Dense conjugate initialization for deterministic PSO in applications: ORTHOinit+

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