Jul 2026· Annual Conference on Genetic and Evolutionary Computation· 0 citations· 28 references
Computer Science
TL;DR
By employing a difficulty-aware weighting scheme, the approach biases aggregation toward higher-dimensional instances, enabling a more discriminative assessment of scalability, robustness, and performance.
Abstract
To ensure empirical evaluation of multi- and many-objective evolutionary algorithms, researchers perform benchmarking across test problems and algorithms. Due to the volume of performance data and the heterogeneity of problem characteristics, analyzing results becomes complex and prone to misinterpretation. Performance profiles have proven effective for visualizing and interpreting such results; however, they do not account for the relative difficulty or importance of individual problems and may overweight easy or less informative cases, potentially obscuring distinctions between algorithm performance. In this work, we address this limitation by extending the classical performance profile approach with a difficulty-aware weighting scheme that emphasizes more challenging problems. Weights can be assigned either a priori, based on problem characteristics such as the number of objectives or decision variables, or a posteriori, based on computational effort. We define and prove key mathematical properties of classical performance profiles, including local and global stability, and show that these properties extend to the proposed weighted formulation. By employing a difficulty-aware weighting scheme, the approach biases aggregation toward higher-dimensional instances, enabling a more discriminative assessment of scalability, robustness, and performance. The advantages of the weighted approach are demonstrated through experiments with algorithms applied to problem sets with numbers of objectives.
We propose a couple of novel tools for benchmarking optimization algorithms which possibly converge to different solutions on a test set: the quality profiles and the test set profiles. Their aim is to assess and compare algorithms in terms of quality (i.e. value of the objective function) of the obtained solutions, as well as to assess the consistency of the test set. A key distinguishing feature of the quality profiles we propose is its comparative deterministic procedure that emphasizes the accuracy of the solution, rather than the computational burden of solvers. In this regard, several test set--dependent approaches for both comparing and ranking algorithms have already been proposed in the literature, representing widely used benchmarking procedures. We believe that the joint use of such procedures, along with the novel quality profiles detailed here, should enhance the benchmarking process, in all those cases where the comparison encompasses exact methods as well as heuristics. Moreover, the literature on numerical optimization seems to have paid less attention, in the last decade, to determining how appropriate a test set used for benchmarking the selected solvers may be. This motivates the introduction of test set profiles, which assess the appropriateness of a test set and represent the flip side of evaluating the robustness of the solvers on that test set. This paper also includes extensive numerical experiments, showing the usefulness of quality profiles in both smooth and nonsmooth (derivative--free) optimization, along with the reference to a MATLAB code for plotting quality profiles and test set profiles.
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.
Shakiba Shahbandegan, Jose Guadalupe Hernandez, Emily L. Dolson· 0 citations
An objective-wise variable analysis method that first evaluates the sensitivity of each objective to all decision variables, and then comprehensively aggregates the sensitivity information across multiple objectives to estimate the overall importance of decision variables is proposed.
Chuanlong Ye, Fazhi He, Xiaoxin Gao et al.· Journal of King Saud Univers...· 0 citations
This study introduces a novel constrained multi-objective evolutionary algorithm, termed DPCME, which employs two interacting populations that exchange information, enabling effective global exploration and reducing the risk of convergence to local optima.
Results show that integrating local search significantly enhances performance, while a principled method for setting hybrid parameters ensures robustness and reproducibility, highlighting the potential of combining mathematical programming techniques with evolutionary algorithms for high-dimensional many-objective optimization problems.
Regina C. L. C. de Sousa, Dênis E. C. Vargas, Elizabeth F. Wanner et al.· Journal of Heuristics· 0 citations