The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
입자 군집 최적화(PSO)는 군집 지능 알고리즘으로 검색 성능이 뛰어나고 구현이 단순합니다. PSO는 그 특성으로 인해 다양한 최적화 문제에 적용되었습니다. 그러나 CPSO(클래식 PSO)의 검색 성능은 각 목적 함수에 대한 솔루션 공간의 참조 프레임에 따라 달라집니다. CPSO는 솔루션 공간의 참조 프레임에 대한 변환 및 스케일 변경을 통한 불변 알고리즘이지만 회전 변형 알고리즘입니다. 따라서 CPSO의 검색 성능은 회전되지 않은 문제를 해결하는 것보다 회전된 문제를 해결하는 경우 더 나쁩니다. 참조 프레임 불변성에서 최적화 알고리즘의 검색 성능은 선호하는 최적화 알고리즘의 속성인 솔루션 공간의 참조 프레임에 대한 회전, 변환 또는 크기 변경에 독립적입니다. 이전 연구에서는 회전 문제를 해결하는 데 효과적인 PPSO(Piecewise-Linear Particle Swarm Optimizer)가 제안되었습니다. PPSO 입자는 좌표계에 의존하지 않고 솔루션 공간에서 자유롭게 이동할 수 있으므로 PPSO 알고리즘은 회전 불변성을 가질 수 있습니다. 그러나 PPSO의 참조 프레임 불변성에 대한 이론적 분석은 수행되지 않았습니다. 또한, 각 입자의 거동은 PPSO 매개변수에 따라 달라지지만, 다양한 최적화 문제를 해결하기 위한 좋은 매개변수 조건은 충분히 명확하지 않습니다. 본 논문에서는 PPSO의 참조 프레임 불변성을 이론적으로 분석하고, 참조 프레임 변경 시 PPSO가 불변인지 여부를 조사했습니다. 수치모사를 통해 각 입자의 움직임과 PPSO의 성능에 영향을 미치는 PPSO의 제어변수를 명확히 한다.
Tomoyuki SASAKI
Shonan Institute of Technology
Hidehiro NAKANO
Tokyo City University
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Tomoyuki SASAKI, Hidehiro NAKANO, "Analysis and Investigation of Frame Invariance and Particle Behavior for Piecewise-Linear Particle Swarm Optimizer" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 12, pp. 1956-1967, December 2019, doi: 10.1587/transfun.E102.A.1956.
Abstract: 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 non-rotated 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, piecewise-linear 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1956/_p
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@ARTICLE{e102-a_12_1956,
author={Tomoyuki SASAKI, Hidehiro NAKANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis and Investigation of Frame Invariance and Particle Behavior for Piecewise-Linear Particle Swarm Optimizer},
year={2019},
volume={E102-A},
number={12},
pages={1956-1967},
abstract={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 non-rotated 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, piecewise-linear 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.},
keywords={},
doi={10.1587/transfun.E102.A.1956},
ISSN={1745-1337},
month={December},}
부
TY - JOUR
TI - Analysis and Investigation of Frame Invariance and Particle Behavior for Piecewise-Linear Particle Swarm Optimizer
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1956
EP - 1967
AU - Tomoyuki SASAKI
AU - Hidehiro NAKANO
PY - 2019
DO - 10.1587/transfun.E102.A.1956
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2019
AB - 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 non-rotated 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, piecewise-linear 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.
ER -