We review major developments in multi-objective optimization over the past decades. Although mathematical foundations and basic concepts have been established earlier, substantial progress in methods for constructing and identifying preferred solutions started in the late 1950s. We classify these approaches into two broad categories: mathematical programming-based and population-based. The former originated in the late 1950s, and its growth accelerated from the 1970s onward. We differentiate between approaches dealing with problems that operate in a continuous solution space and combinatorial problems where some variables are restricted to integer values. Population-based approaches flourished in the 1990s. Our focus is on evolutionary computation techniques that either aim to discover the entire Pareto front or incorporate the decision maker’s preferences to select the most favorable solution(s) or bias the search toward preferred regions. For all categories, we discuss those approaches that, in our opinion, have made major impacts. We examine current research trends and speculate on future directions in the field.
This paper studies hypothesis testing for structured scale matrices in the multivariate t distribution. We develop likelihood ratio and Rao score tests for general structural constraints on the scale matrix and derive the Wald test for hypotheses in which the scale matrix is restricted to a quadratic subspace. The latter class includes, in particular, diagonality, sphericity, compound symmetry, circular Toeplitz structures, and their block extensions with structured subblocks. Since the construction of the test statistics requires maximum likelihood estimation, we derive the likelihood equations under quadratic subspace restrictions. Although likelihood ratio and score tests have been investigated for covariance structure in the multivariate normal model, the Wald test has not been developed in that setting. Because the multivariate normal distribution arises as a limiting case of the multivariate t model, our results also provide a new contribution to the normal framework. Finite sample performance is examined via simulation, and a real data example illustrates the proposed methodology.
The development of the renewable energy sector, especially solar energy, is essential to mitigate the rapidly progressing climate change. However, the inherent uncertainty related to the stability of solar energy production capabilities prevents large-scale integration of solar-based sources into power grids. Therefore, this work addresses this practical challenge by presenting a systematic, large-scale synthesis and validation of a comprehensive neural network-based image enhancement pipeline for ground-based solar forecasting. This consolidated pipeline includes a Sun mask, optical flow, a cloud channel, and a novel irradiance value channel for early-stage spatio-temporal fusion. As a second key methodological novelty, we introduce the mean adaptive BerHu penalty as a loss function, which is shown to be uniquely suited for robustly handling the high dynamic range of solar irradiance values. The proposed comprehensive pipeline, when evaluated on a spatio-temporal model, outperforms existing methods from the literature. This strong performance is not architecture-specific, as demonstrated by our cross-architecture study, in which the pipeline’s portability achieves an average forecast skill of 19.35% among evaluated models for the 15-minute forecasting horizon. This is due to physically referenced, representation-level enhancements that act as an architecture-agnostic driver of forecasting skill going beyond incremental, model-specific tuning. Its practical applicability is further confirmed by its effectiveness across multiple intra-hour time horizons, with significant skill improvements for both ultra-short 5-minute (16.22%) and longer 30-minute (22.52%) periods. Finally, its practical deployability was confirmed through extensive validation on resource-constrained edge devices. The source code used in this study is publicly available to promote research reproducibility.
Blue-Green Infrastructure (BGI) is a key urban strategy for climate change adaptation, playing a crucial role in promoting environmental sustainability. Despite its growing importance, BGI remains insufficiently integrated into spatial planning processes. The research presented in this article aims to assess the applicability of reasoning maps as a new decision support tool and to estimate the impact of spatial policy choices in urban areas. Reasoning maps offer a qualitative, expert-based method for structuring complex decision problems, particularly those involving conflicting interests and uncertain outcomes. In spatial policy, location decisions are rarely made by a single entity; groups of stakeholders collectively negotiate them. Therefore, decision support methods that fail to account for group-based deliberation often fall short in practice. In this study, initial variables (nodes) refer to input planning factors, such as land price, BGI accessibility, or infrastructure costs. In contrast, final nodes are aggregated goals that reflect desired urban outcomes—namely, climate change adaptation, residents’ satisfaction, and increased housing value. Through expert panel evaluations, ten influencing nodes were identified and analyzed across two alternative spatial development scenarios using connection strength operators. The results reveal that greater BGI accessibility—particularly under compact development scenarios—enhances urban climate resilience and strengthens cities' capacity to adapt to environmental risks. That enables more informed and equitable planning aligned with sustainability objectives. The proposed method proved effective as a support tool for spatial decision-making. Recommendations are provided for urban policymakers regarding both the location of residential areas and ensuring equal access to BGI as part of sustainable urban development.
Neural Radiance Fields achieve high-fidelity scene representation but suffer from costly training and rendering, while 3D Gaussian splatting offers real-time performance with strong empirical results. Recently, solutions that harness the best of both worlds by using Gaussians as proxies to guide neural field evaluations, still suffer from significant computational inefficiencies. They typically rely on stochastic volumetric sampling to aggregate features, which severely limits rendering performance. To address this issue, a novel framework named IRIS (Intersection-aware Ray-based Implicit Editable Scenes) is introduced as a method designed for efficient and interactive scene editing. To overcome the limitations of standard ray marching, an analytical sampling strategy is employed that precisely identifies interaction points between rays and scene primitives, effectively eliminating empty space processing. Furthermore, to address the computational bottleneck of spatial neighbor lookups, a continuous feature aggregation mechanism is introduced that operates directly along the ray. By interpolating latent attributes from sorted intersections, costly 3D searches are bypassed, ensuring geometric consistency, enabling high-fidelity, real-time rendering, and flexible shape editing.
