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Interval Arithmetic for Guaranteed Bounds in linear programming

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1973年第1期12卷 1-5页

作者： Stewart, N. F. Univ Montreal Dept Informat Montreal PQ Canada

In this note, we show how interval arithmetic can be used to give a solution to the linear programming problem which is guaranteed to be on the safe side of the true solution, where roundoff error is taken into account.

关键词： linear programming problem Interval Arithmetic Final Basis Roundoff Error Nonbasic Variable

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CONTROL OF RANDOM SEQUENCES IN problemS WITH CONSTRAINTS

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THEORY OF PROBABILITY AND ITS APPLICATIONS 1994年第4期38卷 751-762页

作者： PIUNOVSKII, AB MOSCOW PHYS & TECH PROBLEMS INST MOSCOW RUSSIA

We consider the optimal control problem for a stochastic sequence (not necessarily Markov) in which besides the main criterion there are a number of other functionals of the sample paths;their expectations must satisfy a certain system of inequalities. The life time of the process is assumed to be finite and all basic spaces are Borel spaces. The paper studies some properties of the space of strategy measures (for example, we prove that the selectors correspond to extreme points of this space). The optimal control problem is reformulated in terms of the theory of abstract linear programming which allows us to obtain necessary and sufficient conditions of optimality. Moreover, the paper proves the existence of an optimal strategy and its form is established (a finite mixture of selectors);at the end some exactly solved examples are cited.

关键词： OPTIMAL CONTROL STOCHASTIC SEQUENCE CONTROL STRATEGY linear programming problem EXTREME POINT linear-QUADRATIC SYSTEM

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problem STATEMENTS FOR k-NODE SHORTEST PATH AND k-NODE SHORTEST CYCLE IN A COMPLETE GRAPH

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CYBERNETICS AND SYSTEMS ANALYSIS 2016年第1期52卷 71-75页

作者： Stetsyuk, P. I. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

The author formulates mixed Boolean linear programming problems to find the shortest route and the shortest cycle that pass through the given number of nodes in a complete graph. Their special cases provide formulations of problems for finding the shortest Hamiltonian path and the shortest Hamiltonian cycle. The problems include no more than 2n(2) variables and no more than (n+1)(2) constraints, where n is the number of nodes of the complete graph.

关键词： complete graph shortest path linear programming problem Hamiltonian path Hamiltonian cycle traveling salesman problem

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Newsvendor problems with Interval Probabilities

Newsvendor Problems with Interval Probabilities

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International Conference on Industrial Engineering and Engineering Management

作者： Guo, Peijun Tanaka, Hideo Yokohama Natl Univ Fac Business Adm Yokohama Kanagawa 240 Japan Hiroshima Int Univ Fac Psychol Sci Higashihiroshima Japan

ISBN: (纸本)9781424426294

In this paper, the uncertainty of the demand in newsvendor problems is characterized by interval probabilities. The characteristics of interval probabilities, the method for estimating interval probabilities from subject and decision criteria with interval probabilities are addressed. The newsvendor models under interval probabilities are proposed for obtaining the optimal order quantity.

关键词： Newsvendor problem interval probabilities linear programming problem

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An Assembly problem with Mobile Robots 19

An Assembly Problem with Mobile Robots

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19th IEEE International Conference on Emerging Technology and Factory Automation (ETFA)

作者： Kloetzer, Marius Mahulea, Cristian Tech Univ Gheorghe Asachi Iasi Dept Automat Control & Appl Informat Iasi Romania Univ Zaragoza Dept Comp Sci & Syst Engn E-50009 Zaragoza Spain

ISBN: (纸本)9781479948451

This paper proposes a solution for solving a specific problem that requires a team of identical robots to collect in a specific order different types of resources scattered throughout an environment. A Petri net with outputs models the environment, the team possible movements and the regions with resources. An iterative solution plans the team such that each robot collects and assembles resources in the required order. Each iteration step is based on a linear programming problem that is guaranteed to return a feasible firing vector for the Petri net system. A pseudo-code description of the procedure is given and a simulation example is included.

关键词： Petri nets iterative methods linear programming mobile robots robotic assembly Petri net system assembly problem feasible firing vector identical robots iterative solution linear programming problem outputs models pseudo-code description team possible movements Assembly Mobile robots Modeling Planning Silicon Vectors

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Validation of subgradient optimization

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Mathematical programming 1974年第1期6卷 62-88页

作者： Held, Michael Wolfe, Philip Crowder, Harlan P. IBM Systems Research Institute New York United States IBM Watson Research Center Yorktown Heights New York United States

The “relaxation” procedure introduced by Held and Karp for approximately solving a large linear programming problem related to the traveling-salesman problem is refined and studied experimentally on several classes of specially structured large-scale linear programming problems, and results on the use of the procedure for obtaining exact solutions are given. It is concluded that the method shows promise for large-scale linear programming © 1974, The Mathematical programming Society. All rights reserved.

关键词： Exact Solution Mathematical Method programming problem linear programming problem Subgradient Optimization

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Balanced matrices

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Mathematical programming 1972年第1期2卷 19-31页

作者： Berge, C. Centre National de Recherche Scientifique Paris France

This paper studies some properties of hypergraphs in connection with a class of integer linear programming problems. The main result (theorem 3) states that the strong chromatic number of a balanced hypergraph is equal to its rank;this generalizes a result known for unimodular hypergraphs. Two applications of this result are given, the first one to Graph theory (theorem 5), the second one to integral linear programming (theorem 6). © 1972 North-Holland Publishing Company.

关键词： Graph Theory Mathematical Method programming problem Integer linear programming linear programming problem

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Note on linear fractional functionals programming

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Metrika 1968年第1期13卷 72-77页

作者： Swarup, Kanti Faculty of Mathematics University of Delhi India

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On the foundations of linear and integer linear programming I

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Mathematical programming 1975年第1期9卷 207-226页

作者： Graver, Jack E. Syracuse University Syracuse New York United States

In this paper we consider the question: how does the flow algorithm and the simplex algorithm work? The usual answer has two parts: first a description of the "improvement process", and second a proof that if no further improvement can be made by this process, an optimal vector has been found. This second part is usually based on duality -a technique not available in the case of an arbitrary integer programming problem. We wish to give a general description of "improvement processes" which will include both the simplex and flow algorithms, which will be applicable to arbitrary integer programming problems, and which will in themselves assure convergence to a solution. Geometrically both the simplex algorithm and the flow algorithm may be described as follows. At the ith stage, we have a vertex (or feasible flow) to which is associated a finite set of vectors, namely the set of edges leaving that vertex (or the set of unsaturated paths). The algorithm proceeds by searching among this special set for a vector along which the gain function is increasing. If such a vector is found, the algorithm continues by moving along this vector as far as is possible while still remaining feasible. The search is then repeated at this new feasible point. We give a precise definition for sets of vectors, called test sets, which will include those sets described above arising in the simplex and flow algorithms. We will then prove that any "improvement process" which searches through a test set at each stage converges to an optimal point in a finite number of steps. We also construct specific test sets which are the natural extensions of the test sets employed by the flow algorithm to arbitrary linear and integer linear programming problems. © 1975 The Mathematical programming Society.

关键词： programming problem Integer linear programming Natural Extension linear programming problem Optimal Point

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Interval linear Optimization problems with Fuzzy Inequality Constraints

Interval Linear Optimization Problems with Fuzzy Inequality ...

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2014 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM)

作者： Alolyan, Ibraheem King Saud Univ Coll Sci Dept Math POB 2455 Riyadh 11451 Saudi Arabia

ISBN: (纸本)9781479944675

In many real-life situations, we come across problems with imprecise input values. Imprecisions are dealt with by various ways. One of them is interval based approach in which we model imprecise quantities by intervals, and suppose that the quantities may vary independently and simultaneously within their intervals. In most optimization problems, they are formulated using imprecise parameters. Such parameters can be considered as fuzzy intervals, and the optimization tasks with interval cost function are obtained. When realistic problems are formulated, a set of intervals may appear as coefficients in the objective function or the constraints of a linear programming problem. In this paper, we introduce a new method for solving linear optimization problems with interval parameters in the objective function and the inequality constraints, and we show the efficiency of the proposed method by presenting a numerical example.

关键词： fuzzy set theory linear programming fuzzy inequality constraints fuzzy intervals imprecise parameters interval linear optimization problems linear programming problem Cost function Educational institutions Fuzzy sets linear programming programming Vectors linear programming Fuzzy Set Theory Cost functions Educational institutions inequality constraint programming Objective function

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