A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

Nesting Arbitrary Shapes Using Geometric Mating

2002 ◽  
Vol 2 (3) ◽  
pp. 171-178
Author(s):  
Chan Yu ◽  
Souran Manoochehri
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Computation Time ◽  
Search Space ◽  
Optimization Method ◽  
The Other ◽  
Reasonable Time ◽  
Common Features ◽  
Object Relative ◽  
Arbitrary Shapes

A genetic algorithm-based optimization method is proposed for solving the problem of nesting arbitrary shapes. Depending on the number of objects and the size of the search space, realizing an optimal solution within a reasonable time may not be possible. In this paper, a mating concept is introduced to reduce the solution time. Mating between two objects is defined as the positioning of one object relative to the other by merging common features that are assigned by the mating condition between them. A constrained move set is derived from a mating condition that allows the transformation of the object in each mating pair to be fully constrained with respect to the other. Properly mated objects can be placed together, thus reducing the overall computation time. Several examples are presented to demonstrate the efficiency of utilizing the mating concept to solve a nesting optimization problem.

An Optimal Soft Landing Control for Moon Lander by Means of Measures

2011 ◽  
Vol 52-54 ◽  
pp. 1861-1867
Author(s):  
J.A. Fakharzadeh ◽  
Sajad Salehi
Keyword(s):  
Dynamical System ◽  
Control Strategy ◽  
Measure Space ◽  
Optimization Problem ◽  
Optimal Solution ◽  
The Other ◽  
Solution Path ◽  
Soft Landing ◽  
Variational Form ◽  
Landing Control

Designing a new control strategy for a moon lander to achieve an optimal soft landing, is the main purpose of this paper. For the dynamical system of the propeller to achieve the lowest level of fuel consumption, the problem of soft landing is presented as an optimal control one. Representing this into a variational form, transferring to an optimization problem on a measure space and then determining the optimal solution via a linear programming problem is the new solution path. This method has some important advantages in compare with the other, which are explain within a numerical simulation.

scholarly journals Convex projection and convex multi-objective optimization

2021 ◽  
Author(s):  
Gabriela Kováčová ◽  
Birgit Rudloff
Keyword(s):  
Linear Programming ◽  
Approximate Solution ◽  
Convex Optimization ◽  
Optimization Problem ◽  
Approximate Solutions ◽  
Convex Optimization Problem ◽  
Multi Objective ◽  
Convex Case ◽  
Projection Problem ◽  
Polyhedral Projection

AbstractIn this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the solution to that problem also solves the convex projection (and vice versa), which is analogous to the result in the polyhedral convex case considered in Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016). In practice, however, one can only compute approximate solutions in the (bounded or self-bounded) convex case, which solve the problem up to a given error tolerance. We will show that for approximate solutions a similar connection can be proven, but the tolerance level needs to be adjusted. That is, an approximate solution of the convex projection solves the multi-objective problem only with an increased error. Similarly, an approximate solution of the multi-objective problem solves the convex projection with an increased error. In both cases the tolerance is increased proportionally to a multiplier. These multipliers are deduced and shown to be sharp. These results allow to compute approximate solutions to a convex projection problem by computing approximate solutions to the corresponding multi-objective convex optimization problem, for which algorithms exist in the bounded case. For completeness, we will also investigate the potential generalization of the following result to the convex case. In Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016), it has been shown for the polyhedral case, how to construct a polyhedral projection associated to any given vector linear program and how to relate their solutions. This in turn yields an equivalence between polyhedral projection, multi-objective linear programming and vector linear programming. We will show that only some parts of this result can be generalized to the convex case, and discuss the limitations.

scholarly journals Freddie: Annotation-independent Detection and Discovery of Transcriptomic Alternative Splicing Isoforms

2021 ◽  
Author(s):  
Baraa Orabi ◽  
Brian McConeghy ◽  
Cedric Chauve ◽  
Faraz Hach
Keyword(s):  
Alternative Splicing ◽  
Optimization Problem ◽  
Intron Retention ◽  
False Positive Rate ◽  
Dynamic Programming Algorithm ◽  
Cancer Cell Line ◽  
Cancer Therapeutics ◽  
The Other ◽  
Programming Algorithm ◽  
Junction Site

AbstractAlternative splicing (AS) is an important mechanism in the development of many cancers, as novel or aberrant AS patterns play an important role as an independent onco-driver. In addition, cancer-specific AS is potentially an effective target of personalized cancer therapeutics. However, detecting AS events remains a challenging task, especially if these AS events are not pre-annotated. This is exacerbated by the fact that existing transcriptome annotation databases are far from being comprehensive, especially with regard to cancer-specific AS. Additionally, traditional sequencing technologies are severely limited by the short length of the generated reads, that rarely spans more than a single splice junction site. Given these challenges, transcriptomic long-read (LR) sequencing presents a promising potential for the detection and discovery of AS.We present Freddie, a computational annotation-independent isoform discovery and detection tool. Freddie takes as input transcriptomic LR sequencing of a sample and computes a set of isoforms for the given sample. Freddie takes as input the genomic alignment of the transcriptomic LRs generated by a splice aligner. It then partitions the reads to sets that can be processed independently and in parallel. For each partition, Freddie segments the genomic alignment of the reads into canonical exon segments. The goal of this segmentation is to be able to represent any potential isoform as a subset of these canonical exons. This segmentation is formulated as an optimization problem and is solved with a Dynamic Programming algorithm. Then, Freddie reconstructs the isoforms by jointly clustering and error-correcting the reads using the canonical segmentation as a succinct representation. The clustering and error-correcting step is formulated as an optimization problem – the Minimum Error Clustering into Isoforms (MErCi) problem – and is solved using Integer Linear Programming (ILP).We compare the performance of Freddie on simulated datasets with other isoform detection tools with varying dependence on annotation databases. We show that Freddie outperforms the other tools in its recall, including those given the complete ground truth annotation. In terms of false positive rate, Freddie performs comparably to the other tools. We also run Freddie on a transcriptomic LR dataset generated in-house from a prostate cancer cell line. Freddie detects a potentially novel Androgen Receptor isoform that includes novel intron retention. We cross-validate this novel intron retention using orthogonal publicly available short-read RNA-seq datasets.AvailabilityFreddie is open source and available at https://bitbucket.org/baraaorabi/freddie

scholarly journals Comparison of Integer Linear Programming and Dynamic Programming Approaches for ATM Cash Replenishment Optimization Problem

2020 ◽  
Vol 11 (3) ◽  
pp. 120-132
Author(s):  
Fazilet Özer ◽  
Ismail Hakki Toroslu ◽  
Pinar Karagoz
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Real Data ◽  
The Other ◽  
Other Hand ◽  
Automated Teller Machine ◽  
The Cost

With the automated teller machine (ATM) cash replenishment problem, banks aim to reduce the number of out-of-cash ATMs and duration of out-of-cash status. On the other hand, they want to reduce the cost of cash replenishment, as well. The problem conventionally involves forecasting ATM cash withdrawals, and then cash replenishment optimization based on the forecast. The authors assume that reliable forecasts are already obtained for the amount of cash needed in ATMs. The focus of the article is cash replenishment optimization. After introducing linear programming-based solutions, the authors propose a solution based on dynamic programming. Experiments conducted on real data reveal that the proposed approach can find the optimal solution more efficiently than linear programming.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

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