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Probabilistic Lookahead Strong Branching via a Stochastic Abstract Branching Model 1

21st International Conference on the Integration of Constraint programming, Artificial Intelligence, and Operations Research (CPAIOR)

作者： Mexi, Gioni Shamsi, Somayeh Besancon, Mathieu Le Bodic, Pierre Zuse Inst Berlin Berlin Germany Monash Univ Clayton Vic Australia Univ Grenoble Alpes LIG INRIA Grenoble France

ISBN: (数字)9783031605994

ISBN: (纸本)9783031606014;9783031605994

Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of mixed-integer programming solvers. In its full form, SB evaluates all variables to branch on and then selects the one producing the best relaxation, leading to small trees, but high runtimes. State-of-the-art branching rules therefore use SB with working limits to achieve both small enough trees and short run times. So far, these working limits have been established empirically. In this paper, we introduce a theoretical approach to guide how much SB to use at each node within the BnB. We first define an abstract stochastic tree model of the BnB algorithm where the geometric mean dual gains of all variables follow a given probability distribution. This model allows us to relate expected dual gains to tree sizes and explicitly compare the cost of sampling an additional SB candidate with the reward in expected tree size reduction. We then leverage the insight from the abstract model to design a new stopping criterion for SB, which fits a distribution to the dual gains and, at each node, dynamically continues or interrupts SB. This algorithm, which we refer to as Probabilistic Lookahead Strong Branching, improves both the tree size and runtime over MIPLIB instances, providing evidence that the method not only changes the amount of SB, but allocates it better.

关键词： mixed-integer programming Branch-and-Bound Strong Branching Abstract Branching Tree Stochastic Model

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Bound Tightening Using Rolling-Horizon Decomposition for Neural Network Verification 21st

Bound Tightening Using Rolling-Horizon Decomposition for Neu...

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21st International Conference on the Integration of Constraint programming, Artificial Intelligence, and Operations Research (CPAIOR)

作者： Zhao, Haoruo Hijazi, Hassan Jones, Haydn Moore, Juston Tanneau, Mathieu Van Hentenryck, Pascal Georgia Inst Technol Atlanta GA 30308 USA Los Alamos Natl Lab Los Alamos NM 87545 USA Univ Penn Philadelphia PA 19104 USA

ISBN: (纸本)9783031606014;9783031605994

Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable deployment in safety-critical applications. This paper introduces a new approach to neural network verification using a novel mixed-integer programming (MIP) rolling-horizon decomposition method. The algorithm leverages the layered structure of neural networks by employing optimization-based bound tightening (OBBT) on smaller sub-graphs of the original network in a rolling-horizon fashion and tightening the bounds in parallel. This strategy strikes a balance between achieving tighter bounds and ensuring the tractability of the underlying mixed-integer programs. Extensive numerical experiments, conducted on instances from the VNN-COMP benchmark library, demonstrate that the proposed approach yields significantly improved bounds compared to existing efficient bound propagation methods. Notably, the proposed method proves effective in solving open verification problems. Our code is built and released as part of the open-source mathematical modeling tool Gravity (https://***/ coin- or/Gravity), which is extended to support generic neural network models.

关键词： Neural Network Verification Optimization-Based Bound Tightening mixed-integer programming Decomposition

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Path Planning for Autonomous Vehicle Turning at Intersections with Signal Temporal Logic Specifications 16

Path Planning for Autonomous Vehicle Turning at Intersection...

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16th International Conference on Computer and Automation Engineering (ICCAE)

作者： Wang, Yujin Huang, Zhaoyan Dong, Shiying Chu, Hongqing Yin, Xiang Gao, Bingzhao Tongji Univ Sch Automot Studies Shanghai Peoples R China Jilin Univ Dept Control Sci & Engn Changchun Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai Peoples R China

ISBN: (纸本)9798350370058;9798350370164

This work establishes signal temporal logic specifications for driving tasks that autonomous vehicle should execute when turning at intersections. The specifications are based on traffic regulations of China. By encoding signal temporal logic specifications as mixed-integer constraints, optimization problems could be established for path planning. By solving the problems with Gurobi optimizer, safe paths could be obtained. Through this work, it is demonstrated that signal temporal logic is a profound tool for formalizing driving tasks and solving path planning problems in autonomous driving. The feasibility of the proposed method is demonstrated via a numerical experiment.

关键词： path planning signal temporal logic mixed-integer programming autonomous vehicle

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Minimizing transportation cost of prefabricated modules in modular construction projects

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ENGINEERING CONSTRUCTION AND ARCHITECTURAL MANAGEMENT 2022年第10期29卷 3847-3867页

作者： Almashaqbeh, Mohammad El-Rayes, Khaled Hashemite Univ Dept Civil Engn Zarqa Jordan Univ Illinois Dept Civil & Environm Engn Champaign IL 61820 USA

Purpose The objective of this research study is to formulate and develop a novel optimization model that enables planners of modular construction to minimize the total transportation and storage costs of prefabricated modules in modular construction projects. Design/methodology/approach The model is developed by identifying relevant decision variables, formulating an objective function capable of minimizing the total transportation and storage costs and modelling relevant constraints. The model is implemented by providing all relevant planner-specified data and performing the model optimization computations using mixed-integer programming to generate the optimal solution. Findings A case study of hybrid modular construction of a healthcare facility is used to evaluate the model performance and demonstrate its capabilities in minimizing the total transportation and onsite storage costs of building prefabricated modules. Research limitations/implications The model can be most effective in optimizing transportation for prefabricated modules with rectangular shapes and might be less effective for modules with irregular shapes. Further research is needed to consider the shape of onsite storage area and its module arrangement. Practical implications The developed model supports construction planners in improving the cost effectiveness of modular construction projects by optimizing the transportation of prefabricated modules from factories to construction sites. Originality/value The original contributions of this research is selecting an optimal module truck assignment from a feasible set of trucks, identifying an optimal delivery day of each module as well as its location and orientation on the assigned truck and complying with relevant constraints including the non-overlap of modules on each truck, shipment weight distribution and aerodynamic drag reduction.

关键词： Modular construction Hybrid modular construction Offsite construction Optimization Minimizing transportation cost mixed-integer programming

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Scheduling of waterways with tide and passing box

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NAVAL RESEARCH LOGISTICS 2022年第4期69卷 609-621页

作者： Nehrke, Lara Schulz, Arne Univ Hamburg Inst Operat Management Moorweidenstr 18 D-20148 Hamburg Germany

Due to the increasing amount of goods transported by vessels and the resulting increased size of the vessels, waterway scheduling becomes a challenging task. Waterways can often only be expanded with enormous costs and environmental damage. Therefore, this paper investigates a scheduling problem on a restricted waterway. Wide vessels are only allowed to pass in a passing box and vessels with deep draught can only pass the waterway in a time window around high tide. We present a mixed-integer program (MIP) for the problem setting and develop techniques which allow us to fix variables and reduce the number of variables and constraints of the model. The resulting model formulations are evaluated in a comprehensive computational study on a real-world setting at the river Elbe next to Hamburg (Germany).

关键词： mixed-integer programming passing box tide-dependent waterway vessel scheduling

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Exploiting complete linear descriptions for decentralized power market problems with integralities

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2022年第3期95卷 451-474页

作者： Huembs, Lukas Martin, Alexander Schewe, Lars Friedrich Alexander Univ Erlangen Nurnberg Dept Data Sci Cauerstr 11 Erlangen Germany Univ Edinburgh Sch Math James Clerk Maxwell Bldg Edinburgh EH9 3FD Midlothian Scotland

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

关键词： mixed-integer programming Competitive equilibrium Linear prices Total unimodularity

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Scheduling deferrable electric appliances in smart homes: a bi-objective stochastic optimization approach

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第1期19卷 34-65页

作者： Rossit, Diego G. Nesmachnow, Segio Toutouh, Jamal Luna, Francisco Univ Nacl Sur Dept Engn Bahia Blanca Buenos Aires Argentina INMABB UNS CONICET Bahia Blanca Buenos Aires Argentina Univ Republica Montevideo Uruguay Univ Malaga Dept Lenguajes & Ciencias Comp Malaga Spain

In the last decades, cities have increased the number of activities and services that depends on an efficient and reliable electricity service. In particular, households have had a sustained increase of electricity consumption to perform many residential activities. Thus, providing efficient methods to enhance the decision making processes in demand-side management is crucial for achieving a more sustainable usage of the available resources. In this line of work, this article presents an optimization model to schedule deferrable appliances in households, which simultaneously optimize two conflicting objectives: the minimization of the cost of electricity bill and the maximization of users satisfaction with the consumed energy. Since users satisfaction is based on human preferences, it is subjected to a great variability and, thus, stochastic resolution methods have to be applied to solve the proposed model. In turn, a maximum allowable power consumption value is included as constraint, to account for the maximum power contracted for each household or building. Two different algorithms are proposed: a simulation-optimization approach and a greedy heuristic. Both methods are evaluated over problem instances based on real-world data, accounting for different household types. The obtained results show the competitiveness of the proposed approach, which are able to compute different compromising solutions accounting for the trade-off between these two conflicting optimization criteria in reasonable computing times. The simulation-optimization obtains better solutions, outperforming and dominating the greedy heuristic in all considered scenarios.

关键词： smart cities smart homes urban data analysis household energy planning stochastic optimization mixed-integer programming Monte Carlo simulation bi-objective optimization greedy heuristic

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Enhancing Active Distribution Systems Resilience by Fully Distributed Self-Healing Strategy

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IEEE TRANSACTIONS ON SMART GRID 2022年第2期13卷 1023-1034页

作者： Nejad, Reza Roofegari Sun, Wei OSI Digital Grid Solut Dept Power Syst Dev Medina MN 55340 USA Univ Cent Florida Dept Elect & Comp Engn Orlando FL 32816 USA

Distributed restoration can exploit smart grid technologies to enhance the resilience of active distribution networks toward a self-healing smart grid. However, the large number of decision variables, especially the binary ones for reconfiguration, bring challenges to developing scalable distributed distribution service restoration (DDSR) strategies. This paper proposes a fully distributed solution procedure based on the alternating direction method of multipliers (ADMM) for mixed-integer programming problems and applies to develop the DDSR framework. The method consists of relax-drive-polish phases, 1) relaxing binary variables, and applying the convex ADMM as a warm start;2) driving the solutions toward Boolean values through a proximal operator;3) fixing the obtained binding binary variables and solving the rest of the problem to polish results and achieve a high-quality suboptimal solution. Then, an autonomous clustering strategy and consensus ADMM are integrated with the proposed method to realize the fully distributed cluster-based framework of DDSR. This framework can first determine DER scheduling and switch status for reconfiguration to energize the out-of-service areas from local faults, and then provide the load restoration solution in a distributed manner for total blackouts in large-scale distribution networks. The effectiveness and scalability of the proposed DDSR framework are demonstrated through testing on the IEEE 123-node, IEEE 8500-node, and synthetic 100k-node test feeders.

关键词： Switches Convex functions Smart grids programming Convergence Security Scalability Alternating direction method of multipliers (ADMM) distributed energy resources fully distributed service restoration mixed-integer programming reconfiguration

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Optimised redesign of reverse logistics network with multi-level capacity choices for household appliances

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2022年第18期60卷 5615-5632页

作者： Che, Ada Lei, Jieyu Jiang, Zhibin Northwestern Polytech Univ Sch Management Xian Peoples R China Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai Peoples R China

Reverse logistics networks reintroduce end-of-life products to remanufacturing, which is significant for sustainable development and environmental protection. In this paper, we investigate the current reverse logistics network of household appliances in China and redesign a new network that introduces necessary facilities: disassembly centres and three types of remanufacturing plants to improve recycling rates. A mixed-integer linear programming model with multi-level capacity choices is proposed to determine the locations and capacities for disassembly centres and remanufacturing plants. An efficient decomposition-and-expansion heuristic is developed to solve the model. The redesigned network is evaluated using a real case. The results indicate that the recycling rate is largely improved by the new network in which almost all useful materials can be recycled, whereas, in the traditional network, only metals are efficiently recycled. A sensitivity analysis of model parameters is conducted using the Taguchi method to identify their effects on recycling decisions. The proposed algorithm is further evaluated using a set of randomly generated instances. The results show that the algorithm can yield high-quality solutions within a short time. The best configuration of the algorithm is suggested via sensitivity analysis of parameters using the generated instances.

关键词： Reverse logistics network redesign facility location capacity choices mixed-integer programming decomposition-and-expansion heuristic

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Battery Storage Formulation and Impact on Day Ahead Security Constrained Unit Commitment

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第5期37卷 3995-4005页

作者： Chen, Yonghong Baldick, Ross Midcontinent Independent Syst Operator Inc MISO Carmel IN 46032 USA Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA

This paper discusses battery storage formulations and analyzes the impact of the constraints on the computational performance of security constrained unit commitment (SCUC). Binary variables are in general required due to mutual exclusiveness of charging and discharging modes. We use valid inequalities to improve the SOC constraints. Adding batteries to the MISO day ahead market clearing cases reveals the impact of binary variables and the valid inequalities on SCUC solving time. Warm start and lazy constraint techniques are applied to improve the performance and make the valid inequalities more effective, reducing computation time to acceptable levels for implementation.

关键词： Batteries State of charge MISO communication Generators Sufficient conditions Analytical models Security mixed-integer programming storage tight formulation

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