EURO Journal on Computational Optimization最新文献

Properties of enclosures in multiobjective optimization 多目标优化中围护结构的性质

IF 1.7

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-04-17 DOI: 10.1016/j.ejco.2026.100127

Gabriele Eichfelder, Daniel Hoff

{"title":"Properties of enclosures in multiobjective optimization","authors":"Gabriele Eichfelder, Daniel Hoff","doi":"10.1016/j.ejco.2026.100127","DOIUrl":"10.1016/j.ejco.2026.100127","url":null,"abstract":"<div><div>A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we provide properties of enclosures and their width in multiobjective optimization. To apply enclosures for warm-start strategies and for approximations of optimal sets, we discuss under which conditions enclosures have nonempty interior and whether they coincide with the closure of their interior. We extend the optimality concepts of <span><math><mi>ε</mi></math></span>-minimality and <span><math><mi>ε</mi></math></span>-weak minimality from multiobjective optimization and introduce new optimality concepts for multiobjective optimization caused by relaxations of multiobjective optimization problems. We show that the enclosures and their widths are suitable for determining these new optimal points. We provide some calculation and estimation rules for the width of enclosures, such as a monotonicity, decomposition, and combination property and a triangular inequality-like relation. These are important for convergence examinations for approximation algorithms. All our examinations are driven by the requirements to further explore enclosure-based algorithms for the numerical computation of optimal points in multiobjective optimization. Hence, this paper provides a toolbox of theoretical results for enclosures that supports the development of convergence proofs of image-space-based approximation methods for several classes of multiobjective optimization problems.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100127"},"PeriodicalIF":1.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147802604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming icnn增强的2SP：利用输入凸神经网络求解两阶段随机规划

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-09-11 DOI: 10.1016/j.ejco.2026.100141

Yu Liu, Fabricio Oliveira, Jan Kronqvist

{"title":"ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming","authors":"Yu Liu, Fabricio Oliveira, Jan Kronqvist","doi":"10.1016/j.ejco.2026.100141","DOIUrl":"10.1016/j.ejco.2026.100141","url":null,"abstract":"<div><div>Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a challenge due to the computational complexity of recourse function evaluation. Existing learning-based methods like Neural Two-Stage Stochastic Programming (Neur2SP) employ neural networks (NNs) as recourse function surrogates but rely on computationally intensive mixed-integer programming (MIP) formulations. We propose ICNN-enhanced 2SP, a method that leverages Input Convex Neural Networks (ICNNs) to exploit linear programming (LP) representability in convex 2SP problems. By architecturally enforcing convexity and enabling exact inference through LP, our approach eliminates the need for integer variables inherent in the conventional MIP-based formulation while retaining an exact embedding of the ICNN surrogate within the 2SP framework. This results in a more computationally efficient alternative, and we show that good solution quality can be maintained. Comprehensive experiments reveal that ICNNs incur only marginally longer training times while achieving validation accuracy on par with their standard NN counterparts. Across benchmark problems, ICNN-enhanced 2SP often exhibits considerably faster solution times than the MIP-based formulations while preserving solution quality, with these advantages becoming significantly more pronounced as problem scale increases. For the most challenging instances, the method achieves speedups of up to 100<span><math><mo>×</mo></math></span> with solution quality superior to MIP-based formulations.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100141"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149140709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation and exact penalization in simple bilevel variational problems 简单两级变分问题的逼近与精确惩罚

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-09-23 DOI: 10.1016/j.ejco.2026.100144

Giancarlo Bigi, Riccardo Tomassini

引用次数: 0

MineReduce-based heuristic for the maximum diversity problem 最大分集问题的基于minereduce的启发式算法

IF 1.7

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2025-10-16 DOI: 10.1016/j.ejco.2025.100121

Fernando Chagas , Alexandre Plastino , Isabel Rosseti , Glaubos Clímaco

{"title":"MineReduce-based heuristic for the maximum diversity problem","authors":"Fernando Chagas , Alexandre Plastino , Isabel Rosseti , Glaubos Clímaco","doi":"10.1016/j.ejco.2025.100121","DOIUrl":"10.1016/j.ejco.2025.100121","url":null,"abstract":"<div><div>The Maximum Diversity Problem (MDP) is a challenging NP-hard optimization problem with applications in various domains, including social network analysis, bioinformatics, and facility location. Traditional heuristics often struggle to find high-quality solutions for large-scale MDP instances within reasonable time limits. Recent hybrid heuristics have incorporated data mining techniques to guide the search process, yielding improved solution quality. MineReduce is a successful example of such recent proposals. Its approach leverages mined patterns to contract portions of the problem space, facilitating a more focused and efficient search. In this work, we propose a new heuristic that integrates the MineReduce technique with the MDM_KLD, a previously proposed hybrid heuristic, to solve the MDP. Our approach aims to alleviate the computational burden by periodically solving a reduced version of the problem without compromising the quality of the solutions obtained for the original problem. Computational experiments conducted on three different sets of instances demonstrate the effectiveness of our approach compared to MDM_KLD, achieving superior solution quality in most instances within the same computational time.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100121"},"PeriodicalIF":1.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The risk quadrangle in optimization: An overview with recent results and extensions 优化中的风险四边形：包含最新结果和扩展的概述

IF 1.7

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-06-01 DOI: 10.1016/j.ejco.2026.100129

Bogdan Grechuk , Anton Malandii , R.Tyrrell Rockafellar , Stan Uryasev

{"title":"The risk quadrangle in optimization: An overview with recent results and extensions","authors":"Bogdan Grechuk , Anton Malandii , R.Tyrrell Rockafellar , Stan Uryasev","doi":"10.1016/j.ejco.2026.100129","DOIUrl":"10.1016/j.ejco.2026.100129","url":null,"abstract":"<div><div>This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four stochastic-oriented functionals — risk, deviation, regret, and error, along with an associated statistic, and articulates their revealing and in some ways surprising interrelationships and dualizations. Additions to the RQ framework that have come to light since 2013 are reviewed in a synthesis focused on both theoretical advancements and practical applications. New quadrangles — superquantile, superquantile norm, expectile, biased mean, quantile symmetric average union, and <span><math><mi>φ</mi></math></span>-divergence-based quadrangles — offer novel approaches to risk-sensitive decision-making across various fields such as machine learning, statistics, finance, and PDE-constrained optimization. The theoretical contribution comes in axioms for “subregularity” relaxing “regularity” of the quadrangle functionals, which is too restrictive for some applications. The main RQ theorems and connections are revisited and rigorously extended to this more ample framework. Examples are provided in portfolio optimization, regression, and classification, demonstrating the advantages and the role played by duality, especially in ties to robust optimization and generalized stochastic divergences.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100129"},"PeriodicalIF":1.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148184053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Scheduling resource-constrained projects with alternative subgraphs to minimise cost 使用可选子图调度资源受限的项目以最小化成本

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-07-13 DOI: 10.1016/j.ejco.2026.100134

Rojin Nekoueian, Tom Servranckx, Mario Vanhoucke

{"title":"Scheduling resource-constrained projects with alternative subgraphs to minimise cost","authors":"Rojin Nekoueian, Tom Servranckx, Mario Vanhoucke","doi":"10.1016/j.ejco.2026.100134","DOIUrl":"10.1016/j.ejco.2026.100134","url":null,"abstract":"<div><div>The resource-constrained project scheduling problem aims to schedule project activities given precedence relations and limited resources. This well-known scheduling problem has been extended into the so-called resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). In this variant, the project network comprises multiple alternatives for executing work packages, which are smaller parts of the project, with the challenge of selecting and scheduling some of these alternatives such that the project makespan is minimised. This study introduces cost objectives and cumulative resource constraints in the RCPSP-AS, leading to the formulation of a new problem referred to as the RCPSP-ASC, where <em>C</em> signifies the incorporation of new cost objectives. To address this problem, novel priority rules are devised, and existing ones are adjusted. We present three empirical production case studies to underscore the relevance of these problem extensions in real-life settings. Moreover, a proposed mixed-integer mathematical model is validated using Gurobi and the computational efficiency of obtaining (near-)optimal solutions is investigated. Using existing project complexity indicators, we show that time- and resource-based priority rules are competitive for projects with low complexity. Moreover, the time-based priority rule is the best-performing rule for time minimisation and an additional combined heuristic is proposed for further improving the solutions. We also test the cost performance of a dynamic genetic algorithm (GA) from the existing literature on a subset of project instances for which the GA produces either low-quality or high-quality results in terms of time performance. Finally, an off-the-shelf constraint programming (CP) satisfiability (SAT) solver is implemented that shows improved results for the high-quality subset of instances compared to the dynamic GA and comparable results for the low-quality subset.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100134"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148523295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Building robust counterfactual explanations with statistical guarantees 用统计保证建立强有力的反事实解释

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-07-27 DOI: 10.1016/j.ejco.2026.100135

Emilio Carrizosa, Antonio Navas-Orozco

{"title":"Building robust counterfactual explanations with statistical guarantees","authors":"Emilio Carrizosa, Antonio Navas-Orozco","doi":"10.1016/j.ejco.2026.100135","DOIUrl":"10.1016/j.ejco.2026.100135","url":null,"abstract":"<div><div>Counterfactual explanations (CEs) are powerful tools within the thriving field of explainable machine learning, consisting of finding a minimal perturbation to a given instance so that its output in a certain predictive model satisfies some desirable property. Since counterfactuals are computed from an empirical model trained on a dataset, it is not evident that the resulting counterfactual explanations satisfy the requirements of the ground-truth model, which may differ from the empirical one. In this paper, we address this issue and build robust counterfactuals, in the sense that they fulfill the desired property on the ground-truth model with a given probability. We propose a statistical test to obtain performance guarantees for our robust counterfactual explanations, not only under the empirical model, but also under the ground-truth model. We particularize to generalized linear models (GLMs), a broad family of models that includes both classification, such as the logistic regression model, and regression, such as the linear regression model. We show that, for GLMs, there is a strong connection between CEs with ground-truth model guarantees and parameter-robust CEs. Finding a robust counterfactual explanation in the GLM framework amounts to solving a second-order cone program, readily solvable by off-the-shelf solvers such as Gurobi.</div></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"14 ","pages":"Article 100135"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148640353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-fidelity constraints in blackbox optimization 黑盒优化中的多保真约束

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-10-03 DOI: 10.1016/j.ejco.2026.100147

Stéphane Alarie, Charles Audet, Miguel Diago, Sébastien Le Digabel, Xavier Lebeuf

引用次数: 0

Dai–Liao-type Riemannian optimization for solving the Gough–Stewart platform 求解Gough-Stewart平台的dai - liao型黎曼优化

IF 1.2

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2026-09-17 DOI: 10.1016/j.ejco.2026.100142

Nasiru Salihu, Poom Kumam, Kanokwan Sitthithakerngkiet, Supak Phiangsungnoen

引用次数: 0

Local upper bounds based on polyhedral ordering cones 基于多面体排序锥的局部上界

IF 1.7

EURO Journal on Computational Optimization Pub Date : 2026-01-01 Epub Date: 2025-12-15 DOI: 10.1016/j.ejco.2025.100124

Gabriele Eichfelder , Firdevs Ulus

引用次数: 0