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运筹学学报 >

2026 , Vol. 30 >Issue 1: 1 - 23

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2026.01.001

共识优化算法的研究进展综述

  • 魏佳祯 ,
  • 边伟
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  • 哈尔滨工业大学数学学院, 黑龙江哈尔滨 150001

收稿日期: 2025-04-06

  网络出版日期: 2026-03-16

基金资助

国家自然科学基金 (Nos. 12425115, 12271127, 62176073)

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A survey on research advances in consensus-based optimization algorithm

  • WEI Jiazhen ,
  • BIAN Wei
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  • School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China

Received date: 2025-04-06

  Online published: 2026-03-16

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摘要

全局优化问题在科学研究、工程、经济学及人工智能等多个领域均有着广泛的应用。共识优化算法作为一类多智能体元启发式无导数优化算法,旨在解决非光滑非凸的全局优化问题,且易于理论分析和算法实现。本文首先介绍经典共识优化算法的基本原理及其分析结果;随后, 详细论述共识优化算法及其变形的最新进展,并简述其在机器学习、图像处理等领域的应用; 最后,从理论创新、算法设计和应用拓展三个维度对未来研究方向进行了展望。

关键词： 全局优化; 非光滑非凸优化; 共识优化算法; 群体智能算法; 有限粒子系统

本文引用格式

魏佳祯 , 边伟 . 共识优化算法的研究进展综述[J]. 运筹学学报, 2026 , 30(1) : 1 -23 . DOI: 10.15960/j.cnki.issn.1007-6093.2026.01.001

Abstract

Global optimization problems have widespread applications across various fields such as scientific research, engineering, economics, and artificial intelligence. Consensus-based optimization algorithm is a class of multi-agent, meta-heuristic and derivative-free algorithms. It is designed to solve global nonsmooth and nonconvex optimization problems, while also being conducive to theoretical analysis and algorithm implementation. In this paper, we first introduce the fundamental principles and analytical results of the original algorithm. Subsequently, the latest development of the consensus-based optimization algorithms and their variants are discussed in detail. And the applications in fields such as machine learning and image processing are briefly described. Finally, we explore future research directions across three key areas: theoretical innovation, algorithm design, and application expansion.

Key words： global optimization; nonsmooth and nonconvex optimization; consensus-base optimization algorithm; swarm intelligence algorithm; finite particle system

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