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

Streaming data-driven dynamic multi-objective optimization requires algorithms to track time-varying Pareto fronts using only sequential observations under concept drift. However, systematic evaluation remains difficult because real-world problems usually lack ground-truth optima, drift annotations, and controllable conditions, while existing benchmarks provide limited support for standardized comparison. This paper proposes SDDMO-Bench, a benchmark suite that transforms classical dynamic multi-objective test problems into streaming environments by combining intrinsic objective-mapping evolution, controllable distributional drift, and sequential data revelation. By combining five representative time-dependent base functions with six distributional drift patterns, SDDMO-Bench constructs 30 scenarios with diverse levels of non-stationarity, problem complexity, sample-distribution variation, and Pareto-front evolution. Experiments with representative evolutionary algorithms demonstrate that SDDMO-Bench provides challenging and discriminative test scenarios, offering a standardized, controllable, and reproducible benchmark for evaluating adaptability, robustness, and Pareto-front tracking in streaming data-driven dynamic multi-objective optimization.

Many-objective optimization has been a field of interest over the past two decades and several evolutionary optimization algorithms have been introduced to tackle these problems; yet two fundamental questions remain underexplored: (i) What happens when the number of objectives grows beyond the typical many-objective regime of about fifteen and becomes massive? (ii) How do problem characteristics, such as the nature of interactions between objectives, influence algorithmic performance? To answer these questions we employ a diagnostic benchmark suite that allows control over problem characteristics and can be scaled to extremely high objective counts. Using this framework we evaluate several state-of-the-art evolutionary algorithms including NSGA-II, NSGA-III, MOEA/D and lexicase selection across a range of dimensionalities and diagnostic problem landscapes. Our experiments reveal that problem characteristics significantly affect algorithm performance. In particular, the nature of interactions between objectives appears important. These results highlight the importance of understanding these properties before selecting an algorithm for a specific problem. We also show that lexicase selection, an algorithm originally designed for genetic programming, compares favorably with state-of-the-art many-objective optimization algorithms while avoiding the dependence on predefined reference directions.

This paper investigates the role of dynamic population sizes in evolutionary multi-objective optimization. Although such approaches are widely used in practice, their benefits remain poorly understood, and rigorous runtime analyses explaining when and why they help are still scarce. To address this, we introduce the bi-objective problem class CLIMB and analyze the runtime of GSEMO and the widely used NSGA-II on this problem. Our results show that allowing a dynamic population size for NSGA-II can lead to a moderate improvement, yielding a speedup of order $Ω(\sqrt{n}/\log n)$. In particular, we prove that GSEMO and NSGA-II-DYN, a version of NSGA-II with dynamic population sizes we propose in this paper, can find the Pareto front of CLIMB in expected $O(n \log n)$ fitness evaluations, whereas NSGA-II with a fixed population size requires $Ω(n^{1.5})$ fitness evaluations in expectation. To the best of our knowledge, this is the first rigorous runtime analysis in multi-objective optimization demonstrating a super-constant speedup of GSEMO over NSGA-II. Our analysis builds on concepts from single-objective optimization, like the evolution of population diversity over time, and employs the well-known family-three method to prove the lower bound.