The Design of Approximation Algorithms

Williamson, David P.; Shmoys, David B.

doi:10.1017/cbo9780511921735

Cited by 848 publications

(461 citation statements)

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“…It is well-known that one can construct a solution to the knapsack problem in (9) by using its continuous relaxation in (11) and the objective value of this solution would deviate from the optimal objective value of the knapsack problem by no more than a factor of two; see Williamson and Shmoys (2011). The proof of Theorem 10 implicitly makes use of this result.…”

Section: Theorem 8 If We Allow the Preference Weights Of The No Purchmentioning

confidence: 99%

Assortment Optimization Under Variants of the Nested Logit Model

Davis

Gallego

Topaloğlu

2014

Operations Research

285

158

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We study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model. There is a fixed revenue associated with each product. The objective is to find an assortment of products to offer so as to maximize the expected revenue per customer. We show that the problem is polynomially solvable when the nest dissimilarity parameters of the choice model are less than one and the customers always make a purchase within the selected nest. Relaxing either of these assumptions renders the problem NP-hard. To deal with the NP-hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. We also formulate a convex program whose optimal objective value is an upper bound on the optimal expected revenue. Thus, we can compare the expected revenue provided by an assortment with the upper bound on the optimal expected revenue to get a feel for the optimality gap of the assortment. By using this approach, our computational experiments test the performance of the parsimonious collections of candidate assortments that we develop.

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Section: Theorem 8 If We Allow the Preference Weights Of The No Purchmentioning

confidence: 99%

Assortment Optimization Under Variants of the Nested Logit Model

Davis

Gallego

Topaloğlu

2014

Operations Research

285

158

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“…We will now prove two lemmas that will help us relate the cost of our solution to that of the constructed dual feasible solution. Lemma 4.2 is well known [23]; we prove it below for sake of completeness. Proof.…”

Section: (D) For Every Job J That Has a Nonzeromentioning

confidence: 95%

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Davis

Gandhi

Kothari

2013

Operations Research Letters

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We study the problem of minimizing the weighted sum of completion times of jobs with release dates on a single machine with the aim of shedding new light on "the simplest [linear program] relaxation" [17]. Specifically, we analyze a 3-competitive online algorithm [16], using dual-fitting. In the offline setting, we develop a primal-dual algorithm with approximation guarantee 1 + √ 2. The latter implies that the cost of the optimal schedule is within a factor of 1 + √ 2 of the cost of the optimal LP solution.

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“…There are three commonly used approximation algorithms: response surface model, kriging model, and radial basis function neural network model [23] . As mentioned before, the scaling factor X 1 , X 2 , X 3 , X 4 of parameters C 1 , C 2 , K 1 , K 2 are chosen as the design variable, RMS of the boom roll angle and RMS of the boom center vibration displacement are used as the objective functions Y 1 , Y 2 respectively.…”

Section: Approximation Model For Predicting Objective Functionsmentioning

confidence: 99%

Design optimization and test for a pendulum suspension of the crop sprayer boom in dynamic conditions based on a six DOF motion simulator

Cui

Mao

Xue

et al. 2018

International Journal of Agricultural and Biological Engineering

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Spray deposit distribution from a field sprayer is mainly affected by the boom movements when the tractor is driven over a rough soil surface, the pendulum suspension that used to reduce and control the movement of spray boom by isolating the boom from vibrations of the tractor will directly enhance uniform deposition of chemicals. However, how to match the parameters of the suspension with the properties of the boom is the key problem. The dynamic rigid-flexible coupling model of the virtual prototype of the spray boom suspension system was established by using ADAMS and ABAQUS software. An optimization of the suspension parameters for a large spay boom was carried out based on the optimal Latin hypercube design, radial basis function neural network, and multi-objective genetic algorithm NSGA-II. After modified parameters of the suspension, the travel of the sprayer on a typical field motion track was simulated based on a six DOF motion simulator, and the dynamic behavior of the boom suspension was measured. The results show that RMS of the measured boom roll angle and the boom center displacement for optimized solution were reduced by 14.76% and 12.43% compared with the original suspension. Finally, the inertial measurement unit (IMU) was used to measure the movements of the sprayer vehicle during the pesticide application on the Hongze Lake Farm, the experiment of field condition reproduced by using the six DOF motion simulator, the standard deviation of the roll angle and vibration displacement for the optimized sprayer boom are only 0.6382° and 62.279 mm respectively. The research provides theoretical basis and experimental method for parameter optimization of large scale boom suspension.

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The Design of Approximation Algorithms

Cited by 848 publications

References 0 publications

Assortment Optimization Under Variants of the Nested Logit Model

Assortment Optimization Under Variants of the Nested Logit Model

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Design optimization and test for a pendulum suspension of the crop sprayer boom in dynamic conditions based on a six DOF motion simulator

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