Benchmarking Continuous Dynamic Multi-Objective Optimization: Survey and Generalized Test Suite

TL;DR

This work addresses the need for realistic, discriminative benchmarks in dynamic multi-objective optimization by introducing the Generalized Test Suite (GTS). GTS modularly encodes PS/PF dynamics on hypersurfaces, imbalanced variable contributions, dynamic variable interactions via time-varying rotation matrices, temporally irregular dynamics using digits of $oldsymbol{ ho}$, and a time-linkage mechanism to model history-dependent changes. Through extensive experiments against DF/FDA benchmarks with six diverse algorithms, GTS demonstrates improved realism and its ability to differentiate algorithmic strengths and tradeoffs, while maintaining manageable runtimes and reproducibility. The framework establishes a new standard for DMOP benchmarking and provides an open-source implementation to support future research and method development.

Abstract

Dynamic multi-objective optimization (DMOO) has recently attracted increasing interest from both academic researchers and engineering practitioners, as numerous real-world applications that evolve over time can be naturally formulated as dynamic multi-objective optimization problems (DMOPs). This growing trend necessitates advanced benchmarks for the rigorous evaluation of optimization algorithms under realistic conditions. This paper introduces a comprehensive and principled framework for constructing highly realistic and challenging DMOO benchmarks. The proposed framework features several novel components: a generalized formulation that allows the Pareto-optimal Set (PS) to change on hypersurfaces, a mechanism for creating controlled variable contribution imbalances to generate heterogeneous landscapes, and dynamic rotation matrices for inducing time-varying variable interactions and non-separability. Furthermore, we incorporate a temporal perturbation mechanism to simulate irregular environmental changes and propose a generalized time-linkage mechanism that systematically embeds historical solution quality into future problems, thereby capturing critical real-world phenomena such as error accumulation and time-deception. Extensive experimental results validate the effectiveness of the proposed framework, demonstrating its superiority over conventional benchmarks in terms of realism, complexity, and its capability for discriminating state-of-the-art algorithmic performance. This work establishes a new standard for dynamic multi-objective optimization benchmarking, providing a powerful tool for the development and evaluation of next-generation algorithms capable of addressing the complexities of real-world dynamic systems.

Figures (9)

• Figure 1: PS of GTS1
• Figure 2: PF of GTS1
• Figure 3: PS of GTS4
• Figure 4: PF of GTS4
• Figure 5: DMIGD for DF, GTS Group 1, GTS Group 2, and GTS Group 3 test suites.

Theorems & Definitions (1)

• Theorem 3.1