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Dead-End Elimination for Weighted CSP

Dead-End Elimination for Weighted CSP

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19th Annual international conference on Principles and Practice of Constraint programming (CP)

作者： de Givry, Simon Prestwich, Steven D. O'Sullivan, Barry INRA UR 875 MIA T F-31320 Castanet Tolosan France Univ Coll Cork Cork Constraint Computat Ctr Cork Ireland

ISBN: (纸本)9783642406263;9783642406270

Soft neighborhood substitutability (SNS) is a powerful technique to automatically detect and prune dominated solutions in combinatorial optimization. Recently, it has been shown in [26] that enforcing partial SNS (PSNSr) during search can be worthwhile in the context of Weighted Constraint Satisfaction Problems (WCSP). However, for some problems, especially with large domains, PSNSr is still too costly to enforce due to its worst-case time complexity in O(ned(4)) for binary WCSP. We present a simplified dominance breaking constraint, called restricted dead-end elimination (DEEr), the worst-case time complexity of which is in O(ned(2)). Dead-end elimination was introduced in the context of computational biology as a preprocessing technique to reduce the search space [13, 14, 16, 17, 28, 30]. Our restriction involves testing only one pair of values per variable instead of all the pairs, with the possibility to prune several values at the same time. We further improve the original dead-end elimination criterion, keeping the same time and space complexity as DEEr. Our results show that maintaining DEEr during a depth-first branch and bound (DFBB) search is often faster than maintaining PSNSr and always faster than or similar to DFBB alone.

关键词： combinatorial optimization dominance rule weighted constraint satisfaction problem soft neighborhood substitutability

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A polyhedral study of the cardinality constrained knapsack problem

A polyhedral study of the cardinality constrained knapsack p...

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9th international conference on integer programming and combinatorial optimization, IPCO 2002

作者： De Farias Jr., Ismael R. Nemhauser, George L. CORE 34 Voie du Roman Pays 1348 Louvain-la-Neuve Belgium School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta GA 30332 United States

ISBN: (纸本)9783540478676

A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. this structure occurs, for example, in areas such as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous and the 0-1 variables. We use an alternative approach, in which we keep in the model only the continuous variables, and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities valid for the convex hull of the feasible set in the space of the continuous variables. To derive the valid inequalities, we extend the concepts of cover and cover inequality, commonly used in 0-1 programming, to this class of problems, and we show how cover inequalities can be lifted to derive facet-defining inequalities. We present three families of non-trivial facet-defining inequalities that are lifted cover inequalities. Finally, we report computational results that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0-1 variables over the traditional MIP approach for this class of problems. © 2002 Springer-Verlag Berlin Heidelberg.

关键词： combinatorial optimization

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Communication-conscious mapping of regular nested loop programs onto massively parallel processor arrays

Communication-conscious mapping of regular nested loop progr...

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18th IASTED international conference on Parallel and Distributed Computing and Systems

作者： Siegel, Sebastian Merker, Renate Hannig, Frank Teich, Juergen Tech Univ Dresden Inst Circuits & Syst D-01062 Dresden Germany Univ Erlangen Nurnberg Dept Comp Sci 12 D-91058 Erlangen Germany

ISBN: (纸本)9780889866386

Methods for an efficient mapping of algorithms to parallel architectures are of utmost importance because many state-of-the-art embedded digital systems deploy parallelism to increase their computational power. this paper deals with the mapping of loop programs onto processor arrays implemented in an FPGA or available as (reconfigurable) coarsegrained processor architectures. Most existing work is closely related to approaches from the DSP domain and is not able to exploit the full parallelism of a given algorithm and the computational potential of a typical 2-dimensional array. In contrast, we present a mapping methodology which incorporates many important parameters of the target architecture in one approach. these are: number of processing elements, resources of the data path and memory within a processing element, and interconnection within the processor array. Based on these parameters, we formulate an optimization problem whose solution specifies an efficient mapping of an algorithm to the target architecture. We can optimize for speed of the algorithm and/or hardware cost caused by the communication and computation resources of the architecture.

关键词： processor array interconnection data path hardware mapping integer linear programming

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the semidefinite relaxation of the κ-partition polytope is strong

The semidefinite relaxation of the κ-partition polytope is ...

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9th international conference on integer programming and combinatorial optimization, IPCO 2002

作者： Eisenblätter, Andreas Takustr. 7 D-14195 Berlin Germany

ISBN: (纸本)9783540478676

Radio frequency bandwidth has become a very scarce resource. this holds true in particular for the popular mobile communication system GSM. Carefully planning the use of the available frequencies is thus of great importance to GSM network operators. Heuristic optimization methods for this task are known, which produce frequency plans causing only moderate amounts of disturbing interference in many typical situations. In order to thoroughly assess the quality of the plans, however, lower bounds on the unavoidable interference are in demand. the results obtained so far using linear programming and graph theoretic arguments do not suffice. By far the best lower bounds are currently obtained from semidefinite programming. the link between semidefinite programming and the bound on unavoidable interference in frequency planning is the semidefinite relaxation of the graph minimum κ-partition problem. Here, we take first steps to explain the surprising strength of the semidefinite relaxation. this bases on a study of the solution set of the semidefinite relaxation in relation to the circumscribed κ-partition polytope. Our focus is on the huge class of hypermetric inequalities, which are valid and in many cases facet-defining for the κ-partition polytope. We show that a "slightly shifted version" of the hypermetric inequalities is implicit to the semidefinite relaxation. In particular, no feasible point for the semidefinite relaxation violates any of the facet-defining triangle inequalities for the κ-partition polytope by more than √2 - 1 or any of the (exponentially many) facet-defining clique constraints by 1/2 or more. © 2002 Springer-Verlag Berlin Heidelberg.

关键词： Linear programming

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9th international conference on Machine Learning, optimization, and Data Science, LOD 2023

9th International Conference on Machine Learning, Optimizati...

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9th international conference on Machine Learning, optimization, and Data Science, LOD 2023

ISBN: (纸本)9783031539688

the proceedings contain 34 papers. the special focus in this conference is on Machine Learning, optimization, and Data Science. the topics include: Alternating Mixed-integer programming and Neural Network Training for Approximating Stochastic Two-Stage Problems;heaviest and Densest Subgraph Computation for Binary Classification. A Case Study;SMBOX: A Scalable and Efficient Method for Sequential Model-Based Parameter optimization;accelerated Graph Integration with Approximation of Combining Parameters;improving Reinforcement Learning Efficiency with Auxiliary Tasks in Non-visual Environments: A Comparison;a Hybrid Steady-State Genetic Algorithm for the Minimum Conflict Spanning Tree Problem;reinforcement Learning for Multi-Neighborhood Local Search in combinatorial optimization;evaluation of Selected Autoencoders in the Context of End-User Experience Management;application of Multi-agent Reinforcement Learning to the Dynamic Scheduling Problem in Manufacturing Systems;solving Mixed Influence Diagrams by Reinforcement Learning;exploring Image Transformations with Diffusion Models: A Survey of Applications and Implementation Code;multi-scale Heat Kernel Graph Network for Graph Classification;PROS-C: Accelerating Random Orthogonal Search for Global optimization Using Crossover;a Multiclass Robust Twin Parametric Margin Support Vector Machine with an Application to Vehicles Emissions;LSTM Noise Robustness: A Case Study for Heavy Vehicles;ensemble Clustering for Boundary Detection in High-Dimensional Data;learning Graph Configuration Spaces with Graph Embedding in Engineering Domains;towards an Interpretable Functional Image-Based Classifier: Dimensionality Reduction of High-Density Diffuse Optical Tomography Data;on Ensemble Learning for Mental Workload Classification;decision-Making over Compact Preference Structures;user-Like Bots for Cognitive Automation: A Survey;geolocation Risk Scores for Credit Scoring Models;On Channel Selection for EEG-Based Mental Workload Clas

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Facility Location with Client Latencies: Linear programming Based Techniques for Minimum Latency Problems

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15th international conference on integer programming and combinatorial optimization (IPCO)

作者： Chakrabarty, Deeparnab Swamy, Chaitanya Univ Penn Deptartment CIS Philadelphia PA 19104 USA Univ Waterloo Combinator & Optimizat Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9783642208072

We introduce a problem that is a common generalization of the uncapacitated facility location and minimum latency (ML) problems, where facilities need to be opened to serve clients and also need to be sequentially activated before they can provide service. Formally, we are given a set F of n facilities with facility-opening costs f(i), a set D of m clients, connection costs c(ij) specifying the cost of assigning a client j to a facility i, a root node r denoting the depot, and a time metric d on F.{r}. Our goal is to open a subset F of facilities, find a path P starting at r and spanning F to activate the open facilities, and connect each client j to a facility phi(j) epsilon F, so as to minimize Sigma(i epsilon F) f(i) + Sigma(j epsilon D)(c(phi(j)),(j) + t(j)), where t(j) is the time taken to reach phi(j) along path P. We call this the minimum latency uncapacitated facility location (MLUFL) problem. Our main result is an O(log n . max(log n, logm))-approximation for MLUFL. We also show that any improvement in this approximation guarantee, implies an improvement in the (current-best) approximation factor for group Steiner tree. We obtain constant approximations for two natural special cases of the problem: (a) related MLUFL (metric connection costs that are a scalar multiple of the time metric);(b) metric uniform MLUFL (metric connection costs, uniform time-metric). Our LP-based methods are versatile and easily adapted to yield approximation guarantees for MLUFL in various more general settings, such as (i) when the latency-cost of a client is a function of the delay faced by the facility to which it is connected;and (ii) the k-route version, where k vehicles are routed in parallel to activate the open facilities. Our LP-based understanding of MLUFL also offers some LP-based insights into ML, which we believe is a promising direction for obtaining improvements for ML.

关键词： Location

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24th international Workshop on Graph-theoretic Concepts in Computer Science, WG 1998

24th International Workshop on Graph-Theoretic Concepts in C...

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5th international conference integer programming and combinatorial optimization, IPCO 1996

ISBN: (纸本)3540613102

the proceedings contain 30 papers. the special focus in this conference is on Graph-theoretic Concepts in Computer Science. the topics include: Linear time solvable optimization problems on graphs of bounded clique width;minus domination in small-degree graphs;the vertex-disjoint triangles problem;communication in the two-way listen-in vertex-disjoint paths mode;broadcasting on anonymous unoriented tori;families of graphs having broadcasting and gossiping properties;optical all-to-all communication in inflated networks;a generalization of AT-free graphs and a generic algorithm for solving treewidth, minimum fill-in and vertex ranking;a polynomial-time algorithm for finding total colorings of partial k-trees;rankings of directed graphs;triangles in euclidean arrangements;internally typed second-orderterm graphs;compact implicit representation of graphs;graphs with bounded induced distance;diameter determination on restricted graph families;independent tree spanners;upgrading bottleneck constrained forests;edge forwarding index and hamiltonian decomposition;improved compressions of cube-connected cycles networks;efficient embeddings of grids into grids;integral uniform flows in symmetric networks;splitting number is NP-complete;tree spanners in planar graphs;a linear-time algorithm to find four independent spanning trees in four-connected planar graphs;linear algorithms for a k-partition problem of planar graphs without specifying bases;domination and steiner tree problems on graphs with few P4s;minimum fill-in and treewidth for graphs modularly decomposable into chordal graphs;interval completion with the smallest max-degree and an estimate of the tree-width of a planar graph which has not a given planar grid as a minor.

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Target Coverage with Minimum Number of Camera Sensors 1

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15th Annual international conference on combinatorial optimization and Applications (COCOA)

作者： Yao, Pei Guo, Longkun Li, Shuangjuan Peng, Huihong Fuzhou Univ Fuzhou Peoples R China South China Agr Univ Guangzhou Peoples R China

ISBN: (数字)9783030926816

ISBN: (纸本)9783030926816;9783030926809

With the development of the smart city, camera sensors have attracted more and more research interests from both academic researchers and industrial engineers. Given a set of points of interests (POI) and a set of cameras, practical applications require to deploy these cameras with the minimum cost so that these POIs can be fully covered by these cameras. In this paper, we study a problem called Min-Num LTC-CS, which is, given a set of POIs located on a line segment and a set of cameras distributed on the plane, to choose a minimum number of cameras so that these POIs can be fully covered by the sensing ranges of these cameras. We first propose a grouping algorithm by grouping the POIs according to whether they can be covered by the same camera with certain rotation angle and then construct a graph using these POI groups. We show that there exists a feasible constrained st-flow if and only if there exists a subset of cameras that can completely cover these POIs. then we propose an LP formulation for the constrained flow problem and prove that any basic solution of the LP formulation is integral, which consequently leads to an optimal solution to Min-Num LTC-CS by solving this LP formulation. Lastly, extensive numerical experiments are conducted to demonstrate the practical performance of our algorithms.

关键词： Camera sensor network Constrained flow Linear programming integer optimal solution

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Distributed Lagrangian Relaxation Protocol for the Over-constrained Generalized Mutual Assignment Problem

Distributed Lagrangian Relaxation Protocol for the Over-cons...

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14th international conference on Agents in Principles and Agents in Practice

作者： Hanada, Kenta Hirayama, Katsutoshi Kobe Univ Higashinada Ku Kobe Hyogo 6580022 Japan

ISBN: (纸本)9783642250439

the Generalized Mutual Assignment Problem (GMAP) is a distributed combinatorial optimization problem in which, with no centralized control, multiple agents search for an optimal assignment of goods that satisfies their individual knapsack constraints. Previously, in the GMAP protocol, problem instances were assumed to be feasible, meaning that the total capacities of the agents were large enough to assign the goods. However, this assumption may not be realistic in some situations. In this paper, we present two methods for dealing with such "over-constrained" GMAP instances. First, we introduce a disposal agent who has an unlimited capacity and is in charge of the unassigned goods. With this method, we can use any off-the-shelf GMAP protocol since the disposal agent can make the instances feasible. Second, we formulate the GMAP instances as an integer programming (IP) problem, in which the assignment constraints are described with inequalities. With this method, we need to devise a new protocol for such a formulation. We experimentally compared these two methods on the variants of Generalized Assignment Problem (GAP) benchmark instances. Our results indicate that the first method finds a solution faster for fewer over-constrained instances, and the second finds a better solution faster for more over-constrained instances.

关键词： generalized mutual assignment problem distributed optimization Lagrangian relaxation

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9th international conference on Machine Learning, optimization, and Data Science, LOD 2023

9th International Conference on Machine Learning, Optimizati...

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9th international conference on Machine Learning, optimization, and Data Science, LOD 2023

ISBN: (纸本)9783031539657

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