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Distributed mixed-integer linear programming via Cut Generation and Constraint Exchange

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第4期65卷 1456-1467页

作者： Testa, Andrea Rucco, Alessandro Notarstefano, Giuseppe Univ Salento Dept Engn I-73100 Lecce Italy Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

Many problems of interest for cyber-physical network systems can be formulated as mixed-integer linear programs in which the constraints are distributed among the agents. In this paper, we propose a distributed algorithmic framework to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. At each communication round, agents locally solve a small linear program, generate suitable cutting planes, and communicate a fixed number of active constraints. Within the distributed framework, we first propose an algorithm that, under the assumption of integer-valued optimal cost, guarantees finite-time convergence to an optimal solution. Second, we propose an algorithm for general problems that provides a suboptimal solution up to a given tolerance in a finite number of communication rounds. Both algorithms work under asynchronous, directed, unreliable networks. Finally, through numerical computations, we analyze the algorithm scalability in terms of the network size. Moreover, for a multi-agent multi-task assignment problem, we show, consistently with the theory, its robustness to packet loss.

关键词： Distributed algorithms Approximation algorithms Optimization Task analysis mixed integer linear programming Peer-to-peer computing Convergence Cutting planes distributed optimization mixed-integer multi-agent multi-task assignment

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A finite-time cutting plane algorithm for distributed mixed integer linear programming

A finite-time cutting plane algorithm for distributed mixed ...

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IEEE Annual Conference on Decision and Control

作者： Andrea Testa Alessandro Rucco Giuseppe Notarstefano Department of Engineering Università del Salento Lecce Italy

Many problems of interest for cyber-physical network systems can be formulated as mixed integer linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.

关键词： Distributed algorithms Optimization Convergence Algorithm design and analysis mixed integer linear programming Routing

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Generating Longest Counterexample: On the Cross-roads of mixed integer linear programming and SMT

Generating Longest Counterexample: On the Cross-roads of Mix...

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American Control Conference

作者： Manish Goyal David Bergman Parasara Sridhar Duggirala Department of Computer Science University of North Carolina Chapel Hill NC USA School of Business University of Connecticut Storrs CT USA

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

We present a technique for obtaining the longest counterexample - the execution that stays in the unsafe set for the longest (not necessarily contiguous) time, for a safety specification of linear hybrid systems. Given that hybrid systems are infinite state systems, the number of counterexamples for safety violations are potentially infinite. Therefore, searching for the right counterexample is very challenging. We employ two frameworks for solving this problem: first is an mixed integer linear Program (MILP) formulation and second is to encode counterexamples using Satisfiability Module Theory (SMT) solvers. We evaluate these frameworks on several linear hybrid systems with up to 30 dimensions.

关键词： hybrid systems Counter example mixed integer linear programming safety specification Frameworks pull rope Unsafe

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Design of cascade-form IIR filters with powers-of-two coefficients using mixed integer linear programming

Design of cascade-form IIR filters with powers-of-two coeffi...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Hyuk Jun Oh Woo Jin Oh Yong Hoon Lee Department of Electrical Engineering Korea Advanced Institute of Science and Technology Taejon South Korea

We propose an optimal design method for digital IIR filters with powers-of-two coefficients. This method is based upon the formulation of a linear optimization problem that minimizes the filter's complexity for given specifications. It is shown that by taking the logarithm to the transfer function of cascade-form IIR filters, the design problem becomes linear and can be solved by mixed integer linear programming (MILP). Design examples are presented to demonstrate the efficiency of the proposed method.

关键词： IIR filters Finite impulse response filter Passband Transfer functions mixed integer linear programming Design methodology Digital filters Polynomials Electronic mail Optimization methods

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Functional vector generation for combinational circuits based on data path coverage metric and mixed integer linear programming

Functional vector generation for combinational circuits base...

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IEEE International Symposium on Quality Electronic Design

作者： J. Sosa J.A. Montiel-Nelson H. Navarro J.C. Garcia Department of Electronic Engineering and Automation University of Las Palmas de Gran Canaria Las Palmas de Gran Canaria Spain

In this paper a functional vector generation method to maximize the data path coverage of a combinational circuit is introduced. We present a new gate model based on sensitization requirements for transition propagation, and introduce a new methodology to obtain functional vectors of maximum coverage based on mixed integer linear programming (MILP). Performance comparison and results based on a large set of MCNC'91 benchmark circuits are given. Experimental results show significant speedups over a greedy SAT method.

关键词： Vectors Combinational circuits mixed integer linear programming Circuit simulation Circuit testing Logic Computer bugs Microelectronics Data engineering Automation

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PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via mixed integer linear programming

PAAMP: Polytopic Action-Set And Motion Planning for Long Hor...

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IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Akshay Jaitly Siavash Farzan Robotics Engineering Department Worcester Polytechnic Institute Worcester MA USA Electrical Engineering Department California Polytechnic State University San Luis Obispo CA USA

ISBN: (数字)9798350377705

ISBN: (纸本)9798350377712

Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging nonconvex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a linear Program. This reformulation enables us to address motion planning as a mixed integer linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

关键词： Dynamics Optimization methods Transforms Autonomous aerial vehicles Planning Trajectory mixed integer linear programming Dynamic programming Intelligent robots

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An approximate mixed integer linear programming (MILP) model for the design of water reuse/recycle networks with minimum emergy

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING 2007年第6期2卷 566-574页

作者： Tan, R. R. Foo, D. C. Y. Ng, D. K. S. Chiang, C. L. Hu, S. Ku-Pineda, V. De La Salle Univ Dept Chem Engn Manila 1004 Philippines Univ Nottingham Malaysia Sch Chem & Environm Engn Semenyih 43500 Selangor Malaysia Inst Technol Cambodia Chem & Food Technol Dept Phnom Penh Cambodia

Recent trends in process engineering have placed increased emphasis on the design of inherently clean and efficient processes. For example, a wide range of pinch analysis and mathematical programming methods have been developed for designing schemes for water reuse/recycle in industrial plants for both grassroot design and plant retrofit. In the latter case, the conventional approach is to maximize water recovery and thereby minimize fresh water demand and effluent volume. However, it is possible that with such an approach the reductions in environmental impact brought about by saving water can be offset by other impacts arising from increased use of energy and materials in the plant after retrofit. This work presents a model for minimizing the total resource consumption impact of a water reuse/recycle network. The total impact is expressed in terms of emergy - a measure of cumulative solar energy inputs into a life cycle system. A simplified model is proposed that focuses on the impact contributions of water, electrical power and material for capital goods. Two case studies illustrate the approach. Results show that the network with the lowest total impact can be found by sacrificing water recovery for savings in energy and material use. (c) 2007 Curtin University of Technology and John Wiley & Sons, Ltd.

关键词： water reuse/recycle networks mixed integer linear programming life cycle emergy

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Parallel-processing VLSI architecture for mixed integer linear programming

Parallel-processing VLSI architecture for mixed integer line...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Hiroki Noguchi Junichi Tani Yusuke Shimai Hiroshi Kawaguchi Masahiko Yoshimoto Kobe University Kobe Japan

This paper describes parallel processor architecture for a mixed integer linear programming (MILP) solver to realize motion planning and hybrid system control in robot applications. It features pipeline architecture with an MILP-specific configuration and two-port SRAM. Based on the architecture, both FPGA and VLSI implementations have been done to solve sample problems including 16 variables. The FPGA implementation can reduce the power consumption to 13 W: an 85.4% reduction compared to a 3.0-GHz processor (Pentium 4; Intel Corp.). The VLSI solver further reduces the power to 6.4 W using 0.18-μm CMOS technology.

关键词： Very large scale integration mixed integer linear programming Field programmable gate arrays CMOS technology Power system planning Motion planning Process planning Motion control Robot control Control systems

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Research on the Optimization of Wind-Solar Energy Storage Systems in Park Microgrids Based on mixed integer linear programming and Monte Carlo Simulation

Research on the Optimization of Wind-Solar Energy Storage Sy...

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Sensors, Electronics and Computer Engineering (ICSECE), IEEE International Conference on

作者： Dongbin Wen Fan Zhang Chengyue Li Peizhi Sheng Huaneng Clean Energy Research Institute Beijing China School of Statistics and Information Shanghai University of International Business and Economics Shanghai China College of Mathematics and Computer Shantou University Shantou China School of Computer and Information Science School of Software Southwest University Chongqing China

ISBN: (数字)9798350373646

ISBN: (纸本)9798350373653

This paper delves into the optimization and economic benefits of wind-solar energy storage systems in park microgrids. By constructing and refining multiple mathematical models, the study provides scientific decision support for system configuration, aiming to meet the increasing demand for load and enhance overall economic benefits. Firstly, the paper proposes the Photovoltaic and Energy Storage Coordination Optimization Model (PCSO-Model), which combines mixed integer linear programming (MILP) with Monte Carlo simulation, effectively reducing the total supply cost of the park. Subsequently, considering the aging effect of energy storage systems, load forecasting errors at different time scales, and the impact of electricity price fluctuations on economic viability, the PCSO model is improved and solved using an improved genetic algorithm. Simulation and optimization results demonstrate that the introduction of energy storage systems reduces costs by approximately 10 % on average, decreases the curtailment of wind and solar power by about 15%, and increases the utilization rate of wind and solar power generation by 20%.

关键词： Wind energy generation Photovoltaic systems Costs Monte Carlo methods Optimization models Microgrids Wind power generation mixed integer linear programming Optimization Energy storage

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A mixed integer linear programming formulation of the dynamic traffic assignment problem

A mixed integer linear programming formulation of the dynami...

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IEEE International Conference on Systems, Man and Cybernetics

作者： D.E. Kaufman J. Nonis R.L. Smith Department of Industrial and Operations Engineering University of Michigan Ann Arbor MI USA

The authors propose a new model for dynamic traffic assignment, modeling the traffic system by a mixed integer linear program solvable in finite time. The model represents link travel times, which must be the same for all vehicles which enter a link together during a single time period by means of 0-1 integer variables. Given the values of these variables, the problem is to assign traffic, modeled as multiperiod multicommodity flow, subject to constraints on capacity implied by the link travel times. An optimal solution to the model gives the vehicle routings corresponding to minimum total travel time, achieving the most efficient use of road capacity. The solution gives unambiguous link travel times as a function of time of entry to the link, suitable for individual route optimization if all but a small priority class of traffic accepts the system-optimal routing.< >

关键词： mixed integer linear programming Dynamic programming Vehicle dynamics Vehicles Traffic control Telecommunication traffic Road transportation Network topology Upper bound Impedance

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