Low-discrepancy Sampling in the Expanded Dimensional Space: An Acceleration Technique for Particle Swarm Optimization

TL;DR

This paper introduces a low-discrepancy sampling acceleration technique for particle swarm optimization (PSO), which reduces error and improves convergence speed by better covering the search space in expanded dimensions.

Contribution

It proposes a novel acceleration method using low-discrepancy sampling in expanded dimensional space, enhancing PSO performance based on error analysis.

Findings

Improved algorithms converge faster than standard PSO.

Low-discrepancy sampling reduces error bounds per iteration.

Enhanced PSO variants outperform original in speed under same accuracy.

Abstract

Compared with random sampling, low-discrepancy sampling is more effective in covering the search space. However, the existing research cannot definitely state whether the impact of a low-discrepancy sample on particle swarm optimization (PSO) is positive or negative. Using Niderreiter's theorem, this study completes an error analysis of PSO, which reveals that the error bound of PSO at each iteration depends on the dispersion of the sample set in an expanded dimensional space. Based on this error analysis, an acceleration technique for PSO-type algorithms is proposed with low-discrepancy sampling in the expanded dimensional space. The acceleration technique can generate a low-discrepancy sample set with a smaller dispersion, compared with a random sampling, in the expanded dimensional space; it also reduces the error at each iteration, and hence improves the convergence speed. The acceleration technique is combined with the standard PSO and the comprehensive learning particle swarm optimization, and the performance of the improved algorithm is compared with the original algorithm. The experimental results show that the two improved algorithms have significantly faster convergence speed under the same accuracy requirement.