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12th International Symposium on Imprecise Probabilities - Theories and Applications (ISIPTA)

作者： Nakharutai, Nawapon Troffaes, Matthias C. M. Chiang Mai Univ Fac Sci Dept Stat Chiang Mai Thailand Univ Durham Dept Math Sci Durham England

We propose two improved algorithms for evaluating the Hurwicz criterion in the context of decision making with lower previsions, along with a new benchmarking algorithm for measuring these improvements. The Hurwicz criterion is a well-known criterion for decision making with lower previsions under severe uncertainty when decision makers want to balance between pessimistic and optimistic extremes. When the domain of the lower prevision, the set of possible outcomes and the set of possible decisions are all finite, the classic method for applying this criterion goes by solving a sequence of linear programs. We show how to improve this classic algorithm, based on similar improvements that we have proposed for other decision criteria. Additionally, to allow benchmarking these improvements, we provide a new algorithm for randomly generating artificial decision problems with a set number of Hurwicz gambles. In our simulation, our proposed algorithms for Hurwicz outperform the standard algorithm in most scenarios except when the set of outcomes is small, the domain of the lower prevision is large, and there are many Hurwicz optimal decisions at once, in which case our proposed algorithms are slightly slower.

关键词： lower prevision decision Hurwicz algorithm primal-dual method linear program

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Assessment of two optimisation methods for renewable energy capacity expansion planning

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APPLIED ENERGY 2022年第PartA期306卷 117988-117988页

作者： Keck, Felix Juette, Silke Lenzen, Manfred Li, Mengyu Univ Sydney Sch Phys A28 ISA Sydney NSW 2006 Australia IU Int Univ Appl Sci Bad Honnef Germany

When deciding on a country's future energy policy, it is essential to accurately estimate the future generation mix and technology costs, as well as future generation site locations in electricity power grids. This estimate needs to allow for changing levels of demand and increasing levels of renewable energy supply, with both having high fluctuations geographically and temporally. This objective leads to high-dimensional mathematical models with high computational complexity that cannot be solved analytically. Various simplifications and heuristics are proposed globally, however, these need to be anchored in terms of an indication of their likely performance. We offer a novel parallel investigation of a near-optimal and heuristic optimisation approach on a country scale. The linear programming (LP) optimisation problem finds the global minimum for the chosen set of input variables, this however comes at the cost of limitations regarding model size due to complexity. The alternative heuristic model limits connectivity of model parameters but rather than aggregating variables over space or time, it maintains a high resolution to allow for more granular estimates. We compare the quality and performance of a heuristic and LP optimisation method, using two configurations for the example of Australia and find relevant solutions for both. The solution space requires substantial simplification for the LP to be solvable and leads to overly optimistic capacity factors, installed capacity and cost, due to spatial aggregation. The heuristic approach has a significant performance advantage requiring only 3% of the near-optimal runtime and a fraction of calculation iterations.

关键词： Renewable energy supply Capacity planning Computational complexity Optimisation methods linear program Heuristic optimisation

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A New Integer programming Formulation of the Graphical Traveling Salesman Problem 22nd

A New Integer Programming Formulation of the Graphical Trave...

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22nd International Conference on Integer programming and Combinatorial Optimization (IPCO)

作者： Carr, Robert D. Simonetti, Neil Univ New Mexico Dept Comp Sci Albuquerque NM 87131 USA Bryn Athyn Coll Business Comp Sci & Math Dept Bryn Athyn PA 19009 USA

ISBN: (纸本)9783030738792;9783030738785

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost c(ij) of traveling from city i to city j, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of constraints that are either polynomial in number or polynomially separable, while addressing an open question proposed by Denis Naddef.

关键词： linear program Relaxation TSP Traveling Salesman Problem GTSP Graphical Traveling Salesman Problem

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A new structural reliability analysis method under non-parameterized probability box variables

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022年第11期65卷 322-322页

作者： Xie, Huichao Li, Jinwen Liao, Daihui Cent South Univ Forestry & Technol Coll Mat Sci & Engn Changsha 410004 Peoples R China Cent South Univ Forestry & Technol Coll Mech & Elect Engn Changsha 410004 Peoples R China

The probability box (P-box) model is an effective quantification tool that can deal with aleatory and epistemic uncertainties and can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box ones. This paper proposes a new structural reliability analysis method with the non-parameterized P-box uncertainty, through which bounds of the failure probability can be obtained efficiently. For the convenience of calculation, the reliability analysis problems are divided into the univariate and multivariate ones. Firstly, structural failure probability bound analysis for the univariate problem is converted into solving two linear programming models by discretizing the cumulative distribution function (CDF) of the P-box variable, which can be solved efficiently by the simplex algorithm. Secondly, an iterative technique is used to decompose the multivariate problem into a series of univariate problems, in which only one non-parameterized P-box's CDF is optimized and the remaining counterparts are fixed. Hence, the failure probability bounds can be obtained by solving a series of linear programming problems. Finally, the effectiveness of the proposed method is demonstrated by investigating three numerical examples.

关键词： Structural reliability analysis Non-parameterized P-box linear program Failure probability bounds

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On Optimizing Max Min Rate in Rechargeable Wireless Sensor Networks with Energy Sharing

IEEE TRANSACTIONS ON SUSTAINABLE COMPUTING

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IEEE TRANSACTIONS ON SUSTAINABLE COMPUTING 2020年第1期5卷 107-120页

作者： He, Tengjiao Chin, Kwan-Wu Soh, Sieteng Yang, Changlin Jinan Univ Coll Informat Sci & Technol Guangzhou 510000 Peoples R China Univ Wollongong Sch Elect Comp & Telecommun Engn Wollongong NSW 2522 Australia Curtin Univ Sch Elect Engn Comp & Math Sci Perth WA 6102 Australia Zhongyuan Univ Technol Sch Comp Sci Zhengzhou 451191 Henan Peoples R China

We consider Rechargeable Wireless Sensor Networks (R-WSNs) where nodes harvest energy from both solar and the Radio Frequency (RF) transmissions of their neighbors. Our aim is to maximize the minimum source or sensing rate of nodes. This rate is determined by the available energy at sensor nodes as well as link capacity, which is determined by the set of transmitting nodes. In this paper, we first study and show the benefits of energy sharing. Intuitively, a sensor node should share its energy if doing so increases source rates. We present a novel linear program (LP) to determine the routing, link schedule, energy transmission, and reception time that maximize the minimum source rate of a given R-WSN. Our numerical results indicate that, on average, the minimum transmission rate of sensor nodes increased by 16.03 percent when nodes share energy. This motivates the development of a practical protocol called E-RSVP that iteratively increases the time slots of each source node. It also considers using time slots for transmission or reception of energy. Our simulation results show E-RSVP yields minimum source rates that are 14.80 percent higher as compared to the case without energy sharing.

关键词： Protocols Wireless sensor networks Routing Radio frequency Energy harvesting Throughput Relays linear program optimization data transmission and energy sharing protocol

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INVERSE OPTIMAL TRANSPORT

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SIAM JOURNAL ON APPLIED MATHEMATICS 2020年第1期80卷 599-619页

作者： Stuart, Andrew M. Wolfram, Marie-Therese CALTECH Pasadena CA 91125 USA Univ Warwick Coventry CV4 7AL W Midlands England Austrian Acad Sci RICAM Linz 4040 Australia

Discrete optimal transportation problems arise in various contexts in engineering, the sciences, and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal transportation plans. The algorithm requires only the ability to solve the forward optimal transport problem, which is a linear program, and to generate random numbers. It has a Bayesian interpretation and may also be viewed as a form of stochastic optimization. We illustrate the developed methodologies using the example of international migration flows. Reported migration flow data captures (noisily) the number of individuals moving from one country to another in a given period of time. It can be interpreted as a noisy observation of an optimal transportation map, with costs related to the geographical position of countries. We use a graph-based formulation of the problem, with countries at the nodes of graphs and nonzero weighted adjacencies only on edges between countries which share a border. We use the proposed algorithm to estimate the weights, which represent cost of transition, and to quantify uncertainty in these weights.

关键词： optimal transport international migration flows linear program parameter estimation Bayesian inversion

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Adjustive linear Regression and Its Application to the Inverse QSAR

Adjustive Linear Regression and Its Application to the Inver...

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13th International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS) held as part of 15th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC)

作者： Zhu, Jianshen Haraguchi, Kazuya Nagamochi, Hiroshi Akutsu, Tatsuya Kyoto Univ Dept Appl Math & Phys Kyoto 6068501 Japan Kyoto Univ Bioinformat Ctr Inst Chem Res Uji 6110011 Japan

ISBN: (纸本)9789897585524

In this paper, we propose a new machine learning method, called adjustive linear regression, which can be regarded as an ANN on an architecture with an input layer and an output layer of a single node, wherein an error function is minimized by choosing not only weights of the arcs but also an activation function at each node in the two layers simultaneously. Under some conditions, such a minimization can be formulated as a linear program (LP) and a prediction function with adjustive linear regression is obtained as an optimal solution to the LP. We apply the new machine learning method to a framework of inferring a chemical compound with a desired property. From the results of our computational experiments, we observe that a prediction function constructed by adjustive linear regression for some chemical properties drastically outperforms that by Lasso linear regression.

关键词： Machine Learning linear Regression Integer programming linear program Cheminformatics Materials Informatics QSAR/QSPR Molecular Design

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Solving linear programs in the Current Matrix Multiplication Time 2019

Solving Linear Programs in the Current Matrix Multiplication...

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51st Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Cohen, Michael B. Lee, Yin Tat Song, Zhao MIT Cambridge MA 02139 USA Microsoft Res Redmond WA 98052 USA Univ Washington Seattle WA 98195 USA UT Austin Austin TX USA

ISBN: (纸本)9781450367059

This paper shows how to solve linear programs of the form min(Ax=b, x >= 0) c (inverted perpendicular) x with n variables in time O*((n(omega) + n(2.5-alpha/2) + n(2+1/6)) log(n/delta)) where omega is the exponent of matrix multiplication, alpha is the dual exponent of matrix multiplication, and delta is the relative accuracy. For the current value of omega similar to 2.37 and alpha similar to 0.31, our algorithm takes O*(n(omega) log(n/delta)) time. When omega = 2, our algorithm takes O*(n(2+1/6) log(n/delta)) time. Our algorithm utilizes several new concepts that we believe may be of independent interest: (1) We define a stochastic central path method. (2) We show how to maintain a projection matrix root WA(inverted perpendicular)(AWA(inverted perpendicular))(-1)A root W in sub-quadratic time under l(2) multiplicative changes in the diagonal matrix W.

关键词： linear program interior point method matrix multiplication

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BREAKING 1-1/e BARRIER FOR NONPREEMPTIVE THROUGHPUT MAXIMIZATION

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2020年第3期34卷 1649-1669页

作者： Im, Sungjin Li, Shi Moseley, Benjamin Univ Calif Elect Engn & Comp Sci Merced CA 95343 USA Univ Buffalo Buffalo NY 14221 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA

In this paper we consider one of the most basic scheduling problems where jobs have their respective arrival times and deadlines. The goal is to schedule as many jobs as possible nonpreemptively by their respective deadlines on m identical parallel machines. For the last decade, the best approximation ratio known for the single-machine case (m = 1) has been 1 - 1/e - epsilon approximate to 0.632 due to Chuzhoy, Ostrovsky, and Rabani [FOCS 2001] and NOR 2006]. We break this barrier and give an improved 0.644-approximation. For the multiple-machine case, we give an algorithm whose approximation guarantee becomes arbitrarily close to 1 as the number of machines increases. This improves upon the previous best 1 - 1/(1+1/m)(m) approximation due to Bar-Noy et al. [STOC 1999] and [SICOMP 2009], which converges to 1 - 1/e as m goes to infinity. Our result for the multiple-machine case extends to the weighted throughput objective where jobs have different weights, and the goal is to schedule jobs with the maximum total weight. Our results show that the 1 - 1/e approximation factor widely observed in various coverage problems is not tight for the nonpreemptive maximum throughput scheduling problem.

关键词： scheduling approximation nonpreemptive throughput linear program rounding

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Size Constrained Clustering With MILP Formulation

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IEEE ACCESS 2020年 8卷 1587-1599页

作者： Tang, Wei Yang, Yang Zeng, Lanling Zhan, Yongzhao Jiangsu Univ Sch Comp Sci & Commun Engn Zhenjiang 212013 Jiangsu Peoples R China

Clustering is one of the essential tools for data mining since it reveals the natural structures of the unlabeled data. Many clustering algorithms have been proposed in the last decades. However, few of them are designed to adapt prior knowledge that is available in many real applications, such as the sizes of clusters. In this paper, we propose a novel iterative clustering algorithm that can impose the constraints on the sizes of clusters. Given an unordered set of cluster size constraints, the proposed method minimizes the mean squared error (MSE) while simultaneously considers the size constraints. Each iteration of the proposed method consists of two steps, namely an assignment step and an update step. In the assignment step, the observations are assigned into clusters under the size constraints. The assignment task is modeled as an integer linear programming (ILP) problem. We prove that part of the constraint matrix of this ILP problem is total unimodular. Therefore, the integer constraints on most of the variables can be omitted so that the problem would become a mixed integer programming (MILP) problem which is much easier to solve. In the update step, new cluster centroids will be updated as the centers of the observations in the corresponding clusters. Experiments on UCI data sets indicate that (1) imposing the size constraints as proposed could improve the clustering performance;(2) compared with the state-of-the-art size constrained clustering methods, the proposed method could efficiently derive better clustering results.

关键词： Clustering mean squared error size constraints linear program

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