A framework using nested partitions algorithm for convergence analysis of population distribution-based methods

Stochastic optimization algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), estimation of dis-tribution algorithms (EDAs), and nested partitions algorithm (NPA) are used in many problems including nonlinear model predictive control and task assignment. Some of these al-gorithms, however, lack global convergence guarantee such as PSO, or require strict convergence assumptions such as NPA. To enhance these methods in terms of convergence, a common underlying framework towards representing the seemingly unrelated methods is established as the up dat -ing of the distribution of the population through iterative sampling, and the methods that fit into this framework are called population distribution-based methods. Global conver-gence conditions for this framework are innovatively devel-oped by building a shadow NPA structure for the population evolution process. The result is generic and is capable of an-alyzing convergence of many methods including GA, PSO, EDA, and NPA. It can be further exploited to improve conver-gence by modifying these methods. The existing and modified variants of these methods are then applied to case studies to show the improvement. & COPY; 2023 The Author(s). Published by Elsevier Ltd on behalf of Association of European Operational Research Societies (EURO). This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).