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Upgrading edges in the maximal covering location problem 最大覆盖位置问题中的边缘升级
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11883
Marta Baldomero-Naranjo, Jörg Kalcsics, Alfredo Marín, Antonio M. Rodríguez-Chía
{"title":"Upgrading edges in the maximal covering location problem","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Alfredo Marín, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11883","DOIUrl":"https://doi.org/arxiv-2409.11883","url":null,"abstract":"We study the upgrading version of the maximal covering location problem with\u0000edge length modifications on networks. This problem aims at locating p\u0000facilities on the vertices (of the network) so as to maximise coverage,\u0000considering that the length of the edges can be reduced at a cost, subject to a\u0000given budget. Hence, we have to decide on: the optimal location of p facilities\u0000and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three\u0000different mixed-integer formulations and a preprocessing phase for fixing\u0000variables and removing some of the constraints. Moreover, we strengthen the\u0000proposed formulations including valid inequalities. Finally, we compare the\u0000three formulations and their corresponding improvements by testing their\u0000performance over different datasets.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254597","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
Trading with propagators and constraints: applications to optimal execution and battery storage 利用传播者和约束条件进行交易：应用于优化执行和电池存储
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.12098
Eduardo Abi Jaber, Nathan De Carvalho, Huyên Pham
{"title":"Trading with propagators and constraints: applications to optimal execution and battery storage","authors":"Eduardo Abi Jaber, Nathan De Carvalho, Huyên Pham","doi":"arxiv-2409.12098","DOIUrl":"https://doi.org/arxiv-2409.12098","url":null,"abstract":"Motivated by optimal execution with stochastic signals, market impact and\u0000constraints in financial markets, and optimal storage management in commodity\u0000markets, we formulate and solve an optimal trading problem with a general\u0000propagator model under linear functional inequality constraints. The optimal\u0000control is given explicitly in terms of the corresponding Lagrange multipliers\u0000and their conditional expectations, as a solution to a linear stochastic\u0000Fredholm equation. We propose a stochastic version of the Uzawa algorithm on\u0000the dual problem to construct the stochastic Lagrange multipliers numerically\u0000via a stochastic projected gradient ascent, combined with a least-squares Monte\u0000Carlo regression step to approximate their conditional expectations. We\u0000illustrate our findings on two different practical applications with stochastic\u0000signals: (i) an optimal execution problem with an exponential or a power law\u0000decaying transient impact, with either a `no-shorting' constraint in the\u0000presence of a `sell' signal, a `no-buying' constraint in the presence of a\u0000`buy' signal or a stochastic `stop-trading' constraint whenever the exogenous\u0000price drops below a specified reference level; (ii) a battery storage problem\u0000with instantaneous operating costs, seasonal signals and fixed constraints on\u0000both the charging power and the load capacity of the battery.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254595","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
Second-Order Constrained Dynamic Optimization 二阶受限动态优化
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11649
Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou
{"title":"Second-Order Constrained Dynamic Optimization","authors":"Yuichiro Aoyama, Oswin So, Augustinos D. Saravanos, Evangelos A. Theodorou","doi":"arxiv-2409.11649","DOIUrl":"https://doi.org/arxiv-2409.11649","url":null,"abstract":"This paper provides an overview, analysis, and comparison of second-order\u0000dynamic optimization algorithms, i.e., constrained Differential Dynamic\u0000Programming (DDP) and Sequential Quadratic Programming (SQP). Although a\u0000variety of these algorithms has been proposed and used successfully, there\u0000exists a gap in understanding the key differences and advantages, which we aim\u0000to provide in this work. For constrained DDP, we choose methods that\u0000incorporate nolinear programming techniques to handle state and control\u0000constraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual\u0000Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers.\u0000Both DDP and SQP are provided in single- and multiple-shooting formulations,\u0000where constraints that arise from dynamics are encoded implicitly and\u0000explicitly, respectively. In addition to reviewing these methods, we propose a\u0000single-shooting PDAL DDP. As a byproduct of the review, we also propose a\u0000single-shooting PDAL DDP which is robust to the growth of penalty parameters\u0000and performs better than the normal AL variant. We perform extensive numerical\u0000experiments on a variety of systems with increasing complexity towards\u0000investigating the quality of the solutions, the levels of constraint violation,\u0000iterations for convergence, and the sensitivity of final solutions with respect\u0000to initialization. The results show that DDP often has the advantage of finding\u0000better local minima, while SQP tends to achieve better constraint satisfaction.\u0000For multiple-shooting formulation, both DDP and SQP can enjoy informed initial\u0000guesses, while the latter appears to be more advantageous in complex systems.\u0000It is also worth highlighting that DDP provides favorable computational\u0000complexity and feedback gains as a byproduct of optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254601","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
Multi-stage stochastic linear programming for shared autonomous vehicle system operation and design with on-demand and pre-booked requests 多阶段随机线性规划，用于按需和预定请求的共享自动驾驶车辆系统运营和设计
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11611
Riki Kawase
{"title":"Multi-stage stochastic linear programming for shared autonomous vehicle system operation and design with on-demand and pre-booked requests","authors":"Riki Kawase","doi":"arxiv-2409.11611","DOIUrl":"https://doi.org/arxiv-2409.11611","url":null,"abstract":"This study presents optimization problems to jointly determine long-term\u0000network design, mid-term fleet sizing strategy, and short-term routing and\u0000ridesharing matching in shared autonomous vehicle (SAV) systems with pre-booked\u0000and on-demand trip requests. Based on the dynamic traffic assignment framework,\u0000multi-stage stochastic linear programming is formulated for joint optimization\u0000of SAV system design and operations. Leveraging the linearity of the proposed\u0000problem, we can tackle the computational complexity due to multiple objectives\u0000and dynamic stochasticity through the weighted sum method and stochastic dual\u0000dynamic programming (SDDP). Our numerical examples verify that the solution to\u0000the proposed problem obtained through SDDP is close enough to the optimal\u0000solution. We also demonstrate the effect of introducing pre-booking options on\u0000optimized infrastructure planning and fleet sizing strategies. Furthermore,\u0000dedicated vehicles to pick-up and drop-off only pre-booked travelers can lead\u0000to incentives to reserve in advance instead of on-demand requests with little\u0000reduction in system performance.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254603","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
Qualitative Properties of $k-$Center Problems k-$中心问题的定性特性
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.12091
Vo Si Trong Long, Nguyen Mau Nam, Jacob Sharkansky, Nguyen Dong Yen
{"title":"Qualitative Properties of $k-$Center Problems","authors":"Vo Si Trong Long, Nguyen Mau Nam, Jacob Sharkansky, Nguyen Dong Yen","doi":"arxiv-2409.12091","DOIUrl":"https://doi.org/arxiv-2409.12091","url":null,"abstract":"In this paper, we study generalized versions of the k-center problem, which\u0000involves finding k circles of the smallest possible equal radius that cover a\u0000finite set of points in the plane. By utilizing the Minkowski gauge function,\u0000we extend this problem to generalized balls induced by various convex sets in\u0000finite dimensions, rather than limiting it to circles in the plane. First, we\u0000establish several fundamental properties of the global optimal solutions to\u0000this problem. We then introduce the notion of local optimal solutions and\u0000provide a sufficient condition for their existence. We also provide several\u0000illustrative examples to clarify the proposed problems.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254604","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
On the complexity of the upgrading version of the maximal covering location problem 论最大覆盖位置问题升级版的复杂性
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11900
Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía
{"title":"On the complexity of the upgrading version of the maximal covering location problem","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11900","DOIUrl":"https://doi.org/arxiv-2409.11900","url":null,"abstract":"In this article, we study the complexity of the upgrading version of the\u0000maximal covering location problem with edge length modifications on networks.\u0000This problem is NP-hard on general networks. However, in some particular cases,\u0000we prove that this problem is solvable in polynomial time. The cases of star\u0000and path networks combined with different assumptions for the model parameters\u0000are analysed. In particular, we obtain that the problem on star networks is\u0000solvable in O(nlogn) time for uniform weights and NP-hard for non-uniform\u0000weights. On paths, the single facility problem is solvable in O(n^3) time,\u0000while the p-facility problem is NP-hard even with uniform costs and upper\u0000bounds (maximal upgrading per edge), as well as, integer parameter values.\u0000Furthermore, a pseudo-polynomial algorithm is developed for the single facility\u0000problem on trees with integer parameters.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254606","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
Rapid and finite-time boundary stabilization of a KdV system KdV 系统的快速和有限时间边界稳定
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11768
Hoai-Minh Nguyen
{"title":"Rapid and finite-time boundary stabilization of a KdV system","authors":"Hoai-Minh Nguyen","doi":"arxiv-2409.11768","DOIUrl":"https://doi.org/arxiv-2409.11768","url":null,"abstract":"We construct a static feedback control in a trajectory sense and a dynamic\u0000feedback control to obtain the local rapid boundary stabilization of a KdV\u0000system using Gramian operators. We also construct a time-varying feedback\u0000control in the trajectory sense and a time varying dynamic feedback control to\u0000reach the local finite-time boundary stabilization for the same system.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254600","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
Minmax regret maximal covering location problems with edge demands 有边缘需求的最大遗憾最大覆盖位置问题
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11872
Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía
{"title":"Minmax regret maximal covering location problems with edge demands","authors":"Marta Baldomero-Naranjo, Jörg Kalcsics, Antonio M. Rodríguez-Chía","doi":"arxiv-2409.11872","DOIUrl":"https://doi.org/arxiv-2409.11872","url":null,"abstract":"This paper addresses a version of the single-facility Maximal Covering\u0000Location Problem on a network where the demand is: (i) distributed along the\u0000edges and (ii) uncertain with only a known interval estimation. To deal with\u0000this problem, we propose a minmax regret model where the service facility can\u0000be located anywhere along the network. This problem is called Minmax Regret\u0000Maximal Covering Location Problem with demand distributed along the edges\u0000(MMR-EMCLP). Furthermore, we present two polynomial algorithms for finding the\u0000location that minimises the maximal regret assuming that the demand realisation\u0000is an unknown constant or linear function on each edge. We also include two\u0000illustrative examples as well as a computational study for the unknown constant\u0000demand case to illustrate the potential and limits of the proposed methodology.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254598","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
Parametric Shape Optimization of Flagellated Micro-Swimmers Using Bayesian Techniques 利用贝叶斯技术优化鞭毛虫微型游泳器的参数形状
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11776
Lucas PalazzoloCRISAM, Laëtitia GiraldiCRISAM, Mickael BinoisACUMES, CRISAM, LJAD, Luca BertiIRMA
{"title":"Parametric Shape Optimization of Flagellated Micro-Swimmers Using Bayesian Techniques","authors":"Lucas PalazzoloCRISAM, Laëtitia GiraldiCRISAM, Mickael BinoisACUMES, CRISAM, LJAD, Luca BertiIRMA","doi":"arxiv-2409.11776","DOIUrl":"https://doi.org/arxiv-2409.11776","url":null,"abstract":"Understanding and optimizing the design of helical micro-swimmers is crucial\u0000for advancing their application in various fields. This study presents an\u0000innovative approach combining Free-Form Deformation with Bayesian Optimization\u0000to enhance the shape of these swimmers. Our method facilitates the computation\u0000of generic swimmer shapes that achieve optimal average speed and efficiency.\u0000Applied to both monoflagellated and biflagellated swimmers, our optimization\u0000framework has led to the identification of new optimal shapes. These shapes are\u0000compared with biological counterparts, highlighting a diverse range of\u0000swimmers, including both pushers and pullers.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254599","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
Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems 随机线性-二次方最优控制问题的长期行为
arXiv - MATH - Optimization and Control Pub Date : 2024-09-18 DOI: arxiv-2409.11633
Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong
{"title":"Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems","authors":"Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong","doi":"arxiv-2409.11633","DOIUrl":"https://doi.org/arxiv-2409.11633","url":null,"abstract":"This paper investigates the asymptotic behavior of the solution to a\u0000linear-quadratic stochastic optimal control problems. The so-called probability\u0000cell problem is introduced the first time. It serves as the probability\u0000interpretation of the well-known cell problem in the homogenization of\u0000Hamilton-Jacobi equations. By establishing a connection between this problem\u0000and the ergodic cost problem, we reveal the turnpike properties of the\u0000linear-quadratic stochastic optimal control problems from various perspectives.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254602","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
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