Optimization Letters最新文献_第4页

Affine optimal k-proper connected edge colorings 仿射最优 k-Proper 连接边着色

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-04-13 DOI: 10.1007/s11590-024-02111-2

Robert D. Barish, Tetsuo Shibuya

{"title":"Affine optimal k-proper connected edge colorings","authors":"Robert D. Barish, Tetsuo Shibuya","doi":"10.1007/s11590-024-02111-2","DOIUrl":"https://doi.org/10.1007/s11590-024-02111-2","url":null,"abstract":"We introduce affine optimal k-proper connected edge colorings as a variation on Fujita’s notion of optimal k-proper connected colorings (Fujita in Optim Lett 14(6):1371–1380, 2020. https://doi.org/10.1007/s11590-019-01442-9) with applications to the frequency assignment problem. Here, for a simple undirected graph G with edge set (E_G), such a coloring corresponds to a decomposition of (E_G) into color classes (C_1, C_2, ldots , C_n), with associated weights (w_1, w_2, ldots , w_n), minimizing a specified affine function ({mathcal {A}}, {:=},sum _{i=1}^{n} left( w_i cdot |C_i|right)), while also ensuring the existence of k vertex disjoint proper paths (i.e., simple paths with no two adjacent edges in the same color class) between all pairs of vertices. In this context, we define (zeta _{{mathcal {A}}}^k(G)) as the minimum possible value of ({mathcal {A}}) under a k-proper connectivity requirement. For any fixed number of color classes, we show that computing (zeta _{{mathcal {A}}}^k(G)) is treewidth fixed parameter tractable. However, we also show that determining (zeta _{{mathcal {A}}^{prime }}^k(G)) with the affine function ({mathcal {A}}^{prime } , {:=},0 cdot |C_1| + |C_2|) is NP-hard for 2-connected planar graphs in the case where (k = 1), cubic 3-connected planar graphs for (k = 2), and k-connected graphs (forall k ge 3). We also show that no fully polynomial-time randomized approximation scheme can exist for approximating (zeta _{{mathcal {A}}^{prime }}^k(G)) under any of the aforementioned constraints unless (NP=RP).","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"55 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An improvement of the Goldstein line search 戈德斯坦线搜索的改进

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-04-05 DOI: 10.1007/s11590-024-02110-3

Arnold Neumaier, Morteza Kimiaei

引用次数: 0

An approximation algorithm for k-level squared metric facility location problem with outliers 有异常值的 k 级平方度量设施定位问题的近似算法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-04-04 DOI: 10.1007/s11590-024-02107-y

Li Zhang, Jing Yuan, Qiaoliang Li

引用次数: 0

On penalized reload cost path, walk, tour and maximum flow: hardness and approximation 关于受惩罚的重载成本路径、行走、游览和最大流量：硬度和近似值

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-04-03 DOI: 10.1007/s11590-024-02108-x

Donatella Granata

{"title":"On penalized reload cost path, walk, tour and maximum flow: hardness and approximation","authors":"Donatella Granata","doi":"10.1007/s11590-024-02108-x","DOIUrl":"https://doi.org/10.1007/s11590-024-02108-x","url":null,"abstract":"A meticulous description of a real network with respect to its heterogeneous physical infrastructure and properties is necessary for network design assessment. Quantifying the costs of making these structures work together effectively, and taking into account any hidden charges they may incur, can lead to improve the quality of service and reduce mandatory maintenance requirements, and mitigate the cost associated with finding a valid solution. For these reasons, we devote our attention to a novel approach to produce a more complete representation of the overall costs on the reload cost network. This approach considers both the cost of reloading due to linking structures and their internal charges, which we refer to as the penalized reload cost. We investigate the complexity and approximability of finding an optimal path, walk, tour, and maximum flow problems under penalized reload cost. All these problems turn out to be NP-complete. We prove that, unless P=NP, even if the reload cost matrix is symmetric and satisfies the triangle inequality, the problem of finding a path, tour, and a maximum flow with a minimum penalized reload cost cannot be approximated within any constant (alpha <2), and finding a walk is not approximable within any factor (beta le 3).","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Decentralized bilevel optimization 分散式双层优化

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-26 DOI: 10.1007/s11590-024-02101-4

Xuxing Chen, Minhui Huang, Shiqian Ma

引用次数: 0

On the implementation of ADMM with dynamically configurable parameter for the separable $$ell _{1}/ell _{2}$$ minimization 关于针对可分离的 $$ell _{1}/ell _{2}$ 最小化问题实现带动态可配置参数的 ADMM

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-26 DOI: 10.1007/s11590-024-02106-z

Jun Wang, Qiang Ma

引用次数: 0

The projected splitting iterative methods based on tensor splitting and its majorization matrix splitting for the tensor complementarity problem 基于张量分裂及其大化矩阵分裂的张量互补问题的投影分裂迭代法

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-24 DOI: 10.1007/s11590-024-02104-1

Mengxiao Fan, Jicheng Li

引用次数: 0

Subdifferentials of convex matrix-valued functions 凸矩阵值函数的次微分

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-21 DOI: 10.1007/s11590-024-02105-0

引用次数: 0

Learning to project in a criterion space search algorithm: an application to multi-objective binary linear programming 在标准空间搜索算法中学习预测：多目标二元线性规划的应用

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-18 DOI: 10.1007/s11590-024-02100-5

Alvaro Sierra-Altamiranda, Hadi Charkhgard, Iman Dayarian, Ali Eshragh, Sorna Javadi

{"title":"Learning to project in a criterion space search algorithm: an application to multi-objective binary linear programming","authors":"Alvaro Sierra-Altamiranda, Hadi Charkhgard, Iman Dayarian, Ali Eshragh, Sorna Javadi","doi":"10.1007/s11590-024-02100-5","DOIUrl":"https://doi.org/10.1007/s11590-024-02100-5","url":null,"abstract":"In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of a problem with p objectives by searching on a projected criterion space, i.e., a ((p-1))-dimensional criterion apace. We present an effective and fast learning approach to identify on which projected space the KSA should work. We also present several generic features/variables that can be used in machine learning techniques for identifying the best projected space. Finally, we present an effective bi-objective optimization-based heuristic for selecting the subset of the features to overcome the issue of overfitting in learning. Through an extensive computational study over 2000 instances of tri-objective knapsack and assignment problems, we demonstrate that an improvement of up to 18% in time can be achieved by the proposed learning method compared to a random selection of the projected space. To show that the performance of our algorithm is not limited to instances of knapsack and assignment problems with three objective functions, we also report similar performance results when the proposed learning approach is used for solving random binary integer program instances with four objective functions.","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"16 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Convergence analysis of the DFP algorithm for unconstrained optimization problems on Riemannian manifolds 黎曼流形上无约束优化问题的 DFP 算法收敛性分析

IF 1.6 4区数学

Optimization Letters Pub Date : 2024-03-12 DOI: 10.1007/s11590-024-02103-2

Xiao-bo Li, Kai Tu, Jian Lu

引用次数: 0