To address the issue that existing dynamic multi-objective optimization algorithms mainly rely on individual migration or independent special point sampling after environmental changes, while failing to fully exploit the structural relationships among representative solutions, a Special Point Skeleton Reconstruction based Dynamic Multi-Objective Evolutionary Algorithm (SPSR-DMOEA) is proposed. First, the centroid, knee points, and extreme points are extracted from the Pareto optimal solution set of the current environment, and their positions in the new environment are adaptively predicted according to their movement velocities across consecutive environments. Subsequently, in the decision space, the centroid is connected with other anchor points, and a minimum spanning tree is constructed among the non-centroid anchor points, thereby establishing a prediction skeleton capable of describing the overall population structure. According to the lengths of the skeleton edges, the number of individuals allocated to each edge is determined proportionally. Candidate solutions are uniformly generated along each edge, and random orthogonal perturbations are introduced to expand the search region around the skeleton. Experimental results on the DF dynamic multi-objective benchmark suite demonstrate the effectiveness of the proposed method in dynamic tracking capability.
Dynamic multi-objective optimization with a variable number of objectives is difficult because objective-dimensional variations may significantly change the Pareto front and degrade algorithm adaptability. This paper proposes an unbounded archive-based transfer strategy (UATS), which maintains an unbounded archive of offspring solutions within each environment stage and extracts feasible nondominated solutions as transferable elites when objective changes occur. UATS is embedded into SPEA2SDE to construct UATS-SPEA2SDE, enabling the algorithm to reuse historical evolutionary information while retaining the convergence and diversity advantages of shift-based density estimation. Experiments are conducted on four benchmark problems under three objective-changing settings, where UATS-SPEA2SDE is compared with a restart-based SPEA2SDE baseline and four representative dynamic multi-objective optimization algorithms. The results indicate that the archive-guided transfer improves recovery after environmental changes and enhances adaptability to objective-number variations.
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.
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.