A dynamic multi-objective optimization evolutionary algorithm based on decision variable classification and multi-stage prediction model

HaoYu Wu

doi:10.1007/s10586-026-06634-4

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A dynamic multi-objective optimization evolutionary algorithm based on decision variable classification and multi-stage prediction model

2026-10-03

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DOI：10.1007/s10586-026-06634-4

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Abstract

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Dynamic Multi-Objective Evolutionary Algorithms (DMOEAs) have been extensively employed to address complex real-world optimization problems in which objective functions, decision variables, and constraints change over time. Existing prediction-based DMOEAs mainly focus on predicting the movement of the Pareto Set (PS) or Pareto Front (PF) as a whole, while the different roles of decision variables in convergence and diversity are often not sufficiently considered. This limitation may weaken the adaptability of algorithms when environmental changes are nonlinear, abrupt, or irregular. To address this issue, this paper proposes an Environment-Aware Adaptive Prediction (EAAP) algorithm based on differentiated decision-variable response. The algorithm first employs a Minimum Spanning Tree (MST) strategy to structurally analyze decision variables and classify them into convergence variables and diversity variables. For convergence variables, a multi-stage prediction model is developed. In the first stage, a sliding-window Kalman Filter (KF) is introduced to filter noisy historical centroid information and preliminarily estimate the movement direction. Then, a memory-guided Particle Swarm Optimization (PSO) model is used to further refine the prediction by exploiting historical elite solutions. For diversity variables, Latin hypercube sampling (LHS) is applied to reconstruct a uniformly distributed population in the new environment. Comparative experiments on 22 benchmark functions demonstrate the effectiveness and robustness of EAAP in solving dynamic multi-objective optimization problems.

Keywords:

Dynamic multi-objective optimization

Decision variable classification

Particle swarm prediction

Latin hypercube sampling