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arXiv 2024年

作者： Meng, Chengzhen Huang, Zhenmin Ma, Jun The Robotics and Autonomous Systems Thrust The Hong Kong University of Science and Technology Guangzhou China The Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Hong Kong

Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Currently, most methods are tailored to specific scenarios, and the efficiency of existing optimization and learning methods applicable to diverse scenarios is hindered by the complexity of modeling and data dependency, which limit their real-world applicability. To address these issues, this paper proposes a universal multi-vehicle cooperative decision-making method in structured roads with game theory. We transform the decision-making problem into a graph path searching problem within a way-point graph framework. The problem is formulated as a mixed-integer linear programming problem (MILP) first and transformed into a mixed-integer potential game (MIPG), which reduces the scope of problem and ensures that no player needs to sacrifice for the overall cost. Two Gauss-Seidel algorithms for cooperative decision-making are presented to solve the MIPG problem and obtain the Nash equilibrium solutions. Specifically, the sequential Gauss-Seidel algorithm for cooperative decision-making considers the varying degrees of CAV interactions and flexibility in adjustment strategies to determine optimization priorities, which reduces the frequency of ineffective optimizations. Experimental evaluations across various urban traffic scenarios with different topological structures demonstrate the effectiveness and efficiency of the proposed method compared with MILP and comparisons of different optimization sequences validate the efficiency of the sequential Gauss-Seidel algorithm for cooperative decision-making. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-linear Kernel Approximation

arXiv

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arXiv 2024年

作者： Xie, Yilin Zhang, Shiqiang Paulson, Joel Tsay, Calvin Department of Computing Imperial College London United Kingdom Department of Chemical and Biomolecular Engineering The Ohio State University United States

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for global acquisition function optimization. Specifically, our Piecewise-linear Kernel mixed integer Quadratic programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Visibility polynomials, dual visibility spectrum, and characterization of total mutual-visibility sets

arXiv

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arXiv 2024年

作者： Bujtás, Csilla Klavžar, Sandi Tian, Jing Faculty of Mathematics and Physics University of Ljubljana Slovenia Institute of Mathematics Physics and Mechanics Ljubljana Slovenia Faculty of Natural Sciences and Mathematics University of Maribor Slovenia School of Science Zhejiang University of Science and Technology Zhejiang Hangzhou310023 China

Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such sets to convex and isometric subgraphs are studied. Dual mutual-visibility sets are shown to be intrinsically different from other types of mutual-visibility sets. It is proved that for every finite subset Z of positive integers there exists a graph G that has a dual mutual-visibility set of size i if and only if i ∈ Z ∪ integer, while for the other types of mutual-visibility such a set consists of consecutive integers. Visibility polynomials are introduced and their properties derived. As a surprise, every polynomial with nonnegative integer coefficients and with a constant term 1 is a dual visibility polynomial of some graph. Characterizations are given for total mutual-visibility sets, for graphs with total mutual-visibility number 1, and for sets which are not total mutual-visibility sets, yet every proper subset is such. Along the way an earlier result from the literature is corrected. © 2024, CC BY.

关键词： mixed-integer linear programming

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A graph-structured distance for mixed-variable domains with meta variables

arXiv

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arXiv 2024年

作者： Hallé-Hannan, Edward Audet, Charles Diouane, Youssef Le Digabel, Sébastien Saves, Paul

Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often partitioned into smaller and simpler ones, which may limit the generalizability or performance, especially if data is limited. The first main contribution of this work is a modeling framework that generalizes hierarchical, tree-structured, variable-size or conditional search frameworks. The framework models mixed-variable domains in which variables may be continuous, integer, or categorical, with some identified as meta when they influence the structure of the problem. The second main contribution is a novel distance that compares any pair of mixed-variable points that do not share the same variables, allowing to use whole heterogeneous datasets that reside in mixed-variable domains with meta variables. The contributions are illustrated on several regression experiments, in which the performance of a multilayer perceptron with respect to its hyperparameters is *** Codes 62-xx, 90-xx © 2024, CC BY.

关键词： mixed-integer linear programming

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Two-Stage Optimization for Efficient V2G Coordination in Distribution Power System

arXiv

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arXiv 2024年

作者： Tian, Pengchao Yan, Siqi Pan, Bikang Shi, Ye School of Information Science and Technology ShanghaiTech University China

With the growing popularity of electric vehicles (EVs), maintaining power grid stability has become a significant challenge. To address this issue, EV scheduling control strategies have been developed to manage vehicle-to-grid (V2G) in coordination with the optimal power flow. In existing studies, such coordination optimization is formulated as a mixed-integer nonlinear programming (MINP), which is computationally challenging due to the binary EV charging and discharging variables. To address this challenge, we develop an efficient two-stage optimization method for this mixed-integer nonlinear coordination problem. This method first employs an efficient technique called the difference of convex (DC) to relax the integrality and reformulate MINP into a series of path-following continuous programming. Although the DC approach shows promising efficiency for solving MINP, it cannot guarantee the feasibility of the solutions. Consequently, we propose a trust region optimization method in stage two that constructs a trust region around DC’s solution and then searches for the best feasible solution within this region. Our simulation results demonstrate that, compared to the open-source optimization solver SCIP, our proposed method significantly enhances computational efficiency while achieving near optimality. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized mixed-integer Programs

arXiv

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arXiv 2024年

作者： Qu, Shiyuan Dong, Fenglian Wei, Zhiwei Shang, Chao Department of Automation Beijing National Research Center for Information Science and Technology Tsinghua University Beijing100084 China PetroChina Planning and Engineering Institute Beijing100083 China CNPC Laboratory of Oil & Gas Business Chain Optimization Beijing100086 China

In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of mixed integer programming (MIP) problems. Distinct substantially from existing learning-to-optimize methods, our proposal seeks to train an autoencoder (AE) for binary variables in an unsupervised learning fashion, using data of optimal solutions to historical instances for a parametric family of MIPs. By a deliberate design of AE architecture and exploitation of its statistical implication, we present a simple and straightforward strategy to construct a class of cutting plane constraints from the decoder parameters of an offline-trained AE. These constraints reliably enclose the optimal binary solutions of new problem instances thanks to the representation strength of the AE. More importantly, their integration into the primal MIP problem leads to a tightened MIP with the reduced feasible region, which can be resolved at decision time using off-the-shelf solvers with much higher efficiency. Our method is applied to a benchmark batch process scheduling problem formulated as a mixed integer linear programming (MILP) problem. Comprehensive results demonstrate that our approach significantly reduces the computational cost of off-the-shelf MILP solvers while retaining a high solution quality. The codes of this work are open-sourced at https://***/qushiyuan/AE4BV. © 2024, CC BY.

关键词： mixed-integer linear programming

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Outer Approximation and Super-modular Cuts for Constrained Assortment Optimization under mixed-Logit Model

arXiv

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arXiv 2024年

作者： Pham, Hoang Giang Mai, Tien School of Computing and Information Systems Singapore Management University Singapore

In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the most general and flexible approaches for modeling and predicting customer purchasing behavior. Previous work has primarily relied on mixed-integer linear programming (MILP) or second-order cone (CONIC) reformulations, which allow for exact problem solving using off-the-shelf solvers. However, these approaches often suffer from weak continuous relaxations and are slow when solving large instances. Our research addresses the problem by focusing on components of the objective function that can be proven to be monotonically supper-modular and convex. This allows us to derive valid cuts to outer-approximate the nonlinear objective functions. We then demonstrate that these valid cuts can be incorporated into Cutting Plane or Branch-and-Cut methods to solve the problem exactly. Extensive experiments show that our approaches consistently outperform previous methods in terms of both solution quality and computation time. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Integrating and Comparing Radiality Constraints for Optimized Distribution System Reconfiguration

arXiv

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arXiv 2024年

作者： Cortés, Pablo Tabares, Alejandra Franco, Fredy

The reconfiguration of electrical power distribution systems is a crucial optimization problem aimed at minimizing power losses by altering the system’s topology through the operation of interconnection switches. This problem, typically modelled as a mixed-integer nonlinear program (MINLP) demands high computational resources for large-scale networks and requires specialized radiality constraints for maintaining the tree-like structure of distribution networks. This paper presents a comprehensive analysis that integrates and compares the computational burden associated with different radiality constraint formulations proposed in the specialized literature for the reconfiguration of distribution systems (RDS). By using consistent hardware and software setups, we evaluate the performance of these constraints across several well-known test cases, including systems with 14, 33, 84, 136, and 417 buses. Our findings reveal significant differences in computational efficiency depending on the chosen set of radiality constraints, providing valuable insights for optimizing reconfiguration strategies in practical distribution networks. © 2024, CC BY-NC-SA.

关键词： mixed-integer linear programming

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THE VOLUME POLYNOMIAL OF LATTICE POLYGONS

arXiv

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arXiv 2024年

作者： Soprunov, Ivan Soprunova, Jenya Department of Mathematics and Statistics Cleveland State University ClevelandOH44115 United States Department of Mathematical Sciences Kent State University KentOH44242 United States

We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the Heine–Shephard problem for two bodies in the plane. As an application, we show how to construct a pair of planar tropical curves (or a pair of divisors on a toric surface) with given intersection number and self-intersection *** Codes Primary 52B20, 52A39, Secondary 11H55, 14T10, 14M25 © 2024, CC BY.

关键词： mixed-integer linear programming

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Synergizing Decision Making and Trajectory Planning Using Two-Stage Optimization for Autonomous Vehicles

arXiv

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arXiv 2024年

作者： Liu, Wenru Liu, Haichao Zheng, Lei Huang, Zhenmin Ma, Jun Guangzhou511453 China The Division of Emerging Interdisciplinary Areas The Hong Kong University of Science and Technology Hong Kong

This paper introduces a local planner that syn-ergizes the decision making and trajectory planning modules towards autonomous driving. The decision making and trajectory planning tasks are jointly formulated as a nonlinear programming problem with an integrated objective function. However, integrating the discrete decision variables into the continuous trajectory optimization leads to a mixed-integer programming (MIP) problem with inherent nonlinearity and nonconvexity. To address the challenge in solving the problem, the original problem is decomposed into two sub-stages, and a two-stage optimization (TSO) based approach is presented to ensure the coherence in outcomes for the two stages. The optimization problem in the first stage determines the optimal decision sequence that acts as an informed initialization. With the outputs from the first stage, the second stage necessitates the use of a high-fidelity vehicle model and strict enforcement of the collision avoidance constraints as part of the trajectory planning problem. We evaluate the effectiveness of our proposed planner across diverse multi-lane scenarios. The results demonstrate that the proposed planner simultaneously generates a sequence of optimal decisions and the corresponding trajectory that significantly improves driving performance in terms of driving safety and traveling efficiency as compared to alternative methods. Additionally, we implement the closed-loop simulation in CARLA, and the results showcase the effectiveness of the proposed planner to adapt to changing driving situations with high computational efficiency. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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