Lower Bounding Linear Program for the Perimeter Patrol Optimization Problem

2014 ◽  
Vol 37 (2) ◽  
pp. 558-565 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Myoungkuk Park ◽  
Swaroop Darbha ◽  
David Casbeer ◽  
Phil Chandler ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Linear Program ◽  
Lower Bounding

scholarly journals Increasing Capacity of Intersections with Transit Priority

2016 ◽  
Vol 28 (6) ◽  
pp. 627-637 ◽  
Author(s):  
Yanxi Hao ◽  
Jing Teng ◽  
Yinsong Wang ◽  
Xiaoguang Yang
Keyword(s):  
Numerical Experiment ◽  
Optimization Problem ◽  
Low Cost ◽  
Linear Program ◽  
Signal Timing ◽  
Test Results ◽  
Transit Signal Priority ◽  
Proposed Model ◽  
Micro Simulation ◽  
Bus Lane

Dedicated bus lane (DBL) and transit signal priority (TSP) are two effective and low-cost ways of improving the reliability of transits. However, these strategies reduce the capacity of general traffic. This paper presents an integrated optimization (IO) model to improve the performance of intersections with dedicated bus lanes. The IO model integrated geometry layout, main-signal timing, pre-signal timing and transit priority. The optimization problem is formulated as a Mix-Integer-Non-Linear-Program (MINLP) that can be transformed into a Mix-Integer-Linear-Program (MILP) and then solved by the standard branch-and-bound technique. The applicability of the IO model is tested through numerical experiment under different intersection layouts and traffic demands. A VISSIM micro simulation model was developed and used to evaluate the performance of the proposed IO model. The test results indicate that the proposed model can increase the capacity and reduce the delay of general traffic when providing priority to buses.

Algorithms for Localization and Routing of Unmanned Vehicles in GPS-Denied Environments

2018 ◽  
Author(s):  
Bingyu Wang ◽  
Sivakumar Rathinam ◽  
Rajnikant Sharma ◽  
Kaarthik Sundar
Keyword(s):  
Global Positioning System ◽  
Optimization Problem ◽  
Unmanned Vehicles ◽  
Routing Algorithms ◽  
Linear Program ◽  
Mixed Integer ◽  
Ground Vehicles ◽  
Placement Problem ◽  
Mixed Integer Linear Program ◽  
Global Positioning

A majority of the routing algorithms for unmanned aerial or ground vehicles rely on Global Positioning System (GPS) information for localization. However, disruption of GPS signals, by intention or otherwise, can render these algorithms ineffective. This article provides a way to address this issue by utilizing landmarks to aid localization in GPS-denied environments. Specifically, given a number of vehicles and a set of targets, we formulate a joint routing and landmark placement problem as a combinatorial optimization problem: to compute paths for the vehicles that traverse every target at least once, and to place landmarks to aid the vehicles in localization while each of them traverses its route, such that the sum of the traveling cost and the landmark placement cost is minimized. A mixed-integer linear program is presented, and a set of algorithms and heuristics are proposed for different approaches to address certain issues not covered by the linear program. The performance of each proposed algorithm is evaluated and compared through extensive computational and simulation results.

scholarly journals The Use of the Duality Principle to Solve Optimization Problems

2018 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Rowland Jerry Okechukwu Ekeocha ◽  
Chukwunedum Uzor ◽  
Clement Anetor
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Linear Program ◽  
Duality Gap ◽  
Duality Principle ◽  
Primal Problem ◽  
Optimal Values ◽  
Primal And Dual Problems ◽  
Primal And Dual

<p><span>The duality principle provides that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap. For convex optimization problems, the duality gap is zero under a constraint qualification condition.<span>  </span>In other words given any linear program, there is another related linear program called the dual. In this paper, an understanding of the dual linear program will be developed. This understanding will give important insights into the algorithm and solution of optimization problem in linear programming. <span> </span>Thus the main concepts of duality will be explored by the solution of simple optimization problem.</span></p>

scholarly journals Lower Bounding the AND-OR Tree via Symmetrization

2021 ◽  
Vol 13 (1) ◽  
pp. 1-11
Author(s):  
William Kretschmer
Keyword(s):  
Lower Bound ◽  
Linear Program ◽  
Laurent Polynomials ◽  
Lower Bounding

We prove a simple, nearly tight lower bound on the approximate degree of the two-level AND-OR tree using symmetrization arguments. Specifically, we show that ˜ deg(AND m ˆ OR n ) = ˜ Ω(√ mn ). We prove this lower bound via reduction to the OR function through a series of symmetrization steps, in contrast to most other proofs that involve formulating approximate degree as a linear program [6, 10, 21]. Our proof also demonstrates the power of a symmetrization technique involving Laurent polynomials (polynomials with negative exponents) that was previously introduced by Aaronson et al. [2].

scholarly journals Optimisasi Program Linear Integer Murni Dengan Metode Branch And Bound

2018 ◽  
Vol 1 (2) ◽  
pp. 175-181
Author(s):  
Tondi Marulizar ◽  
Ujian Sinulingga ◽  
Esther Nababan
Keyword(s):  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Simplex Method ◽  
Optimization Problem ◽  
Linear Program ◽  
Integer Linear Program ◽  
Branch And Bound Method ◽  
A Value ◽  
Calculation Process ◽  
Lower Limits

Program Linier Integer Murni merupakan optimisasi kombinatorial yang tidak mudah untuk diselesaikan secara efisien. Metode yang sering digunakan untuk menyelesaikan Program Linier Integer Murni diantaranya adalah metode merative, yang merupakan salah satunya metode Branch and Bound. Metode ini menggunakan hasil dari metode simpleks yang belum bernilai integer sehingga dilakukan pencabangan dan batasan terhadap variabel x_j yang bernilai pecahan terbesar. Metode Branch and Bound dapat menyelesaikan masalah optimisasi suatu produk, tetapi membutuhkan waktu yang lebih lama dalam proses perhitungannya dikarenakan dalam setiap tahap perhitungan harus dicari nilai dari batas atas dan batas bawah yang ditentuan berdasarkan suatubatasandankriteria tertentu. Pure Integer Linear Program is combinatorial optimization that is not easy to solve efficiently. The method that is often used to complete the Pure Integer Linear Program is the merative method, which is one of the Branch and Bound methods. This method uses the results of the simplex method that is not yet an integer value so that the branching and limitation of the x_j variable is the largest fraction. The Branch and Bound method can solve the optimization problem of a product, but requires a longer time in the calculation process because in each calculation phase, a value must be sought from the upper and lower limits determined based on the boundary and certain criteria. 

Learning Entailment Relations by Global Graph Structure Optimization

2012 ◽  
Vol 38 (1) ◽  
pp. 73-111 ◽  
Author(s):  
Jonathan Berant ◽  
Ido Dagan ◽  
Jacob Goldberger
Keyword(s):  
Optimization Problem ◽  
Structure Optimization ◽  
Linear Program ◽  
Graph Structure ◽  
Inference Algorithm ◽  
Target Concept ◽  
Semantic Inference ◽  
Entailment Relations ◽  
Optimal Set ◽  
Global Algorithm

Identifying entailment relations between predicates is an important part of applied semantic inference. In this article we propose a global inference algorithm that learns such entailment rules. First, we define a graph structure over predicates that represents entailment relations as directed edges. Then, we use a global transitivity constraint on the graph to learn the optimal set of edges, formulating the optimization problem as an Integer Linear Program. The algorithm is applied in a setting where, given a target concept, the algorithm learns on the fly all entailment rules between predicates that co-occur with this concept. Results show that our global algorithm improves performance over baseline algorithms by more than 10%.

Optimal Placement of Fixture Clamps: Minimizing the Maximum Clamping Forces

2002 ◽  
Vol 124 (3) ◽  
pp. 686-694 ◽  
Author(s):  
Rodrigo A. Marin ◽  
Placid M. Ferreira
Keyword(s):  
Convex Optimization ◽  
Relative Motion ◽  
Optimization Problem ◽  
Three Dimensional ◽  
Linear Program ◽  
Optimal Placement ◽  
Clamping Force ◽  
Convex Optimization Problem ◽  
Algebraic Technique

This paper addresses the problem of synthesizing robust optimal clamping schemes on three-dimensional parts with planar faces, with and without friction. Given a work part with a pre-defined deterministic 3-2-1 location scheme, a set of polygonal convex regions on its faces are defined as areas of admissible clamp positions. A known set of external disturbing wrenches is also given. The frictionless case is considered first, and a new linear program is formulated to provide clamp locations that minimize the maximum clamping force. A transformation of the solution is presented that permits the extraction of both, the optimal positions of the clamps and the magnitude of the corresponding maximum clamping force. Friction is introduced next, and a linear program is presented that minimizes the maximum normal clamping force. We also extend the earlier formulations to support the case of frictionless clamping contacts on cylindrical faces. The result is a nonlinear (but convex) optimization problem that can be easily solved. Finally, we discuss a linear algebraic technique to find the directions, and associated relative motion rates, along which the clamps can be moved while maintaining the clamping forces constant. These lines of constant clamping force, as we name them, identify an equivalence set of clamping schemes (such that the maximum clamping force, given a set of disturbing wrenches, stays invariant).

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

TAPPI Journal ◽  
2019 ◽  
Vol 18 (10) ◽  
pp. 607-618
Author(s):  
JÉSSICA MOREIRA ◽  
BRUNO LACERDA DE OLIVEIRA CAMPOS ◽  
ESLY FERREIRA DA COSTA JUNIOR ◽  
ANDRÉA OLIVEIRA SOUZA DA COSTA
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Kraft Pulping ◽  
Steam Temperature ◽  
Input Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Multiple Effect ◽  
Sensibility Analysis ◽  
Exergetic Analysis

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

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