Analysis of Reference Frame Invariance for Piecewise-Linear Particle Swarm Optimizer
Tomoyuki Sasaki, Hidehiro Nakano · 2018
Piecewise-linear particle swarm optimizer (PPSO) is one of swarm-based optimization algorithms. Although PPSO is a deterministic particle swarm optimization (D-PSO) algorithm, its performance is better than the classical PSO's performance in solving various optimization problems. In particular, PPSO is effective in solving non-separable problems such as rotated problems. In our previous study, we have investigated that PPSO particles can move not only in a direction parallel to the coordinate axes, but also in various directions. We therefore assumed that PPSO particles do not depend on reference frame. In this paper, we analyzed that PPSO algorithm is reference frame invariant (i.e., scaling, translation, and rotational invariants) theoretically, and in order to study effectiveness of the theoretical analysis, we performed numerical experiments and clarified whether PPSO algorithm is reference frame invariant or not.