Pub Date : 2025-10-25DOI: 10.1007/s10878-025-01358-4
Zeling Xu, Li Liu, Feiyu Guo
{"title":"Hot potato or valuable opportunity: e-tailer’s support for competitor logistics service","authors":"Zeling Xu, Li Liu, Feiyu Guo","doi":"10.1007/s10878-025-01358-4","DOIUrl":"https://doi.org/10.1007/s10878-025-01358-4","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382461","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}
{"title":"Reinforcement learning-guided adaptive large neighborhood search for vehicle routing problem with time windows","authors":"Zhaohui Wang, Qiao Cui, Bin Tan, Xiao Yang, Weibang Zhou, Xiangsheng Huang","doi":"10.1007/s10878-025-01364-6","DOIUrl":"https://doi.org/10.1007/s10878-025-01364-6","url":null,"abstract":"","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382463","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}
Pub Date : 2025-09-04DOI: 10.1007/s10878-025-01345-9
Siddharth Gaur, R. Inkulu
Given a simple polygon P defined with n vertices in the plane, we preprocess P and compute routing tables at every vertex of P. In the routing phase, a packet originating at any source vertex of P is routed to its destination vertex belonging to P. At every vertex v of P along the routing path, until the packet reaches its destination, the next hop is determined using the routing tables at v and the additional information (including the packet’s destination vertex label) in the packet. We show our routing scheme constructs routing tables in
给定一个平面上定义有n个顶点的简单多边形P，我们对P进行预处理，并在P的每个顶点计算路由表。在路由阶段，从P的任何源顶点发出的数据包沿着路由路径被路由到属于P的目标顶点。在P的每个顶点v，直到数据包到达目的地，使用路由表和数据包中的附加信息（包括数据包的目的地顶点标签）来确定下一跳。我们证明了我们的路由方案在O(n(1+ 1λ)(lg∑n)3)O big (n big （1+ frac{1}{epsilon }big) big (lg n{}big)^3 big）时间内构建路由表，并且P所有顶点的路由表一起使用O(n+ nλ (lg∑n)3)O big （n+ frac{n}{epsilon }big (lg n{}big)^3 big）空间。我们的算法计算的路由路径的乘法拉伸因子的上限是（2+ λ）lg (2+ epsilon) lg n。这里，ϵ＆gt;0 {}epsilon >是一个输入参数。
{"title":"A divide-and-conquer based preprocessing for routing in a simple polygon","authors":"Siddharth Gaur, R. Inkulu","doi":"10.1007/s10878-025-01345-9","DOIUrl":"https://doi.org/10.1007/s10878-025-01345-9","url":null,"abstract":"<p>Given a simple polygon <i>P</i> defined with <i>n</i> vertices in the plane, we preprocess <i>P</i> and compute routing tables at every vertex of <i>P</i>. In the routing phase, a packet originating at any source vertex of <i>P</i> is routed to its destination vertex belonging to <i>P</i>. At every vertex <i>v</i> of <i>P</i> along the routing path, until the packet reaches its destination, the next hop is determined using the routing tables at <i>v</i> and the additional information (including the packet’s destination vertex label) in the packet. We show our routing scheme constructs routing tables in <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>O</mi><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mo></mrow></mstyle><mi>n</mi><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mo></mrow></mstyle><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mi>&#x03F5;</mi></mfrac><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mo></mrow></mstyle><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mo></mrow></mstyle><mi>lg</mi><mo>&#x2061;</mo><mrow><mi>n</mi></mrow><msup><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mo></mrow></mstyle><mn>3</mn></msup><mstyle scriptlevel=\"0\"><mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mo></mrow></mstyle></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"3.615ex\" role=\"img\" style=\"vertical-align: -1.006ex;\" viewbox=\"0 -1123.3 8719.1 1556.6\" width=\"20.251ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4F\" y=\"0\"></use><use x=\"763\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><use x=\"1222\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use x=\"1822\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><use x=\"2281\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use><use x=\"3003\" xlink:href=\"#MJMAIN-2B\" y=\"0\"></use><g transform=\"translate(3782,0)\"><g transform=\"translate(342,0)\"><rect height=\"60\" stroke=\"none\" width=\"473\" x=\"0\" y=\"220\"></rect><use transform=\"scale(0.707)\" x=\"84\" xlink:href=\"#MJMAIN-31\" y=\"556\"></use><use transform=\"scale(0.707)\" x=\"131\" xlink:href=\"#MJMATHI-3F5\" y=\"-488\"></use></g></g><use x=\"4718\" xlink:href=\"#MJSZ1-29\" y=\"-1\"></use><use x=\"5176\" xlink:href=\"#MJSZ1-28\" y=\"-1\"></use><g transform=\"translate(5802,0)\"><use xlink:href=\"#MJMAIN-6C\"></use><use x=\"278\" xlink:href=\"#MJMAIN-67\" y=\"0\"></use></g><","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"128 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003501","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}
Pub Date : 2025-08-30DOI: 10.1007/s10878-025-01344-w
Somnath Buriuly, Leena Vachhani, Arpita Sinha, Sivapragasam Ravitharan, Sunita Chauhan
In transportation networks, routing problems are cursed with arbitrary changes occurring in the dataset due to unpredictable events like agent breakdown (sensor or vehicle failure), network connectivity changes, resource/demand fluctuations, etc. Moreover, capacity restriction on the agents may require multi-trip solutions for meeting large demands over networks. For example, a battery-powered inspection wagon can only service a limited number of track sections in a single trip. We investigate a moving horizon approach for the multi-trip dynamic capacitated arc routing problem with limited duration to mitigate the limitations of CARP variants in the literature. The proposed approach addresses arbitrary changes in the underlying network, agent unavailability scenarios, and simultaneously satisfies the time limit on meeting all demands. The moving horizon approach subdivides the planning horizon to determine the current trip (single-trip) for all agents, hence coined as Moving Horizon Capacitated Arc Routing Problem (MH-CARP). The proposed MH-CARP is formulated as a set covering problem that considers both partial and full trips (trips may not start at the depot), making it suitable for tackling arbitrary events by re-planning. Theoretical results for the computation of dual variables are derived and then implemented in the column generation algorithm to obtain lower bounds. The algorithm is validated on a widely available dataset for CARP, having instances of up to 147 tasks that require servicing by up to 20 agents. Using this benchmark data, the partial-trip based re-planning strategy is also validated. Lastly, a simulation study is presented to demonstrate the re-planning strategy and compare an MH-CARP solution to two CARP based solutions - one with no arbitrary events and the other with known arbitrary events. The results also convey that greedy solutions are avoided to satisfy the limited duration restriction, and automatic re-ordering of the trips is achieved to compensate for arbitrary events.
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Pub Date : 2025-08-30DOI: 10.1007/s10878-025-01342-y
Dong Cheng, Huina Zhang, Yong Wu
<p>The maximum expert consensus model (MECM) aims to maximize the number of consensual decision-makers (DMs) within a limited budget. However, it may fail to achieve high group satisfaction or even cannot reach an acceptable consensus due to its neglect of the group consensus level, resulting in type-<span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.412ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -519.5 640.5 607.8" width="1.488ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMATHI-3B1" y="0"></use></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex">alpha </script></span> constraints not being satisfied. To address this issue, we extend the existing MECM by considering both type-<span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.412ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -519.5 640.5 607.8" width="1.488ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMATHI-3B1" y="0"></use></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex">alpha </script></span> and type-<span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>ε</mtext></mrow></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="1.412ex" role="img" style="vertical-align: -0.205ex;" viewbox="0 -519.5 466.5 607.8" width="1.083ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use x="0" xlink:href="#MJMATHI-3B5" y="0"></use></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>ε</mtext></mrow></math></span></span><script type="math/tex">varepsilon </script></span> consensus constraints to enable the group consensus level and the number of consensual DMs as large as possible. Firstly, we construct a dual-MECM that considers the above two constraints. Secondly, we further develop a dual-MECM considering compromise limits (dual-MEC
{"title":"Maximum expert consensus models with both type- $$alpha $$ and type- $$varepsilon $$ constraints","authors":"Dong Cheng, Huina Zhang, Yong Wu","doi":"10.1007/s10878-025-01342-y","DOIUrl":"https://doi.org/10.1007/s10878-025-01342-y","url":null,"abstract":"<p>The maximum expert consensus model (MECM) aims to maximize the number of consensual decision-makers (DMs) within a limited budget. However, it may fail to achieve high group satisfaction or even cannot reach an acceptable consensus due to its neglect of the group consensus level, resulting in type-<span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>&#x03B1;</mi></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 640.5 607.8\" width=\"1.488ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math></span></span><script type=\"math/tex\">alpha </script></span> constraints not being satisfied. To address this issue, we extend the existing MECM by considering both type-<span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>&#x03B1;</mi></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 640.5 607.8\" width=\"1.488ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math></span></span><script type=\"math/tex\">alpha </script></span> and type-<span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mtext>&#x03B5;</mtext></mrow></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"1.412ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -519.5 466.5 607.8\" width=\"1.083ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3B5\" y=\"0\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mtext>ε</mtext></mrow></math></span></span><script type=\"math/tex\">varepsilon </script></span> consensus constraints to enable the group consensus level and the number of consensual DMs as large as possible. Firstly, we construct a dual-MECM that considers the above two constraints. Secondly, we further develop a dual-MECM considering compromise limits (dual-MEC","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003462","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}
Pub Date : 2025-08-19DOI: 10.1007/s10878-025-01341-z
Xiaowei Li, Xiwen Lu
<p>The facility location game, where the agents’ locations are on a line, is considered in this paper. The input consists of the reported locations of agents, which are collected as part of the game setup. We introduce the concept of a fairness baseline and define a function to characterize each agent’s satisfaction with the facility location. Our objective is to establish a mechanism that obtains the true information of agents and outputs a single facility location so that the sum of all agents’ satisfaction with the location is maximized. For the game with two agents, we propose a <span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>4</mn></mfrac></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="3.215ex" role="img" style="vertical-align: -1.006ex;" viewbox="0 -950.8 713.9 1384.1" width="1.658ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect height="60" stroke="none" width="473" x="0" y="220"></rect><use transform="scale(0.707)" x="84" xlink:href="#MJMAIN-35" y="575"></use><use transform="scale(0.707)" x="84" xlink:href="#MJMAIN-34" y="-524"></use></g></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>4</mn></mfrac></math></span></span><script type="math/tex">frac{5}{4}</script></span>-approximate strategy-proof mechanism, which is the best possible. In the general case, we demonstrate that the median mechanism achieves an approximation ratio of <span><span style=""></span><span data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math>' role="presentation" style="font-size: 100%; display: inline-block; position: relative;" tabindex="0"><svg aria-hidden="true" focusable="false" height="3.215ex" role="img" style="vertical-align: -1.006ex;" viewbox="0 -950.8 713.9 1384.1" width="1.658ex" xmlns:xlink="http://www.w3.org/1999/xlink"><g fill="currentColor" stroke="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect height="60" stroke="none" width="473" x="0" y="220"></rect><use transform="scale(0.707)" x="84" xlink:href="#MJMAIN-33" y="575"></use><use transform="scale(0.707)" x="84" xlink:href="#MJMAIN-32" y="-513"></use></g></g></svg><span role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></span></span><script type="math/tex">frac{3}{2}</script></span>. In particular, the median mechanism is an optimal group strategy-proof mechanism for the game with three agents. Additionally, we devise a <span><span style=""></span><span data-mathml='<math xmlns
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Pub Date : 2025-08-19DOI: 10.1007/s10878-025-01337-9
Duy Hieu Do, Thi Ha Duong Phan
We present improvements to famous algorithms for community detection, namely Newman’s spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the process to split each cluster into two, based on the signs of the eigenvector corresponding to the second-largest eigenvalue. Our improvement involves replacing the time-consuming computation of eigenvalues with a random walk during the splitting process. The Louvain algorithm iteratively performs the following steps until no increase in modularity can be achieved anymore: each step consists of two phases–phase 1 for partitioning the graph into clusters, and phase 2 for constructing a new graph where each vertex represents one cluster obtained from phase 1. We propose an improvement to this algorithm by adding our random walk algorithm as an additional phase for refining clusters obtained from phase 1. It maintains a complexity comparable to the Louvain algorithm while exhibiting superior efficiency. To validate the robustness and effectiveness of our proposed algorithms, we conducted experiments using randomly generated graphs and real-world data.
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