Meta-heuristic Optimizer Inspired by the Philosophy of Yi Jing

TL;DR

This work addresses single-objective optimization with low computational overhead by introducing YI, a Yi Jing-inspired optimizer that replaces the Yin-Yang pair with a single Yi-point updated via a heavy-tailed Cauchy flight. The approach uses a dynamical archive and a decreasing archive duration to balance exploration and exploitation, achieving a time complexity of $O(D N_{eval})$. Empirical results on the CEC 2017 benchmark show YI competitive with or superior to dYYPO, CV1.0, and classical optimizers across most functions, with stable performance across dimensions. The study demonstrates that incorporating reversal-inspired principles from Yi Jing yields a simple yet effective optimization strategy and highlights potential for extending YI to multi-objective scenarios.

Abstract

Drawing inspiration from the philosophy of Yi Jing, the Yin-Yang pair optimization (YYPO) algorithm has been shown to achieve competitive performance in single objective optimizations, in addition to the advantage of low time complexity when compared to other population-based meta-heuristics. Building upon a reversal concept in Yi Jing, we propose the novel Yi optimization (YI) algorithm. Specifically, we enhance the Yin-Yang pair in YYPO with a proposed Yi-point, in which we use Cauchy flight to update the solution, by implementing both the harmony and reversal concept of Yi Jing. The proposed Yi-point balances both the effort of exploration and exploitation in the optimization process. To examine YI, we use the IEEE CEC 2017 benchmarks and compare YI against the dynamical YYPO, CV1.0 optimizer, and four classical optimizers, i.e., the differential evolution, the genetic algorithm, the particle swarm optimization, and the simulated annealing. According to the experimental results, YI shows highly competitive performance while keeping the low time complexity. The results of this work have implications for enhancing a meta-heuristic optimizer using the philosophy of Yi Jing. While this work implements only certain aspects of Yi Jing, we envisage enhanced performance by incorporating other aspects.

Figures (2)

• Figure 1: Illustration of the conceptual difference between the Yin-Yang pair optimization (YYPO) and the Yi algorithm (YI). In the Yin-Yang pair of YYPO, two points $P_1$ and $P_2$ are used to facilitate the exploration and exploitation. $P_i$ splits with the corresponding search radius $\delta_i$, where it is modified by the expansion/contraction factor $\alpha$ in the archive stage. The proposed Yi-point of YI implements the reversal and uses Cauchy flight to strike a balance between exploration and exploitation. The flight scope $\epsilon$ is divided by the decay rate $\sigma$ in the archive stage.
• Figure 2: Schematic illustration of the splitting process. We demonstrate the D-way splitting strategy in Eq. \ref{['dway']}, where the search range is $\delta_i/\sqrt{2}$ associated with $P_i$. The best among the generated solution would be picked for the seed of next splitting. The splitting process continues until reaching the archive stage.