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12th International Conference on Learning and Intelligent Optimization (LION)

作者： Gergel, Victor Barkalov, Konstantin Lebedev, Ilya Lobachevsky State Univ Nizhny Novgorod Nizhnii Novgorod Russia

ISBN: (纸本)9783030053482;9783030053475

In the present paper, the mixed-integer global optimization problems are considered. A novel deterministic algorithm for solving the problems of this class based on the information-statistical approach to solving the continuous global optimization problems has been proposed. The comparison of this algorithm with known analogs demonstrating the efficiency of the developed approach has been conducted. The stable operation of the algorithm was confirmed also by solving a series of several hundred mixed-integer global optimization problems.

关键词： Global optimization Non-convex constraints mixed-integer problems

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Parallel Global Optimization for Non-convex mixed-integer problems 5th

Parallel Global Optimization for Non-convex Mixed-Integer Pr...

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5th Russian Supercomputing Days Conference (RuSCDays)

作者： Barkalov, Konstantin Lebedev, Ilya Lobachevsky State Univ Nizhni Novgorod Nizhnii Novgorod Russia

ISBN: (纸本)9783030365929;9783030365912

The paper considers the mixed-integer global optimization problems. A novel parallel algorithm for solving the problems of this class based on the index algorithm for solving the continuous global optimization problems has been proposed. The comparison of this algorithm with known analogs demonstrates the efficiency of the developed approach. The proposed algorithm allows an efficient parallelization including the employment of the graphics accelerators. The results of performed numerical experiments (solving a series of 100 multiextremal mixedinteger problems) confirm a good speedup of the algorithm with the use of GPU.

关键词： Global optimization Non-convex constraints mixed-integer problems Parallel algorithms

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Parallel Global Search Algorithm with Local Tuning for Solving mixed-integer Global Optimization problems

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2021年第7期42卷 1492-1503页

作者： Barkalov, K. A. Gergel, V. P. Lebedev, I. G. Lobachevskii State Univ Nizhny Novgorod Nizhnii Novgorod 603950 Russia

In this paper, we consider mixed-integer global optimization problems and propose a parallel algorithm for solving problems of this class based on information-statistical approach for solving continuous global optimization problems. Within this algorithm, we suggest using a local tuning scheme based on the assumption that the multiextremality of the discussed problem is weak. We also compare the sequential version of the algorithm with other similar methods. The effectiveness of parallelizing the algorithm has been confirmed by solving a series of mixed-integer global optimization problems on the Lobachevskii supercomputer.

关键词： global optimization non-convex constraints mixed-integer problems local tuning parallel algorithms

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NODE-SCREENING TESTS FOR THE L0-PENALIZED LEAST-SQUARES PROBLEM 47

NODE-SCREENING TESTS FOR THE L0-PENALIZED LEAST-SQUARES PROB...

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47th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Guyard, Theo Herzet, Cedric Elvira, Clement Univ Rennes INSA Rennes CNRS IRMAR UMR 6625 F-35000 Rennes France INRIA Rennes Bretagne Atlantique Campus Beaulieu F-35000 Rennes France Cent Supelec SCEE IETR UMR CNRS 6164 F-35510 Cesson Sevigne France

ISBN: (纸本)9781665405409

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l(0)-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost. Our work leverages the concept of safe screening, well known for sparsity-inducing convex problems, and some recent advances in this field for l(0)-penalized regression problems.

关键词： Sparse approximation mixed-integer problems Branch and bound Safe screening

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An Efficient Surrogate Optimization Method for Solving Linear mixed-integer problems with Cross Coupling Constraints

An Efficient Surrogate Optimization Method for Solving Linea...

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10th World Congress on Intelligent Control and Automation (WCICA)

作者： Bragin, Mikhail A. Luh, Peter B. Yan, Joseph H. Univ Connecticut Dept Elect & Comp Engn Storrs CT 06269 USA Calif Edison Rosemead CA 91770 USA

ISBN: (纸本)9781467313988

Many optimization problems that frequently arise and have been extensively used in practice are modeled as linear mixed integer programming problems. Among the many of such problems are transportation and assignment problems. In such problems, constraints that couple decision variables can be viewed as hyperplanes in their respective spaces. These hyperplanes frequently intersect at different angles thus making the feasible set of the problems complex and leading to difficulties defining the convex hull when using the cutting planes method. The efficiency of branch-and-cut is therefore low, since the branching tree grows quickly due to the combinatorial nature of these problems. This paper overcomes these difficulties by using additional cuts that can better define the convex hull. Thus when the Lagrangian relaxation and surrogate optimization method is used, the computational burden of obtaining the multiplier updating directions is significantly reduced. In the surrogate optimization framework, the constraints of the original problem arc relaxed by introducing the Lagrange multipliers. After a good dual solution is found, it is then improved to obtain a good feasible solution, while the dual value provides a lower bound on the feasible cost. Numerical examples indicate that the surrogate optimization can obtain feasible solutions when the standard branch and cut method cannot. Additional cuts help improve the feasible solutions and tighten the lower bound.

关键词： Lagrangian Relaxation Surrogate Optimization mixed-integer problems Branch-and-Cut Cutting Planes Cross-Coupling Constraints

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Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation 11

Numerical Calculation of Nonsmooth Control Lyapunov Function...

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8th International-Federation-of-Automatic-Control (IFAC) Symposium on Mechatronic Systems (MECHATRONICS) / 11th International-Federation-of-Automatic-Control (IFAC) Symposium on Nonlinear Control Systems (NOLCOS)

作者： Baier, Robert Braun, Philipp Gruene, Lars Kellett, Christopher M. Univ Bayreuth Dept Math D-95440 Bayreuth Germany Univ Newcastle Sch Elect Engn & Comp Callaghan NSW 2308 Australia

We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed-integer) linear program. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： (control) Lyapunov function asymptotic stability controllability switched systems piecewise linear analysis linear programming mixed-integer problems

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An Efficient Surrogate Optimization Method for Solving Linear mixed-integer problems with Cross-Coupling Constraints

An Efficient Surrogate Optimization Method for Solving Linea...

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World Congress on Intelligent Control and Automation

作者： Mikhail A. Bragin Peter B. Luh Joseph H. Yan Department of Electrical and Computer Engineering University of Connecticut California Edison

ISBN: (纸本)9781467313971

Many optimization problems that frequently arise and have been extensively used in practice are modeled as linear mixed-integer programming problems. Among the many of such problems are transportation and assignment problems. In such problems, constraints that couple decision variables can be viewed as hyperplanes in their respective spaces. These hyperplanes frequently intersect at different angles thus making the feasible set of the problems complex and leading to difficulties defining the convex hull when using the cutting planes method. The efficiency of branch-and-cut is therefore low, since the branching tree grows quickly due to the combinatorial nature of these problems. This paper overcomes these difficulties by using additional cuts that can better define the convex hull. Thus when the Lagrangian relaxation and surrogate optimization method is used, the computational burden of obtaining the multiplier updating directions is significantly reduced. In the surrogate optimization framework, the constraints of the original problem are relaxed by introducing the Lagrange multipliers. After a good dual solution is found, it is then improved to obtain a good feasible solution, while the dual value provides a lower bound on the feasible cost. Numerical examples indicate that the surrogate optimization can obtain feasible solutions when the standard branch-and-cut method cannot. Additional cuts help improve the feasible solutions and tighten the lower bound.

关键词： Lagrangian Relaxation Surrogate Optimization mixed-integer problems Branch-and-Cut Cutting Planes Cross-Coupling Constraints

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Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation ⁎

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IFAC-PapersOnLine 2019年第16期52卷 370-375页

作者： Robert Baier Philipp Braun Lars Grüne Christopher M. Kellett University of Bayreuth Department of Mathematics 95440 Bayreuth Germany University of Newcastle School of Electrical Engineering and Computing Callaghan NSW 2308 Australia

关键词： (control) Lyapunov function asymptotic stability controllability switched systems piecewise linear analysis linear programming mixed-integer problems

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Hierarchical Distributed mixed-integer Optimization for Reactive Power Dispatch

Hierarchical Distributed Mixed-Integer Optimization for Reac...

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10th IFAC Symposium on Control of Power and Energy Systems (CPES)

作者： Murray, Alexander Engelmann, Alexander Hagenmeyer, Veit Faulwasser, Timm Karlsruhe Inst Technol Inst Automat & Appl Informat Karlsruhe Germany

One key aspect of power system operation is the minimization of line losses while maintaining voltages within certain limits. Doing so can be achieved through the use of voltage regulators, tap changing transformers, and shunt capacitors. However, both tap changing transformers and/or shunt capacitors are operated in a discrete manner, i.e. the inputs can only take finitely many discrete values. Thus, the problem of minimizing line losses while maintaining voltage stability can be cast as a mixed-integer optimization problem. For large grids or cases where independent entities have concurrent control of the system, distributed optimization provides a solution. The present paper discusses a hierarchically distributed approach;i.e. the problem is partitioned into local subproblems and solved using a mixed-integer extension of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) algorithm. We present results for the IEEE 14- and 30-bus systems and compare them with previous approaches, such as particle swarm optimization and genetic algorithms. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Hierarchical Distributed Optimization mixed-integer problems Optimal Power Flow Reactive Power Dispatch

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A hybrid GA-PSO approach for reliability optimization in redundancy allocation problem

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2013年第1-4期68卷 317-338页

作者： Sheikhalishahi, M. Ebrahimipour, V. Shiri, H. Zaman, H. Jeihoonian, M. Ecole Polytech Montreal Math & Ind Engn Dept Quebec City PQ Canada Univ Tehran Coll Engn Dept Ind Engn Tehran Iran

This paper presents a novel hybrid genetic algorithm (GA)-particle swarm optimization (PSO) approach for reliability redundancy allocation problem (RRAP) in series, series-parallel, and complex (bridge) systems. The proposed approach maximizes overall system reliability while minimizing system cost, system weight and volume, simultaneously, under nonlinear constraints. To meet these objectives, an adaptive hybrid GA-PSO approach is developed to identify the optimal solutions and improve computation efficiency for these NP-hard problems. An illustrative example is applied to show the capability and effectiveness of the proposed approach. According to the results, in all three cases, reliability values are improved. Moreover, computational time and variance are decreased compared to the similar studies. The proposed approach could be helpful for engineers and managers to better understand their system reliability and performance, and also to reach a better configuration.

关键词： Redundancy allocation problem Genetic algorithm Particle swarm optimization Reliability optimization mixed-integer problems

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