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integer programming formulations and computations solving phylogenetic and population genetic problems with missing or genotypic data

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13th Annual international conference on Computing and Combinatorics (COCOON 2007)

作者： Gusfield, Dan Frid, Yelena Brown, Dan Univ Calif Davis Dept Comp Sci Davis CA 95616 USA Univ Waterloo Sch Comp Sci Waterloo ON Canada

ISBN: (纸本)9783540735441

Several central and well-known combinatorial problems in phylogenetics and population genetics have efficient, elegant solutions when the input is complete or consists of haplotype data, but lack efficient solutions when input is either incomplete, consists of genotype data, or is for problems generalized from decision questions to optimization questions. Unfortunately, in biological applications, these harder problems arise very often. Previous research has shown that integer-linear programming can sometimes be used to solve hard problems in practice on a range of data that is realistic for current biological applications. Here, we describe a set of related integer linear programming (ILP) formulations for several additional problems, most of which are known to be NP-hard. these ILP formulations address either the issue of missing data, or solve Haplotype Inference Problems with objective functions that model more complex biological phenomena than previous formulations. these ILP formulations solve efficiently on data whose composition reflects a range of data of current biological interest. We also assess the biological quality of the ILP solutions: some of the problems, although not all, solve with excellent quality. these results give a practical way to solve instances of some central, hard biological problems, and give practical ways to assess how well certain natural objective functions reflect complex biological phenomena. Perl code to generate the ILPs (for input to CPLEX) is on the web at ***/similar to gusfield.

关键词： Gene encoding

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An Exact Rational Mixed-integer programming Solver

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

作者： Cook, William Koch, thorsten Steffy, Daniel E. Wolter, Kati Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Zuse Inst Berlin Berlin Germany

ISBN: (纸本)9783642208072

We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. this allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. the software is incorporated into the SCIP optimization framework, using the exact LP solver QSOPT-EX and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann collections.

关键词： integer programming

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From Approximate to Exact integer programming 1

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24th international conference on integer programming and combinatorial optimization (IPCO)

作者： Dadush, Daniel Eisenbrand, Friedrich Rothvoss, thomas CWI Amsterdam Netherlands Ecole Polytech Fed Lausanne Lausanne Switzerland Univ Washington Seattle WA 98195 USA

ISBN: (数字)9783031327261

ISBN: (纸本)9783031327254;9783031327261

Approximate integer programming is the following: For a given convex body K subset of R-n, either determine whether K boolean AND Z(n) is empty, or find an integer point in the convex body 2 center dot (K - c) + c which is K, scaled by 2 from its center of gravity c. Approximate integer programming can be solved in time 2(O(n)) while the fastest known methods for exact integer programming run in time 2(O(n)) center dot n(n). So far, there are no efficientmethods for integer programming known that are based on approximate integer programming. Our main contribution are two such methods, each yielding novel complexity results. First, we showthat an integer point x * is an element of (K boolean AND Z(n)) can be found in time 2(O(n)), provided that the remainders of each component x(i)* mod l for some arbitrarily fixed l >= 5(n + 1) of x * are given. the algorithm is based on a cutting-plane technique, iteratively halving the volume of the feasible set. the cutting planes are determined via approximate integer programming. Enumeration of the possible remainders gives a 2(O(n))n(n) algorithm for general integer programming. this matches the current best bound of an algorithm by Dadush (2012) that is considerably more involved. Our algorithm also relies on a new asymmetric approximate Caratheodory theorem that might be of interest on its own. Our second method concerns integer programming problems in standard equation form Ax = b, 0 <= x <= u, x is an element of Z(n). Such a problem can be reduced to the solution of Pi(i) O(logu(i) + 1) approximate integer programming problems. this implies, for example that knapsack or subset-sum problems with polynomial variable range 0 <= x(i) <= p(n) can be solved in time (logn)(O(n)). For these problems, the best running time so far was n(n) center dot 2(O(n)).

关键词： integer programming

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integer programming and Combinatoral optimization - 15th international conference, IPCO 2011, Proceedings

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15th international conference on integer programming and combinatorial optimization, IPCO 2011

ISBN: (纸本)9783642208065

the proceedings contain 33 papers. the topics discussed include: an excluded minor characterization of seymour graphs;complexity analyses of bienstock-zuckerberg and lasserre relaxations on the matching and stable set polytopes;a probabilistic analysis of the strength of the split and triangle closures;partial convexification of general MIPs by Dantzig-Wolfe reformulation;lift-and-project cuts for mixed integer convex programs;TSP on cubic and subcubic graphs;approximability of capacitated network design;facility location with client latencies: linear programming based techniques for minimum latency problems;an exact rational mixed-integer programming solver;valid inequalities for the pooling problem with binary variables;design and verify: a new scheme for generating cutting-planes;and contact center scheduling with strict resource requirements.

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Assortment optimization with Visibility Constraints 25th

Assortment Optimization with Visibility Constraints

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25th international conference on integer programming and combinatorial optimization (IPCO)

作者： Barre, theo El Housni, Omar Lodi, Andrea Univ Calif Berkeley IEOR Berkeley CA USA Cornell Univ Cornell Tech ORIE New York NY 10021 USA

ISBN: (纸本)9783031598340;9783031598357

Motivated by applications in e-retail and online advertising, we study the problem of assortment optimization under visibility constraints, referred to as APV. We are given a universe of substitutable products and a stream of T customers. the objective is to determine the optimal assortment of products to offer to each customer in order to maximize the total expected revenue, subject to the constraint that each product is required to be shown to a minimum number of customers. the minimum display requirement for each product is given exogenously and we refer to these constraints as visibility constraints. We assume that customer choices follow a Multinomial Logit model. We provide a characterization of the structure of the optimal assortments and present an efficient polynomial time algorithm for solving APV. To accomplish this, we introduce a novel function called the "expanded revenue" of an assortment and establish its supermodularity. Our algorithm takes advantage of this structural property. Additionally, we demonstrate that APV can be formulated as a compact linear program. Finally, we propose a novel, fair strategy for pricing the revenue loss due to the enforcement of visibility constraints.

关键词： Assortment optimization Supermodularity Algorithm Design Multinomial Logit model Visibility Constraints

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Budgeted Data Caching based on k-Median in Mobile Edge Computing 13

Budgeted Data Caching based on k-Median in Mobile Edge Compu...

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13th IEEE international conference on Services Computing (SCC) / 13th IEEE international conference on Web Services (ICWS)

作者： Xia, Xiaoyu Chen, Feifei Cui, Guangming Abdelrazek, Mohamed Grundy, John Jin, Hai He, Qiang Deakin Univ Sch Informat Technol Geelong Vic Australia Swinburne Univ Technol Sch Software & Elect Engn Hawthorn Vic Australia Monash Univ Fac Informat Technol Clayton Vic Australia Huazhong Univ Sci & Technol Sch Comp Sci & Technol Wuhan Hubei Peoples R China Chengdu Univ Informat Technol Sch Software Engn Chengdu Sichuan Peoples R China

ISBN: (纸本)9781728187860

In mobile edge computing (MEC), edge servers are deployed at base stations to provide highly accessible computational resources and storage capacities to nearby mobile devices. Caching data on edge servers can ensure the service quality and network latency for those mobile devices. However, an app vendor needs to ensure that the data caching cost does not exceed its data caching budget. In this paper, we present the budgeted edge data caching (BEDC) problem as a constrained optimization problem to maximize the overall reduction in data retrieval for all its app users within the budget, and prove that it is NP-hard. then, we provide an approach named IP-BEDC for solving the BEDC problem optimally based on integer programming. We also provide an O(k)-approximation algorithm, namely alpha-BEDC, to find near-optimal solutions to the BEDC problems efficiently. Our proposed approaches are evaluated on a real-world data set and a synthesized data set. the results demonstrate that our approaches can solve the BEDC problem effectively and efficiently while significantly outperforming five representative approaches.

关键词： mobile edge computing data caching low-latency services optimization approximation algorithm

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On the Chvatal rank of certain inequalities 1

引用

7th international conference on integer programming and combinatorial optimization (IPCO VII)

作者： Hartmann, M Queyranne, M Wang, YG Univ N Carolina Chapel Hill NC 27599 USA Univ British Columbia Vancouver BC V6T 1Z2 Canada PeopleSoft Inc San Mateo CA 94404 USA

ISBN: (数字)9783540487777

ISBN: (纸本)3540660194

the Chvatal rank of an inequality ax less than or equal to b with integral components and valid for the integral hull of a polyhedron P, is the minimum number of rounds of Gomory-Chvatal cutting planes needed to obtain the given inequality. the Chvatal rank is st most one if b is the integral part of the optimum value z(a) of the linear program max{ax : x is an element of P}. We show that, contrary to what was stated or implied by other authors, the converse to the latter statement, namely, the Chvatal rank is at least two if b is less than the integral part of z(a), is not true in general. We establish simple conditions for which this implication is valid, and apply these conditions to several classes of facet-inducing inequalities for travelling salesman polytopes.

关键词： Linear programming

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Valid Inequalities for Separable Concave Constraints with Indicator Variables 18th

Valid Inequalities for Separable Concave Constraints with In...

引用

18th international conference on integer programming and combinatorial optimization (IPCO)

作者： Lim, Cong Han Linderoth, Jeff Luedtke, James Univ Wisconsin Dept Comp Sci 1210 W Dayton St Madison WI 53706 USA Univ Wisconsin Dept Ind & Syst Engn Madison WI USA

ISBN: (纸本)9783319334615;9783319334608

We study valid inequalities for a set relevant for optimization models that have both binary indicator variables, which indicate positivity of associated continuous variables, and separable concave constraints. Such models reduce to a mixed-integer linear program (MILP) when the concave constraints are ignored, and to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms to solve such problems to global optimality, relaxations are traditionally obtained by using valid inequalities for the MILP ignoring the concave constraints, and by independently relaxing each concave constraint using the secant obtained from the bounds of the associated variable. We propose a technique to obtain valid inequalities that are based on both the MILP and the concave constraints. We begin by analyzing a low-dimensional set that contains a single binary indicator variable, a single concave constraint, and three continuous variables. Using this analysis, for the canonical Single Node Flow Set (SNFS), we demonstrate how to "tilt" a given valid inequality for the SNFS to obtain additional valid inequalities that account for separable concave functions of the arc flows. We present computational results demonstrating the utility of the new inequalities on a fixed plus concave cost transportation problem. To our knowledge, this is one of the first works that simultaneously convexifies both nonconvex functions and binary variables to strengthen the relaxations of practical mixed integer nonlinear programs.

关键词： Mixed integer nonlinear programming Global optimization Valid inequalities

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Application of Aircraft Interval Management Concepts based on the Optimized Scheduling Algorithm

Application of Aircraft Interval Management Concepts based o...

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13th international conference on Control, Automation and Systems (ICCAS)

作者： Song, Jae-Hoon Ryu, Min-Seok Choi, Seongim Korea Aerosp Res Inst Aviat Safety R&D Ctr Taejon South Korea Korea Adv Inst Sci & Technol Dept Aerosp Engn Taejon South Korea

ISBN: (纸本)9788993215052

the main purpose of this paper is to understand the multi-directional performance metrics including the efficiency of airspace usage and aircraft scheduling performance, which should be balanced when the advanced Interval Management (IM) concepts are applied to the practical demand set of flights which composed of different aircraft classes. To improve the scheduling performance, the optimization-based scheduling planner is utilized and predicts the optimum Scheduled Times of Arrival (STAs) at the pre-defined scheduling points in a given route structure. the scheduling planner is integrated in a dynamic planner by interacting with the real-time simulation algorithm to emulate the flight time advancement in a series of update cycles until all aircraft arrive at the runways. the real-time simulation produces the Actual Times of Arrival (ATAs) in consideration of the uncertainties during flight, and the computed ATAs become the initial conditions of the scheduling planner for the next cycle. Combined with the various IM concepts, the dynamic planner computes the relative efficiency of the flight scenarios that have different IM strategies corresponding to the level of equipage of the aircraft.

关键词： Interval Management(IM) Automatic Dependent Surveillance - Broadcast (ADS-B) Ground based Interval Management for Spacing (GIM-S) Flight-deck based Interval Management for Spacing (FIM-S) Mixed integer Linear programming (MILP) discrete optimization

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Constraint programming and Mixed integer Linear programming for Rescheduling Trains under Disrupted Operations A Comparative Analysis of Models, Solution Methods, and their Integration

Constraint Programming and Mixed Integer Linear Programming ...

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6th international conference Integration of AI and OR Techniques in Constraint programming for Combinatial optimization Problems

作者： Acuna-Agost, Rodrigo Michelon, Philippe Feillet, Dominique Gueye, Serigne Univ Avignon & Pays Vaucluse LIA F-84911 Avignon France Ecole Mines Saint Etienne F-13541 Gardenne France Lab Math Appl Havre F-76058 Le Havre France

ISBN: (纸本)9783642019289

the problem of rescheduling trains under disrupted operations has received more attention in the last years because of the increasing demand in railway transportation. Railway networks are more and more saturated and the probability that delayed trains affect others is large. therefore, it is very important to react after incidents by recalculating new arrival/departure times and reassigning tracks/platforms with the aim of minimizing the effect of propagation of incidents. © 2009 Springer Berlin Heidelberg.

关键词： Railroads

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