scholarly journals Ranking Functions for Linear-Constraint Loops

10.29007/rvs4 ◽  
2018 ◽  
Author(s):  
Amir Ben-Amram
Keyword(s):  
Linear Programming ◽  
Complexity Analysis ◽  
Linear Constraint ◽  
Linear Constraints ◽  
Ranking Functions ◽  
Termination Analysis ◽  
Program Parallelization ◽  
Different Types ◽  
Finite Set ◽  
Programming Techniques

Ranking functions are a tool successfully used in termination analysis, complexity analysis, and program parallelization.Among the different types of ranking functions and approaches to finding them, this talk will concentrate onfunctions that are found by linear programming techniques. The setting is that ofa loop that has been pre-abstracted so thatit is described by linear constraints over a finite set of numeric variables.I will review results (more or less recent) regarding the search forranking functions which are either linear or lexicographic-linear.

Uncertain Reliability of a Series System via Non-Linear Programming

2012 ◽  
Vol 263-266 ◽  
pp. 2263-2266
Author(s):  
Huan Bin Liu ◽  
Shao Hua Dang
Keyword(s):  
Linear Programming ◽  
Membership Function ◽  
Series System ◽  
Failure Rates ◽  
Non Linear Programming ◽  
Different Types ◽  
Non Linear ◽  
Programming Techniques ◽  
The Membership Function

In this paper, a new algorithm has been introduced to construct the membership function and non-membership function of uncertain reliability of a series system via non-linear programming techniques, which having components following different types of intuitionistic uncertain failure rates.

Linear Integer Programming Techniques for Portfolio Design Problem

2020 ◽  
pp. 80-102
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Design Problem ◽  
Linear Models ◽  
Linear Constraint ◽  
Quadratic Model ◽  
Linear Integer Programming ◽  
Constraint Systems ◽  
Programming Techniques ◽  
Portfolio Design

This chapter introduces Integer Linear Programming (ILP) approaches for solving efficiently a ðnancial portfolio design problem. The authors proposed a matricial model in Chapter 3, which is a mathematical quadratic model. A linearization step is considered necessary to apply linear programming techniques. The corresponding matricial model shows clearly that the problem is strongly symmetrical. The row and column symmetries are easily handled by adding a negligible number of new constraints. The authors propose two linear models, which are given in detail and proven. These models represent the problem as linear constraint systems with 0-1 variables, which will be implemented in ILP solver. Experimental results in non-trivial instances of portfolio design problem are given.

scholarly journals Linear Phase Transition in Random Linear Constraint Satisfaction Problems

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
David Gamarnik
Keyword(s):  
Phase Transition ◽  
Linear Programming ◽  
Linear Constraint ◽  
Linear Constraints ◽  
Constraint Satisfaction Problems ◽  
Linear Programming Relaxation ◽  
Linear Phase ◽  
Maximum Weight ◽  
Linear Programming Duality ◽  
Convergence Method

International audience Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints $C$ on $K$ variables is fixed. From a pool of $n$ variables, $K$ variables are chosen uniformly at random and a constraint is chosen from $C$ also uniformly at random. This procedure is repeated $m$ times independently. We are interested in whether the resulting linear programming problem is feasible. We prove that the feasibility property experiences a linear phase transition,when $n→∞$ and $m=cn$ for a constant $c$. Namely, there exists a critical value $c^*$ such that, when $c < c^*$, the problem is feasible or is asymptotically almost feasible, as $n→∞$, but, when $c > c^*$, the "distance" to feasibility is at least a positive constant independent of $n$. Our result is obtained using the combination of a powerful local weak convergence method developed in Aldous [1992, 2000], Aldous and Steele [2003], Steele [2002] and martingale techniques. By exploiting a linear programming duality, our theorem impliesthe following result in the context of sparse random graphs $G(n, cn)$ on $n$ nodes with $cn$ edges, where edges are equipped with randomly generated weights. Let $\mathcal{M}(n,c)$ denote maximum weight matching in $G(n, cn)$. We prove that when $c$ is a constant and $n→∞$, the limit $lim_{n→∞} \mathcal{M}(n,c)/n$, exists, with high probability. We further extend this result to maximum weight b-matchings also in $G(n,cn)$.

Linear Programming Techniques for the Construction of Palatable Human Diets

1994 ◽  
Vol 45 (5) ◽  
pp. 489-496 ◽  
Author(s):  
L. R. Fletcher ◽  
P. M. Soden ◽  
A. S. I. Zinober
Keyword(s):  
Linear Programming ◽  
Programming Techniques

An Integer Linear Programming-Based Method for the Extraction of Ontology Alignment

2021 ◽  
Vol 16 (2) ◽  
pp. 25-44
Author(s):  
Naima El Ghandour ◽  
Moussa Benaissa ◽  
Yahia Lebbah
Keyword(s):  
Linear Programming ◽  
Semantic Web ◽  
Integer Linear Programming ◽  
New Method ◽  
Ontology Matching ◽  
Ontology Alignment ◽  
Programming Techniques ◽  
Data Heterogeneity ◽  
Series Of Experiments

The Semantic Web uses ontologies to cope with the data heterogeneity problem. However, ontologies become themselves heterogeneous; this heterogeneity may occur at the syntactic, terminological, conceptual, and semantic levels. To solve this problem, alignments between entities of ontologies must be identified. This process is called ontology matching. In this paper, the authors propose a new method to extract alignment with multiple cardinalities using integer linear programming techniques. The authors conducted a series of experiments and compared them with currently used methods. The obtained results show the efficiency of the proposed method.

THE DS/AHP METHOD UNDER PARTIAL INFORMATION ABOUT CRITERIA AND ALTERNATIVES BY SEVERAL LEVELS OF CRITERIA

2012 ◽  
Vol 11 (02) ◽  
pp. 307-326 ◽  
Author(s):  
LEV V. UTKIN ◽  
NATALIA V. SIMANOVA
Keyword(s):  
Linear Programming ◽  
Incomplete Information ◽  
Decision Problem ◽  
Partial Information ◽  
Decision Makers ◽  
Ahp Method ◽  
Numerical Examples ◽  
Finite Set ◽  
Linear Programming Problems ◽  
Decision Alternatives

An extension of the DS/AHP method is proposed in the paper. It takes into account the fact that the multi-criteria decision problem might have several levels of criteria. Moreover, it is assumed that expert judgments concerning the criteria are imprecise and incomplete. The proposed extension also uses groups of experts or decision makers for comparing decision alternatives and criteria. However, it does not require assigning favorability values for groups of decision alternatives and criteria. The computation procedure for processing and aggregating the incomplete information about criteria and decision alternatives is reduced to solving a finite set of linear programming problems. Numerical examples explain in detail and illustrate the proposed approach.

scholarly journals Linear programming measures for solving the problem of a linear division of convex multiplayers.

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Sarmad H. Ali ◽  
Osamah A. Ali ◽  
Samir C. Ajmi
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Optimal Solution ◽  
Optimal Method ◽  
Linear Separation ◽  
Different Types ◽  
Simplex Methods

In this research, we are trying to solve Simplex methods which are used for successively improving solution and finding the optimal solution, by using different types of methods Linear, the concept of linear separation is widely used in the study of machine learning, through this study we will find the optimal method to solve by comparing the time consumed by both Quadric and Fisher methods.

Three-dimensional path planning for unmanned aerial vehicle based on linear programming

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 773-781 ◽  
Author(s):  
Yang Chen ◽  
Jianda Han ◽  
Xingang Zhao
Keyword(s):  
Linear Programming ◽  
Path Planning ◽  
Real Time ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Linear Constraints ◽  
Flying Height ◽  
Ant Colony Optimization Algorithm ◽  
Optimal Velocity ◽  
Aerial Vehicle

SUMMARYIn this paper, an approach based on linear programming (LP) is proposed for path planning in three-dimensional space, in which an aerial vehicle is requested to pursue a target while avoiding static or dynamic obstacles. This problem is very meaningful for many aerial robots, such as unmanned aerial vehicles. First, the tasks of target-pursuit and obstacle-avoidance are modelled with linear constraints in relative coordination according to LP formulation. Then, two weighted cost functions, representing the optimal velocity resolution, are integrated into the final objective function. This resolution, defined to achieve the optimal velocity, deals with the optimization of a pair of orthogonal vectors. Some constraints, such as boundaries of the vehicle velocity, acceleration, sensor range, and flying height, are considered in this method. A number of simulations, under static and dynamic environments, are carried out to validate the performance of generating optimal trajectory in real time. Compared with ant colony optimization algorithm and genetic algorithm, our method has less parameters to tune and can achieve better performance in real-time application.

scholarly journals Equivalent Transformation of Nonlinear Constraints to Linear Constraints in Petri Nets

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
YuFeng Chen ◽  
Abdulrahman Al-Ahmari ◽  
Chi Tin Hon ◽  
NaiQi Wu
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Constraints ◽  
Linear Programming Model ◽  
Equivalent Transformation ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Integer Linear Programming Model

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach.

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