A Scalable Benchmark Test Suite for Dynamic Multi-Objective Optimization with a Changing Number of Objectives

2026-05-25

AI Summary

This work addresses a critical limitation in existing dynamic multi-objective optimization benchmarks, where changes in the number of objectives are often conflated with implicit modifications to the objective functions themselves, thereby hindering the isolated evaluation of an algorithm’s adaptability to dynamic objective counts. To resolve this issue, the study proposes a novel scalable benchmark suite that keeps all objective functions fixed while dynamically activating subsets of them, thereby enabling, for the first time, a setting where only the number of objectives varies without altering the underlying functions. The approach employs a max-objective problem formulation coupled with a dynamic subset selection mechanism and introduces Minus-DTLZ and Minus-WFG test problems to prevent solution degeneracy. Experimental results demonstrate that the proposed suite offers a more accurate and flexible means of assessing algorithmic performance under dynamically varying objective dimensions, effectively correcting a fundamental theoretical flaw in current benchmarking frameworks.

Abstract

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.

Problem

• Dynamic Multi-Objective Optimization
• Changing Number of Objectives
• Benchmark Test Suite
• Objective Functions
• Scalability

Innovation

• dynamic multi-objective optimization
• changing number of objectives
• scalable benchmark suite
• Minus-DTLZ
• objective function consistency