A Novel Pattern Learning Framework With Enhanced Scalability for Continuous Optimization

Multiobjective optimization problems (MOPs) arise in numerous real-world scenarios, yet finding their solutions with optimal trade-offs can be a formidable challenge. This article studies the continuous optimization problem involving large-scale variables, many objectives, and intricate constraints, which is rarely comprehensively discussed in existing works, due to the coexisting difficulties posed by the curse of dimensionality, selection pressure, and feasibility restrictions. To address these problems, this work pioneers a novel optimization framework, optimization pattern learning, embedded with machine learning (ML) techniques. Within this framework, the concept of measurable order and its corresponding learning mechanism are proposed to extract valuable knowledge from solutions. This measurable order is a general form of those orders used explicitly or implicitly in the existing studies, providing a more flexible means to evaluate solutions for efficient optimization adaptively. By substituting original solutions with their measurable orders, this framework effectively avoids the selection pressure from many objectives and the feasibility restrictions from intricate constraints. Furthermore, two novel ML models based on measurable orders are developed to progressively learn effective optimization patterns from iterative data in high-dimensional search spaces. Leveraging these learned patterns, this framework successfully addresses the curse of dimensionality from large-scale variables and thus achieves efficient optimization. Owing to the strong adaptability and search capabilities of this framework, it also demonstrates excellent scalability as the number of variables, objectives, and constraints increases. Extensive simulations validate the effectiveness of the framework and underscore its competitiveness relative to state-of-the-art algorithms in this field.