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Analysis and Investigation of Frame Invariance and Particle Behavior for PiecewiseLinear Particle Swarm Optimizer
Tomoyuki SASAKI Hidehiro NAKANO
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E102A
No.12
pp.19561967 Publication Date: 2019/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E102.A.1956
Type of Manuscript: PAPER Category: Nonlinear Problems Keyword: particle swarm optimization, swarm intelligence, piecewiselinear system, deterministic system,
Full Text: PDF(4.2MB)>>
Summary:
Particle swarm optimization (PSO) is a swarm intelligence algorithm and has good search performance and simplicity in implementation. Because of its properties, PSO has been applied to various optimization problems. However, the search performance of the classical PSO (CPSO) depends on reference frame of solution spaces for each objective function. CPSO is an invariant algorithm through translation and scale changes to reference frame of solution spaces but is a rotationally variant algorithm. As such, the search performance of CPSO is worse in solving rotated problems than in solving nonrotated problems. In the reference frame invariance, the search performance of an optimization algorithm is independent on rotation, translation, or scale changes to reference frame of solution spaces, which is a property of preferred optimization algorithms. In our previous study, piecewiselinear particle swarm optimizer (PPSO) has been proposed, which is effective in solving rotated problems. Because PPSO particles can move in solution spaces freely without depending on the coordinate systems, PPSO algorithm may have rotational invariance. However, theoretical analysis of reference frame invariance of PPSO has not been done. In addition, although behavior of each particle depends on PPSO parameters, good parameter conditions in solving various optimization problems have not been sufficiently clarified. In this paper, we analyze the reference frame invariance of PPSO theoretically, and investigated whether or not PPSO is invariant under reference frame alteration. We clarify that control parameters of PPSO which affect movement of each particle and performance of PPSO through numerical simulations.

