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

Abstract

Tracking optima in dynamic problems is achieved by a multi-population optimizer based on piecewise-rotational chaotic system (OPRC) using memory update within a tolerance. Tracking optima is a difficult task for multi-population-based optimizers because of two issues, called outdated memory and divergent loss. To solve the outdated memory issue, a simple procedure named memory update within a tolerance is proposed. The proposed procedure is applied to our previous proposed optimizer OPRC, and its outstanding tracking performance is observed. This result shows OPRC can solve the divergent loss issue without any modification of its searching dynamics. The tracking mechanism of OPRC is also considered, and it is uncovered that the searching behavior given by the folding dynamics of the chaotic system contributes to catch the shifting optima.

Multi-solution tracking in shifting sphere function using gravitational particle swarm algorithm

“…To eliminate the stagnation of the original GPSA's 𝑝𝑏 𝑛 (𝑡), we propose 𝜏GPSA by replacing the personal best update rule (5) with the following tolerance update, which we already proposed in [9]:…”

“…In this paper, we firstly apply the original GPSA to a multisolution tracking problem and reveal its drawback. We secondary propose a modified GPSA, called 𝜏GPSA, by replacing original GPSA's update rule for personal bests with a tolerance update rule [9]. Finally, we demonstrate that 𝜏GPSA can track multiple optimal solutions in an one-dimensional shifting sphere function.…”

“…In existing studies, some optimization methods for solving DOPs have been proposed, that utilize periodically restarting the searching procedure [5], worsening the stored fitness values [6,7,8,9], and re-evaluating the fitness values for each time-step [3]. However, these existing methods are not suite to solve DOPs having multiple optimal solutions because they track just an optimal solution.…”