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Linear programming Using Limited-Precision Oracles 20th

Linear Programming Using Limited-Precision Oracles

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20th international conference on integer programming and combinatorial optimization (IPCO)

作者： Gleixner, Ambros Steffy, Daniel E. Konrad Zuse Zentrum Informat Tech Berlin Takustr 7 D-14195 Berlin Germany Oakland Univ Math & Stat Rochester MI 48063 USA

ISBN: (纸本)9783030179533;9783030179526

Linear programming is a foundational tool for many aspects of integer and combinatorial optimization. this work studies the complexity of solving linear programs exactly over the rational numbers through use of an oracle capable of returning limited-precision LP solutions. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. Previous work has often considered oracles that provide solutions of an arbitrary specified precision. While this leads to polynomial-time algorithms, the level of precision required is often unrealistic for practical computation. In contrast, our work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.

关键词： Linear programming Oracle complexity Diophantine approximation Exact solutions Symbolic computation Rational arithmetic Extended-precision arithmetic Iterative refinement

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A Novel Approach for Solving Large-Scale Bike Sharing Station Planning Problems 1

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13th international conference on Learning and Intelligent optimization (LION)

作者： Kloimuellner, Christian Raidl, Guenther R. TU Wien Inst Log & Computat Favoritenstr 9-11-19201 A-1040 Vienna Austria

ISBN: (数字)9783030386290

ISBN: (纸本)9783030386290;9783030386283

In large cities all around the world, individual and motorized traffic is still prevalent. this circumstance compromises the quality of living, and moreover, space inside cities for parking individual vehicles for movement is scarce and is becoming even scarcer. thus, the need for a greener means of transportation and less individual vehicles inside the cities is demanded and rising. An already accepted and established solution possibility to these problems are public bike sharing systems (PBS). Such systems are often freely available to people for commuting within the city and utilize the available space in the city more efficiently than individual vehicles. When building or extending a PBS, a certain optimization goal is to place stations inside a city or a part of it, such that the number of bike trips per time unit is maximized under certain budget constraints. In this context, it is also important to consider rebalancing and maintenance costs as they introduce substantial supplementary costs in addition to the fixed and variable costs when building or extending a PBS. In contrast to the literature, this work introduces a novel approach which is particularly designed to scale well to large real-world instances. Based on our previous work, we propose a multilevel refinement heuristic operating on hierarchically clustered input data. this way, the problem is coarsened until a manageable input size is reached, a solution is derived, and then step by step extended and refined until a valid solution for the whole original problem instance is obtained. As an enhancement to our previous work, we introduce the following extensions. Instead of considering an arbitrary integral number of slots for stations, we now use sets of predefined station configurations. Moreover, a local search is implemented as refinement step in the multilevel refinement heuristic and we now consider real-world input data for the city of Vienna.

关键词： Bike-Sharing Station Planning Problem Multilevel refinement Facility location problem Mixed integer linear programming

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A Gas Lift optimization System with Variable Choke and Action Constraints 13

A Gas Lift Optimization System with Variable Choke and Actio...

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13th Annual IEEE international Systems conference (SysCon)

作者： Harris, Matthew W. Memarzadeh, Mahsa Swanberg, Cassandra El-Bakry, Amr ExxonMobil Upstream Res Co Spring TX 77389 USA

ISBN: (纸本)9781538683965

Gas lift systems are multi-scale industrial systems involving downhole actuators, surface equipment, processing facilities, and control systems connecting them. Gas lifting oil wells works by injecting high pressure gas into the flow stream, decreasing bottom-hole pressure, and increasing oil flow to the surface. From there, fluids move through pipelines, separators, compressors, and other components in the facility. If the gas available for injection is insufficient to optimize every well, then the available gas needs to be optimally allocated to maximize field production - this is the gas lift optimization problem. this paper proposes a mixed-integer linear programming formulation using gas injection and wellhead choke as optimization variables. Surrogate well performance and choke models are piecewise linear. New constraints called action constraints and an enumeration procedure are introduced to make the solutions more easily implemented in the field. Recently published precedence constraints are also included. Numerical results demonstrate the efficacy of this approach, which has been successfully implemented in the field.

关键词： Gas lift system optimization allocation

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Genetic Algorithm for Multi-choice integer Linear programming Problems 7th

Genetic Algorithm for Multi-choice Integer Linear Programmin...

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international conference on Soft Computing for Problem Solving (SocProS)

作者： Mohanty, D. K. Jana, R. K. Biswal, M. P. Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India Indian Inst Management Raipur GEC Campus Sejbahar 492015 India

ISBN: (纸本)9789811315923;9789811315916

Genetic algorithms (GAs) are very powerful techniques to solve difficult combinatorial optimization problems. Multi-choice programming (MCP) belongs to a class of combinatorial optimization problems where the decision maker (DM) has to choose a value from a number of alternative choices and to find a combination which optimizes an objective function subject to a given set of constraints. In many of the real-life optimization problems, the solution of some problems cannot be fractions and must be specified as integers, and solving of such types of problems is called integer programming (IP). In this paper, a genetic algorithm (GA) for nonlinear integer programming (NLIP) to solve a multi-choice integer linear programming (MCILP) problem is proposed. Here, we consider an MCILP problem where some or all right-hand side parameters of the constraints may have multiple choices. the multi-choice parameters in the problem are handled using the interpolating polynomials. After constituting interpolating polynomials corresponding to all multi-choice parameters, an NLIP model is formulated. Using our proposed GA, optimal integer solution of the NLIP model is obtained. Lastly, some illustrative examples are presented to support the solution procedure.

关键词： Genetic algorithms

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A class of linear programs solvable by coordinate-wise minimization 1

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14th international conference on Learning and Intelligent optimization, LION 2020

作者： Dlask, Tomáš Werner, Tomáš Faculty of Electrical Engineering Czech Technical University in Prague Prague Czech Republic

ISBN: (数字)9783030535520

ISBN: (纸本)9783030535513

Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable and/or constrained) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise minimization solves exactly. We show that dual LP relaxations of several well-known combinatorial optimization problems are in this class and the method finds a global minimum with sufficient accuracy in reasonable runtimes. Moreover, for extensions of these problems that no longer are in this class the method yields reasonably good suboptima. though the presented LP relaxations can be solved by more efficient methods (such as max-flow), our results are theoretically non-trivial and can lead to new large-scale optimization algorithms in the future. © Springer Nature Switzerland AG 2020.

关键词： Linear programming

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A Bundle Approach for SDPs with Exact Subgraph Constraints 1

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20th international conference on integer programming and combinatorial optimization (IPCO)

作者： Gaar, Elisabeth Rendl, Franz Alpen Adria Univ Klagenfurt Inst Math Univ Str 65-67 A-9020 Klagenfurt Austria

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

the 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties. We suggest a partial Lagrangian dual, and exploit the fact that its evaluation decomposes into two independent subproblems. this opens the way to use the bundle method from non-smooth optimization to minimize the dual function. Computational experiments on the Max-Cut, stable set and coloring problem show the efficiency of this approach.

关键词： Semidefinite programming Relaxation hierarchy Max-Cut Stable set Coloring

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A New Contraction Technique with Applications to Congruency-Constrained Cuts 20th

A New Contraction Technique with Applications to Congruency-...

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20th international conference on integer programming and combinatorial optimization (IPCO)

作者： Nagele, Martin Zenklusen, Rico Swiss Fed Inst Technol Dept Math Zurich Switzerland

ISBN: (纸本)9783030179533;9783030179526

Minimum cut problems are among the most classical problems in combinatorial optimization and are used in a wide set of applications. Some of the best-known efficiently solvable variants include global minimum cuts, minimum s-t cuts, and minimum odd cuts in undirected graphs. We study a problem class that can be seen to generalize the above variants, namely finding congruency-constrained minimum cuts, i.e., we consider cuts whose number of vertices is congruent to r modulo m, for some integers r and m. Apart from being a natural generalization of odd cuts, congruency-constrained minimum cuts exhibit an interesting link to a long-standing open problem in integer programming, namely whether integer programs described by an integer constraint matrix with bounded subdeterminants can be solved efficiently. We develop a new contraction technique inspired by Karger's celebrated contraction algorithm for minimum cuts, that, together with further insights, leads to a polynomial time randomized approximation scheme for congruency-constrained minimum cuts for any constant modulus m. Instead of contracting edges of the original graph, we use splitting-off techniques to create an auxiliary graph on a smaller vertex set, which is used for performing random edge contractions. this way, a well-structured distribution of candidate pairs of vertices to be contracted is obtained, where the involved pairs are generally not connected by an edge. As a byproduct, our technique reveals new structural insights into near-minimum odd cuts, and, more generally, near-minimum congruency-constrained cuts.

关键词： integer programming

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Strong Mixed-integer programming Formulations for Trained Neural Networks 1

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20th international conference on integer programming and combinatorial optimization (IPCO)

作者： Anderson, Ross Huchette, Joey Tjandraatmadja, Christian Vielma, Juan Pablo Google Res Cambridge MA 02142 USA MIT Cambridge MA 02139 USA

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the input and output variables of the ReLU. We contrast it with an ideal "extended" formulation with a linear number of additional continuous variables, derived through standard techniques. An apparent drawback of our formulation is that it requires an exponential number of inequality constraints, but we provide a routine to separate the inequalities in linear time. We also prove that these exponentially-many constraints are facet-defining under mild conditions. Finally, we study network verification problems and observe that dynamically separating from the exponential inequalities (1) is much more computationally efficient and scalable than the extended formulation, (2) decreases the solve time of a state-of-the-art MIP solver by a factor of 7 on smaller instances, and (3) nearly matches the dual bounds of a state-of-the-art MIP solver on harder instances, after just a few rounds of separation and in orders of magnitude less time.

关键词： Mixed-integer programming Formulations Deep learning

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Real-Time Navigation in Urban Areas Using Mobile Crowd-Sourced Data 13

Real-Time Navigation in Urban Areas Using Mobile Crowd-Sourc...

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13th Annual IEEE international Systems conference (SysCon)

作者： Wan, Xiangpeng Ghazzai, Hakim Massoud, Yehia Stevens Inst Technol Sch Syst & Enterprises Hoboken NJ 07030 USA

ISBN: (纸本)9781538683965

Modern urbanization is demanding smarter technologies to improve a variety of applications in intelligent transportation systems (ITS). Mobile crowd-sourcing enabling automatic sensing tasks constitutes an excellent mean to complement existing technologies. In this paper, we exploit the high amount of data that can be collected by on-board and infrastructure-based sensors to evaluate traffic network statuses and improve the navigation of vehicles in urban areas. the objective is to design real-time route planning algorithms that determine best trajectories in a real-time manner based on the frequent data inputs. Two iterative algorithms with different complexity levels solving integer linear programming problems are developed. Unlike traditional navigation solutions, the algorithms update the vehicle trajectory after a certain period characterized by timely correlated data. Our results show that the crowd-sourcing based real-time algorithms outperform traditional navigation solutions by selecting less congested roads and avoiding blocked streets.

关键词： Intelligent transportation systems mobile crowd-sourcing optimization real-time navigation

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Intersection Cuts for Polynomial optimization 1

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20th international conference on integer programming and combinatorial optimization (IPCO)

作者： Bienstock, Daniel Chen, Chen Munoz, Gonzalo Columbia Univ IEOR New York NY USA Ohio State Univ ISE Columbus OH 43210 USA Polytech Montreal Montreal PQ Canada

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

We consider dynamically generating linear constraints (cutting planes) to tighten relaxations for polynomial optimization problems. Many optimization problems have feasible set of the form S boolean AND P, where S is a closed set and P is a polyhedron. integer programs are in this class and one can construct intersection cuts using convex "forbidden" regions, or S-free sets. Here, we observe that polynomial optimization problems can also be represented as a problem with linear objective function over such a feasible set, where S is the set of real, symmetric matrices representable as outer-products of the form xx(T). Accordingly, we study outer-product-free sets and develop a thorough characterization of several (inclusion-wise) maximal intersection cut families. In addition, we present a cutting plane approach that guarantees polynomial-time separation of an extreme point in P \ S using our outer-product-free sets. Computational experiments demonstrate the promise of our approach from the point of view of strength and speed.

关键词： integer programming

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