Analysis of an optimizer based on piecewise-rotational chaotic system

Abstract

An optimization method based on piecewise-rotational chaotic system (OPRC) is proposed. OPRC is a kind of multi-point searching methods in order to find an optimal solution, and these searching points are updated by piecewise-rotational chaotic dynamics. OPRC is a simple optimizer because these searching points are governed by simple dynamics which contains no stochastic terms. OPRC has significantly better performance than particle swarm optimization and our previous method based on another chaotic system. The relationship between the performance of OPRC and the time-series of the proposed chaotic system is analyzed. Then we clarify that OPRC obtains better solutions when the autocorrelation of the time-series takes negative values with damped oscillation.

Tracking optima in dynamic problems by an optimizer based on piecewise-rotational chaos system

“…In this section, Nelder-Mead method [1], PSO [2,3,25], BBPSO [23], APSO [13] and our previous proposed method, OPRC [22] are introduced. These methods have originally been proposed for static problems.…”

“…OPRC has been proposed in our previous research [22]. OPRC also searches the optimal solution by updating searching points based on a dynamical system likewise PSO, however, the system is chaotic.…”

“…It is guaranteed that PRC exhibits chaos with R > 1 and 0 < θ < π 2 [22]. In this paper, R = 1.4 and θ = 50[deg] are used, by which OPRC obtains good performance in static optimization problems [22]. The typical behavior of x ij (t) and v ij (t) is discussed in Sec.…”

“…In our previous paper, we have proposed a novel optimizer based on piecewise-rotational chaotic system (OPRC), and reported its searching performance for static optimization problems [22]. In this paper, we propose a novel memory update procedure and apply it to OPRC.…”

Swarm intelligence algorithm based on spiking neural-oscillator networks, coupling interactions and search performances

“…On the other hand, various D-PSO algorithms to improve search performances have been proposed [14][15][16][17][18][19]. Optimizer using Swarm of Chaotic Dynamical Particles (OSCDP) [17], Optimizer based on Piecewise-Rotational Chaotic system (OPRC) [18], and Piecewise-linear Particle Swarm Optimization (PPSO) [19], which are one of the piecewise-linear systems, have better search performances than the stochastic PSO. As such, OSCDP, OPRC and PPSO can be theoretically analyzed for behaviors of their particles.…”