A Scalable Benchmark Test Suite for Dynamic Multi-Objective Optimization with a Changing Number of Objectives
For researchers in dynamic multi-objective optimization, this work provides a principled benchmark that enables fair evaluation of algorithms' ability to handle changes in the number of objectives, addressing a critical gap in the field.
The paper identifies a fundamental flaw in existing benchmark test suites for dynamic multi-objective optimization with a changing number of objectives: when the number of objectives changes, the objective functions themselves change implicitly, making it impossible to isolate the effect of the dynamic number of objectives. The authors propose a scalable test suite where objective functions are fixed and only the number of active objectives changes, using Minus-DTLZ and Minus-WFG formulations to avoid degeneracy.
Dynamic multi-objective optimization with a changing number of objectives has recently attracted increasing attention due to its relevance to real-world problems whose evaluation criteria may evolve over time. However, existing benchmark test suites for this problem setting suffer from a fundamental limitation: when the number of objectives changes, the objective functions themselves also change implicitly. This makes it difficult to isolate and evaluate an algorithm's capability to handle dynamics in the number of objectives alone. In this paper, we analyze this issue in detail and show that several theoretical properties claimed in prior studies rely on an assumption that is violated by commonly used test suites. To address this problem, we propose a scalable benchmark test suite in which the objective functions are fixed throughout the optimization process, while the number of active objectives changes over time. Our benchmark is constructed by defining a maximum-objective problem and dynamically selecting subsets of objectives. To avoid degeneracy issues in classical DTLZ and WFG problems, we adopt Minus-DTLZ and Minus-WFG formulations, in which all objectives are mutually conflicting. Extensive benchmark studies using representative algorithms from the literature demonstrate the usefulness and flexibility of the proposed test suite.