Filipe Brandão
VPSolver is a vector packing solver based on an arc-flow formulation with graph compression. In this paper, we present the algorithm introduced in VPSolver 3.0.0 for building compressed arc-flow models for the multiple-choice vector packing problem.
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The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centers and stores, such that the furniture fits inside. Such problems are often formulated and sometimes solved using general-purpose integer programming solvers. This chapter studies the problem of identifying a compact formulation of the multi-dimensional packing component in a general instance of integer linear programming, reformulating it using the disc…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately solving PC-LPs in nearly linear time, where the time complexity scales nearly linearly in $N$, the number of nonzero entries of the matrix, and polynomially in $\varepsilon$, the (multiplicative) approximation error. Unfortunately, all existing nearly linear-time algorithms for solving PC-LPs require time at least proportional to $\varepsilon^{-2}$. In this pape…
PrecPack: An Efficient Open-Source Exact Solver for Bin Packing with Generalized Precedence Constraints
PrecPack是一个开源精确求解器，通过扩展分支-边界-记忆算法并引入广义状态和根列生成，高效求解具有广义优先约束的装箱问题，在基准测试中优于现有实现。
A Parallelizable Acceleration Framework for Packing Linear Programs
本文提出一种可并行加速的线性规划打包框架，通过减少问题规模显著提升求解速度，适用于精确和近似求解器，以及整数线性规划问题。
Application of hybrid classical-quantum annealing technology to the 3D Bin-Packing Problem
本文研究使用混合经典-量子退火技术解决带支撑约束的三维多产品多箱装箱问题，通过开发变量更少的混合整数规划精确模型，并对比Gurobi与D-Wave CQM求解器的性能，为混合量子求解器在复杂商业优化问题中的表现提供了见解。
This paper investigates a critical resource allocation problem in the first party cloud: scheduling containers to machines. There are tens of services and each service runs a set of homogeneous containers with dynamic resource usage; containers of a service are scheduled daily in a batch fashion. This problem can be naturally formulated as Stochastic Bin Packing Problem (SBPP). However, traditional SBPP research often focuses on cases of empty machines, whose objective, i.e., to minimize the number of used machines, is not well-defined for the more common reality with nonempty machines. This p…
The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be used for various types of problems, i.e. Tammes problems, Thomson problems, search of minimal potential energy of micro-clusters, etc. Here we consider a problem of densest packing of equal circles in special geometrical object, so called square flat torus $\mathbb{R}^2/\mathbb{Z}^2$ with the induced metric. It is formulated as Mixed-Integer Nonlinear Proble…
Current integer programming solvers fail to decide whether 12 unit cubes can be packed into a 1x1x11 box within an hour using the natural relaxation of Chen/Padberg. We present an alternative relaxation of the problem of packing boxes into a larger box, which makes it possible to solve much larger instances.
Deep Reinforcement Learning on Item-Compatibility Graphs for One-Dimensional Bin Packing
提出基于物品兼容图的深度强化学习框架，通过图神经网络策略和随机束搜索，零样本泛化求解一维装箱，降低构造式启发式的平均最优性差距至2.31%。
The Quadratic Bin Packing Problem: Exact Formulations and Algorithm
本文研究了扩展经典装箱问题的二次装箱问题，引入了每个使用箱子的固定成本和物品组合的成对成本。通过三种紧凑的混合整数线性规划模型和一种集分割模型，结合改进的连续松弛和定制的分支定价算法，展示了在不同规模实例上的求解效果。
QAL-BP: An Augmented Lagrangian Quantum Approach for Bin Packing
本文提出QAL-BP，一种基于增广拉格朗日方法的QUBO公式，用于在量子退火设备上求解装箱问题，并通过与模拟退火和Gurobi对比验证其正确性与量子计算潜力。
Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where variables represent flows on individual arcs of the network. For $\mathcal{NP}$-hard problems, polynomial-sized arc flow models typically provide weak linear relaxations and may have too much symmetry to be efficient in practice. Instead, arc flow models with a pseudo-polynomial size usually provide strong relaxations and are efficient in practice. The inte…
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