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Minimizing the number of tardy jobs with generalized due-dates and position-dependent processing times 最大限度地减少迟到工作的数量，同时采用通用的到期日和与位置相关的处理时间
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-09-13 DOI: 10.1007/s11590-024-02138-5
Enrique Gerstl, Gur Mosheiov
{"title":"Minimizing the number of tardy jobs with generalized due-dates and position-dependent processing times","authors":"Enrique Gerstl, Gur Mosheiov","doi":"10.1007/s11590-024-02138-5","DOIUrl":"https://doi.org/10.1007/s11590-024-02138-5","url":null,"abstract":"<p>We study a single machine scheduling problem with generalized due-dates and general position-dependent job processing times. The objective function is minimum number of tardy jobs. The problem is proved to be NP-hard in the strong sense. We introduce an efficient algorithm that solves medium size problems in reasonable running time. A simple and efficient heuristic is also introduced, which obtained the optimal solution in the vast majority of our tests.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"35 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183237","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
A projected fixed point method for a class of vertical tensor complementarity problems 一类垂直张量互补问题的投影定点法
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-08-27 DOI: 10.1007/s11590-024-02146-5
Shi-Liang Wu, Mei Long, Cui-Xia Li
{"title":"A projected fixed point method for a class of vertical tensor complementarity problems","authors":"Shi-Liang Wu, Mei Long, Cui-Xia Li","doi":"10.1007/s11590-024-02146-5","DOIUrl":"https://doi.org/10.1007/s11590-024-02146-5","url":null,"abstract":"<p>In this paper, we consider the numerical solution of a class of vertical tensor complementarity problems. By reformulating the involved vertical tensor complementarity problem (VTCP) as an equivalent projected fixed point equation, together with the relevant properties of the power Lipschitz tensor, we propose a projected fixed point method for the involved VTCP, and discuss its convergence properties. Numerical experiments are given to illustrate the effectiveness of the proposed method.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"59 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183238","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
The budgeted maximin share allocation problem 预算最大化股份分配问题
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-08-22 DOI: 10.1007/s11590-024-02145-6
Bin Deng, Weidong Li
{"title":"The budgeted maximin share allocation problem","authors":"Bin Deng, Weidong Li","doi":"10.1007/s11590-024-02145-6","DOIUrl":"https://doi.org/10.1007/s11590-024-02145-6","url":null,"abstract":"<p>We are given a set of indivisible goods and a set of <i>m</i> agents where each good has a size and each agent has an additive valuation function and a budget. The budgeted maximin share allocation problem is to find a feasible allocation such that the size of the bundle allocated to each agent does not exceed its budget, and the minimum ratio of the valuation and the maximin share (MMS) value of any agent is as large as possible, where the MMS value of each agent is that he can achieve by dividing the goods into <i>n</i> bundles, and receiving his least desirable bundle. In this paper, we prove the existence of <span>(frac{n}{3n-2})</span>-approximate MMS allocation and give an instance which does not have a (<span>(frac{3}{4}+epsilon )</span>)-approximate MMS allocation, for any <span>(epsilon in (0,1))</span>. Moreover, we provide a polynomial time algorithm to find an <span>(frac{1}{3})</span>-MMS allocation, and prove that there is no <span>((frac{2}{3} + epsilon ))</span>-approximate algorithm in polynomial time unless <span>(mathcal{P}=mathcal{N}mathcal{P})</span>.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"19 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183239","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
Explicit iterative algorithms for solving the split equality problems in Hilbert spaces 求解希尔伯特空间分割相等问题的显式迭代算法
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-08-20 DOI: 10.1007/s11590-024-02144-7
Truong Minh Tuyen, Nguyen Song Ha
{"title":"Explicit iterative algorithms for solving the split equality problems in Hilbert spaces","authors":"Truong Minh Tuyen, Nguyen Song Ha","doi":"10.1007/s11590-024-02144-7","DOIUrl":"https://doi.org/10.1007/s11590-024-02144-7","url":null,"abstract":"<p>We introduce and study some explicit iterative algorithms for solving the system of split equality problems in Hilbert spaces. The strong convergence of the proposed algorithms is proved by using some milder conditions put on control parameters than the one used in Tuyen (Bull Malays Math Sci Soc 46:44, 2023).\u0000</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"6 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183153","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 rate of projected subgradient method with time-varying step-sizes 具有时变步长的投影子梯度法的收敛率
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-08-08 DOI: 10.1007/s11590-024-02142-9
Zhihan Zhu, Yanhao Zhang, Yong Xia
{"title":"Convergence rate of projected subgradient method with time-varying step-sizes","authors":"Zhihan Zhu, Yanhao Zhang, Yong Xia","doi":"10.1007/s11590-024-02142-9","DOIUrl":"https://doi.org/10.1007/s11590-024-02142-9","url":null,"abstract":"<p>We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"120 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968822","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
A global optimization approach to Berge equilibrium based on a regularized function 基于正则函数的 Berge 平衡全局优化方法
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-07-30 DOI: 10.1007/s11590-024-02141-w
G. Battur, S. Batbileg, R. Enkhbat
{"title":"A global optimization approach to Berge equilibrium based on a regularized function","authors":"G. Battur, S. Batbileg, R. Enkhbat","doi":"10.1007/s11590-024-02141-w","DOIUrl":"https://doi.org/10.1007/s11590-024-02141-w","url":null,"abstract":"<p>This work deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah et al. (Appl Math Lett 20(8):926–932. 2007), we consider BEP with concave objective functions. The existence of Berge equilibrium has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable objective functions. The later allows to apply optimization methods and algorithms to solve the original problem.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"213 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870253","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
New smooth weighted complementarity functions and a cubically convergent method for wLCP 新的平滑加权互补函数和 wLCP 的立方收敛方法
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-07-24 DOI: 10.1007/s11590-024-02139-4
Tiantian Fan, Jingyong Tang
{"title":"New smooth weighted complementarity functions and a cubically convergent method for wLCP","authors":"Tiantian Fan, Jingyong Tang","doi":"10.1007/s11590-024-02139-4","DOIUrl":"https://doi.org/10.1007/s11590-024-02139-4","url":null,"abstract":"<p>The weighted linear complementarity problem (wLCP) can be used for modelling a large class of problems from science and economics. In this paper, we introduce a new class of weighted complementarity functions and show that it is continuously differentiable everywhere. By using this function, we propose a two steps Levenberg–Marquardt-type method to solve the wLCP. Under suitable conditions, we prove that the proposed method is globally convergent and the generated iteration sequence is bounded. Moreover, we show that the proposed method has cubic convergence rate under the local error bound condition. Some numerical results are reported.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"57 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778035","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
Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models 基于概率雅各布模型的 Levenberg-Marquardt 算法的复杂性约束
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-07-18 DOI: 10.1007/s11590-024-02140-x
Ruixue Zhao
{"title":"Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models","authors":"Ruixue Zhao","doi":"10.1007/s11590-024-02140-x","DOIUrl":"https://doi.org/10.1007/s11590-024-02140-x","url":null,"abstract":"<p>In this paper, we present a Levenberg–Marquardt algorithm for nonlinear equations, where the exact Jacobians are unavailable, but their model approximations can be built in some random fashion. We study the complexity of the algorithm and show that the upper bound of the iteration numbers in expectation to obtain a first order stationary point is <span>(O(epsilon ^{-3}))</span>.</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746065","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
Stability approach to CDC truck scheduling problem under uncertainty 不确定条件下 CDC 卡车调度问题的稳定性方法
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-07-09 DOI: 10.1007/s11590-024-02137-6
Gabriela B. Fonseca, Thiago H. Nogueira, Martín G. Ravetti
{"title":"Stability approach to CDC truck scheduling problem under uncertainty","authors":"Gabriela B. Fonseca, Thiago H. Nogueira, Martín G. Ravetti","doi":"10.1007/s11590-024-02137-6","DOIUrl":"https://doi.org/10.1007/s11590-024-02137-6","url":null,"abstract":"<p>One of the most significant challenges in logistics today is managing the complexity, uncertainty, and dynamism of the market. External and internal factors highly influence the efficiency of operations processes. Cross-docking Distribution Centers are one way of adopting a real-time philosophy. This work provides a Stability Approach (SA) for solving multi-dock truck scheduling problems under truck release date uncertainty. We consider time-based objectives for optimization and propose two new heuristics to obtain viable solutions for them. To evaluate the performance of the SA, we develop and analyze two other different scheduling policies, namely, Without Adjustments and Perfect Information. Extensive computational experiments allow us to compare SA with others and show that the methodology can support managers in their daily cross-docking operations, efficiently handling dynamic and uncertain data, and making good decisions quickly.\u0000</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"2016 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572382","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
A faster heuristic for the traveling salesman problem with drone 有无人机的旅行推销员问题的快速启发式
IF 1.6 4区 数学
Optimization Letters Pub Date : 2024-07-08 DOI: 10.1007/s11590-024-02134-9
Pedro Henrique Del Bianco Hokama, Carla Negri Lintzmayer, Mário César San Felice
{"title":"A faster heuristic for the traveling salesman problem with drone","authors":"Pedro Henrique Del Bianco Hokama, Carla Negri Lintzmayer, Mário César San Felice","doi":"10.1007/s11590-024-02134-9","DOIUrl":"https://doi.org/10.1007/s11590-024-02134-9","url":null,"abstract":"<p>The <i>Flying Sidekick Traveling Salesman Problem (FSTSP)</i> consists of using one truck and one drone to perform deliveries to a set of customers. The drone is limited to delivering to one customer at a time, after which it returns to the truck, from where it can be launched again. The goal is to minimize the time required to service all customers and return both vehicles to the depot. In the literature, we can find heuristics for this problem that follow the order-first split-second approach: find a Hamiltonian cycle <i>h</i> with all customers, and then remove some customers to be handled by the drone while deciding from where the drone will be launched and where it will be retrieved. Indeed, they optimally solve the <i>h-FSTSP</i>, which is a variation that consists of solving the FSTSP while respecting a given initial cycle <i>h</i>. We present the Lazy Drone Property, which guarantees that only some combinations of nodes for the launch and retrieval of the drone need to be considered by algorithms for the h-FSTSP. We also present an algorithm that uses the property, and we show experimental results which corroborate its effectiveness in decreasing the running time of such algorithms. Our algorithm was shown to be more than 84 times faster than the previously best-known ones over the literature benchmark. Moreover, on average, it considered an amount of launch and retrieval pairs that is linear on the number of customers, indicating that the algorithm’s performance should be sustainable for larger instances.\u0000</p>","PeriodicalId":49720,"journal":{"name":"Optimization Letters","volume":"29 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572383","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
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