【中秋】ijoc论文20230929

**1.DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems

DiversiTree：一种有效计算混合整数优化问题的各种近最优解集的新方法**
Izuwa Ahanor , Hugh Medal , Andrew C. Trapp
伊祖瓦·阿哈诺尔、休·
Published Online:21 Aug 2023https://doi.org/10.1287/ijoc.2022.0164
网络出版日期：2023年8月21日https：//doi.org/10.1287/ijoc.2022.0164
Izuwa Ahanor, Hugh Medal, Andrew C. Trapp (2023) DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems. INFORMS Journal on Computing 0(0).
Izuwa Ahanor，休奖章，安德鲁 C. 特拉普 （2023） DiversiTree：一种有效计算混合整数优化问题的各种近优解集的新方法。信息计算杂志0（0）。
https://doi.org/10.1287/ijoc.2022.0164
Keywords 关键字
integer programming 整数规划near-optimal solutions 近乎最优的解决方案diversity 多样性node-selection rules 节点选择规则

Abstract 抽象
Although most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Furthermore, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets.
尽管大多数求解混合整数优化问题的方法都计算单个最优解，但一组不同的近最优解通常可以改善结果。我们提出了一种寻找一组多样化解决方案的新方法，通过在寻求接近最优的解决方案中强调多样性。具体来说，在分支和绑定框架内，我们研究了明确考虑多样性的参数化节点选择规则。我们的结果表明，我们的方法显着增加了最终解决方案集的多样性。与两种现有方法相比，我们的方法运行在与常规节点选择方法相似的运行时，并且多样性提高了 12% 到 190%。相比之行的节点选择规则，如最佳优先搜索，在某些情况下比最先进的方法差35%以上，改进不超过130%。此外，我们发现，当在树中达到最小深度后不断强调节点选择的多样性并且解决方案集已经变得足够大时，我们的方法是最有效的。我们的方法可以很容易地合并到整数规划求解器中，并有可能显着增加解决方案集的多样性。

History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis.
历史：由Pascal Van Hentenryck接受，计算建模区域编辑：方法与分析。

Funding: This work was supported by the Army Research Office [Grant W911NF-21-1-0079]. The views expressed in this study do not represent those of the U.S. Government, the U.S. Department of Defense, or the U.S. Army.
资助：这项工作得到了陆军研究办公室[Grant W911NF-21-1-0079]的支持。本研究中表达的观点不代表美国政府、美国国防部或美国陆军的观点。

**2. An Approximation Algorithm for k-Depot Split Delivery Vehicle Routing Problem

一种面向k-Depot拆分配送车辆路径问题的近似算法**
Cite as 引用为
Xiaofan Lai, Liang Xu, Zhou Xu, Yang Du (2023) An Approximation Algorithm for k-Depot Split Delivery Vehicle Routing Problem. INFORMS Journal on Computing 0(0).
赖晓凡， 徐亮， 周旭， 杜洋 （2023） k-depot拆分配送车辆路径问题的近似算法.信息计算杂志0（0）。
https://doi.org/10.1287/ijoc.2021.0193
Keywords 关键字
approximation algorithm 近似算法multiple depot 多仓库vehicle routing problem 车辆配送问题split delivery 拆分交付

Xiaofan Lai , Liang Xu , Zhou Xu , Yang Du
赖晓凡 ， 梁旭 ， 周旭 ， 杨杜
Published Online:25 May 2023https://doi.org/10.1287/ijoc.2021.0193
网络发布日期：2023年5月25日https：//doi.org/10.1287/ijoc.2021.0193
Abstract 抽象
A multidepot capacitated vehicle routing problem aims to serve customers’ demands using a fleet of capacitated vehicles located in multiple depots, such that the total travel cost of the vehicles is minimized. We study a variant of this problem, the k-depot split delivery vehicle routing problem (or k-DSDVRP in short), for the situation where each customer’s demand can be served by more than one vehicle, and the total number of depots, denoted by k≥2
, is a fixed constant. This is a challenging problem with broad applications in the logistics industry, for which no constant ratio approximation algorithm is known. We develop a new approximation algorithm for the k-DSDVRP, ensuring an approximation ratio of (6−4/k)
and a polynomial running time for any fixed constant k≥2
. To achieve this, we propose a novel solution framework based on a new relaxation of the problem, a cycle splitting procedure, and a vehicle assignment procedure. To further enhance its efficiency for practical usage, we adapt the newly developed approximation algorithm to a heuristic, which runs in polynomial time even when k is arbitrarily large. Experimental results show that this heuristic outperforms a commercial optimization solver and a standard vehicle routing heuristic. Moreover, our newly proposed solution framework can be applied to developing new constant ratio approximation algorithms for several other variants of the k-DSDVRP with k≥2
being a fixed constant.
多仓库有容量车辆配送问题旨在使用位于多个仓库的带能力车辆车队来满足客户的需求，从而最大限度地降低车辆的总旅行成本。我们研究了这个问题的一个变体，即 k-depot 拆分送货车辆路径问题（或简称 k-DSDVRP），用于每个客户的需求可以由多辆车提供服务的情况，并且仓库总数（用 表示 k≥2
）是一个固定常数。这是一个具有挑战性的问题，在物流行业中具有广泛的应用，对于物流行业，没有已知的恒定比率近似算法。我们为k-DSDVRP开发了一种新的近似算法，确保任何固定常数 k≥2
的近似比 (6−4/k)
和多项式运行时间。为了实现这一目标，我们提出了一种新的解决方案框架，该框架基于问题的新放宽，周期拆分过程和车辆分配过程。为了进一步提高其实际使用效率，我们将新开发的近似算法调整为启发式算法，即使k任意大，该算法也会在多项式时间内运行。实验结果表明，该启发式算法优于商业优化求解器和标准车辆路径启发式算法。此外，我们新提出的解决方案框架可以应用于为k-DSDVRP 的其他几种变体开发新的常比近似算法，这些变体 k≥2
是固定常数。

History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms.
历史：由启发式搜索和近似算法区域编辑Erwin Pesch接受。

Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 71971177, 71725001, U1811462], Research Grants Council of Hong Kong SAR, China [Grant 15221619], and Guangdong Basic and Applied Basic Research Foundation [Grant 2023A1515030260].
资助：这项工作得到了中国国家自然科学基金[资助71971177,71725001，U1811462]，中国香港特别行政区研究资助局[资助15221619]和广东省基础与应用基础研究基金[资助2023A1515030260]的部分支持。

**3. Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

学习符号表达式：混合整数公式、切割和启发式**
Cite as 引用为
Jongeun Kim, Sven Leyffer, Prasanna Balaprakash (2023) Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics. INFORMS Journal on Computing 0(0).
Jongeun Kim，Sven Leyffer，Prasanna Balaprakash （2023） 学习符号表达式：混合整数公式、切割和启发式。信息计算杂志0（0）。
https://doi.org/10.1287/ijoc.2022.0050
Keywords 关键字
symbolic regression 符号回归mixed-integer nonlinear programming
混合整数非线性规划local branching heuristic
局部分支启发式expression tree 表达式树

Jongeun Kim , Sven Leyffer , Prasanna Balaprakash
金钟根 ， 斯文·莱弗 ， 普拉萨纳·巴拉普拉卡什
Published Online:19 Jul 2023https://doi.org/10.1287/ijoc.2022.0050
网络出版日期：2023年7月19日https：//doi.org/10.1287/ijoc.2022.0050
Abstract 抽象
In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature.
在本文中，我们考虑了在不假设其函数形式的情况下学习回归函数的问题。此问题称为符号回归。表达式树通常用于表示解决方案函数，该函数通过将运算符和操作数分配给节点来确定。Cozad和Sahinidis提出了一种非凸混合整数非线性规划（MINLP），其中二进制变量用于分配运算符，非线性表达式用于通过非线性运算符（如平方，平方根和指数）传播数据值。我们通过添加新的切割来扩展该配方，以改善这种具有挑战性的 MINLP 的解决方案。我们还提出了一种启发式方法，它通过求解受限的 MINLP 来迭代构建表达式树。我们进行计算实验，并将我们的方法与文献中基于混合整数程序的方法和基于神经网络的方法进行比较。

History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis.
历史：由Pascal Van Hentenryck接受，计算建模区域编辑：方法与分析。

Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357].
资助：这项工作得到了美国能源部科学办公室应用数学活动的支持，高级科学计算研究[Grant DE-AC02-06CH11357]。