An Unbounded Archive-based Transfer Strategy for Dynamic Multi-Objective Optimization with a Changing Number of Objectives

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.

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.

Large-scale multi-objective optimization problems (LSMOPs) remain challenging due to the high-dimensional decision spaces, complex variable interactions, and limited function evaluation budgets, which make it difficult to balance the convergence, diversity, and stability. Existing two-archive evolutionary algorithms can alleviate the conflict between convergence and diversity, but they often underuse archive reliability and problem-structure information, leading to inefficient search, incomplete front coverage, and late-stage archive drift. To address these issues, this paper proposes TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm. Archive trustworthiness is defined by integrating evolutionary progress with convergence-archive maturity, and is used to coordinate variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. TRUST-TAEA is evaluated on the LSMOP benchmark suite with 500--5000 decision variables and 2, 3-objectives. Experimental results show that TRUST-TAEA achieves superior and highly competitive performance in terms of convergence, diversity, and stability. A three-objective day-ahead scheduling case of a grid-connected microgrid further demonstrates its practical applicability, where TRUST-TAEA obtains the best IGD$^+$ value and generates a feasible dispatch strategy balancing cost, emissions, and grid-power fluctuation.