Optimization (DPSO) for approximately solving costly unconstrained global optimization problems. The initializations are based on choosing specific dense initial positions and velocities for particles. These choices tend to induce in some sense orthogonality of particles’ trajectories, in the early iterations, in order to better explore the search space. Our proposal is inspired by both a theoretical analysis on a reformulation of PSO iteration, and by possible limits of the proposals reported in Campana et al. (2010); Campana et al. (2013). We explicitly show that, in comparison with other initializations from the literature, our initializations tend to scatter PSO particles, at least in the first iterations. The latter goal is obtained by imposing that the initial choice of particles’ position/velocity satisfies specific conjugacy conditions, with respect to a matrix depending on the parameters of PSO. In particular, by an appropriate condition on particles’ velocities, our initializations also resemble and partially extend a general paradigm in the literature of exact methods for derivative-free optimization. Moreover, we propose dense initializations for DPSO, so that the final approximate global solution obtained is possibly not too sparse, which might cause troubles in some applications. Numerical results, on both Portfolio Selection and Computational Fluid Dynamics problems, validate our theory and prove the effectiveness of our proposal, which applies also in case different neighborhood topologies are adopted in DPSO.

本文介绍了确定性粒子群优化（DPSO）中的一类新颖的初始化方法，用于近似解决代价高昂的不受约束的全局优化问题。初始化基于为粒子选择特定的密集初始位置和速度。这些选择在某种程度上倾向于在早期迭代中引起粒子轨迹的正交性，以便更好地探索搜索空间。我们的提议既受到对PSO迭代重新制定的理论分析的启发，也受到Campana等人报告的提议的可能局限性的启发。（2010）；Campana等。（2013）。我们明确地表明，与文献中的其他初始化相比，我们的初始化至少在第一次迭代中倾向于分散PSO粒子。通过强加粒子的位置/速度的初始选择相对于取决于PSO参数的矩阵满足特定的共轭条件，可以实现后一个目标。特别地，通过对粒子速度的适当条件，我们的初始化也类似于并部分扩展了无导数优化的精确方法文献中的一般范式。此外，我们建议对DPSO进行密集的初始化，以便最终获得的近似全局解可能不太稀疏，这可能在某些应用程序中引起麻烦。关于投资组合选择和计算流体动力学问题的数值结果验证了我们的理论并证明了我们的建议的有效性，这也适用于DPSO采用不同邻域拓扑的情况。