Scatter search is a population-based metaheuristic designed to solve complex optimization problems through structured solution combination and adaptive memory. Unlike traditional evolutionary algorithms, scatter search emphasizes deterministic strategies to balance intensification and diversification. We present a comprehensive review of scatter search and its connection to path relinking, covering their historical development, core methodology, and applications. Key components of scatter search include diversification generation, improvement, reference set updating, subset generation, and solution combination. Advanced strategies such as dynamic reference set updating, tiered memory structures, constructive and destructive neighborhoods, and vocabulary building enhance its performance and scalability. Scatter search has been successfully applied in scheduling, routing, bioinformatics, and software engineering. Hybridizations with other metaheuristics and integration with machine learning further expand its applicability. The review concludes with a tutorial on a scatter search Python implementation for 0-1 knapsack problems that includes a Jupyter Notebook with code, execution traces, visualizations, and didactic analyses.
Computing a neural network is, in essence, a large unconstrained optimization problem, though this fact is often obscured by machine learning jargon. We present a gentle introduction to deep learning for operations researchers, describing in a didactic manner the underlying optimization problem and providing examples developed from scratch. These examples are solved using both standard modeling languages and modern machine learning frameworks. We conclude by discussing applications of neural networks in operations research, illustrated through a concrete example involving the knapsack problem.
Reconciling multidimensional count data across multiple sources is a common challenge in social and economic research. Iterative proportional fitting is widely used for this purpose, but aligning indices under weighted sum-convex constraints calls for a more fexible approach. We introduce the weighted iterative proportional fitting algorithm, which incorporates sum-weighted constraints to adjust indicators-such as death-risk indices by wealth, habitat, and climate-while preserving marginal consistency. Weighted iterative proportional fitting has been implemented in an R package of the same name, enabling scholars, statisticians, and policymakers' advisors, among others, to apply it easily to multidimensional data.
State-of-the-art methods for estimating extreme quantiles (value at risk, VaR) and their tail expectations (conditional tail expectation, CTE) under covariate control primarily rely on quantile regression but lack explicit constraints for non-crossing conditions. To address this, we introduce the non-crossing dual neural network, a deep learning model that simultaneously estimates VaRs and CTEs across multiple quantile levels, incorporates covariate dependence, and enables the reconstruction of individual conditional distributions and risk profles while ensuring the natural order of quantile levels. Using a 2015 telematics dataset, the proposed methodology outperforms benchmark models while enforcing previously unaddressed conditions. The model can be used to identify risk within an insurance portfolio and to analyze extreme right-tail behaviour at the individual level.
Data scientists address real-world problems using multivariate and heterogeneous datasets, characterized by multiple variables of different natures. Selecting a suitable distance function between units is crucial, as many statistical techniques and machine learning algorithms depend on this concept. Traditional distances, such as Euclidean or Manhattan, are unsuitable for mixed-type data, and although Gower distance was designed to handle this kind of data, it may lead to suboptimal results in the presence of outlying units or underlying correlation structure. In this work robust distances for mixed-type data are defned and explored, namely robust generalized Gower and robust related metric scaling. A new Python package is developed, which enables to compute these robust proposals as well as classical ones.
