scholarly journals Stochastic Submodular Maximization with Performance-Dependent Item Costs

2019 ◽  
Vol 33 ◽  
pp. 1485-1494
Author(s):  
Takuro Fukunaga ◽  
Takuya Konishi ◽  
Sumio Fujita ◽  
Ken-ichi Kawarabayashi
Keyword(s):  
Objective Function ◽  
Adaptive Algorithm ◽  
Numerical Experiments ◽  
Adaptive Algorithms ◽  
Budget Constraint ◽  
Maximization Problem ◽  
Maximum Value ◽  
Objective Value ◽  
The Cost ◽  
Submodular Maximization

We formulate a new stochastic submodular maximization problem by introducing the performance-dependent costs of items. In this problem, we consider selecting items for the case where the performance of each item (i.e., how much an item contributes to the objective function) is decided randomly, and the cost of an item depends on its performance. The goal of the problem is to maximize the objective function subject to a budget constraint on the costs of the selected items. We present an adaptive algorithm for this problem with a theoretical guaran-√ tee that its expected objective value is at least (1−1/ 4 e)/2 times the maximum value attained by any adaptive algorithms. We verify the performance of the algorithm through numerical experiments.

Two-stage submodular maximization problem beyond nonnegative and monotone

2021 ◽  
pp. 1-16
Author(s):  
Zhicheng Liu ◽  
Hong Chang ◽  
Ran Ma ◽  
Donglei Du ◽  
Xiaoyan Zhang
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Objective Function ◽  
Modular Function ◽  
Submodular Function ◽  
Maximization Problem ◽  
Cardinality Constraint ◽  
Two Stage ◽  
Time Efficiency ◽  
Submodular Maximization

Abstract We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

scholarly journals Optimal Bidding Strategy for Brand Advertising

2018 ◽  
Author(s):  
Takanori Maehara ◽  
Atsuhiro Narita ◽  
Jun Baba ◽  
Takayuki Kawabata
Keyword(s):  
Objective Function ◽  
Real World ◽  
Maximization Problem ◽  
Memory Retention ◽  
Real World Data ◽  
Real World Setting ◽  
Brand Advertising ◽  
Online Setting ◽  
Optimal Bidding ◽  
Submodular Maximization

Brand advertising is a type of advertising that aims at increasing the awareness of companies or products. This type of advertising is well studied in economic, marketing, and psychological literature; however, there are no studies in the area of computational advertising because the effect of such advertising is difficult to observe. In this study, we consider a real-time biding strategy for brand advertising. Here, our objective to maximizes the total number of users who remember the advertisement, averaged over the time. For this objective, we first introduce a new objective function that captures the cognitive psychological properties of memory retention, and can be optimized efficiently in the online setting (i.e., it is a monotone submodular function). Then, we propose an algorithm for the bid optimization problem with the proposed objective function under the second price mechanism by reducing the problem to the online knapsack constrained monotone submodular maximization problem. We evaluated the proposed objective function and the algorithm in a real-world data collected from our system and a questionnaire survey. We observed that our objective function is reasonable in real-world setting, and the proposed algorithm outperformed the baseline online algorithms.

Developing Schedule With Linear Programming (Case Study: STTF II Project Komplek Sukamukti Banjaran)

2020 ◽  
Vol 4 (02) ◽  
pp. 34-45
Author(s):  
Naufal Dzikri Afifi ◽  
Ika Arum Puspita ◽  
Mohammad Deni Akbar
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Project Scheduling ◽  
Time Limit ◽  
Minimum Time ◽  
Service Cost ◽  
Trade Off ◽  
Overtime Work ◽  
The Cost

Shift to The Front II Komplek Sukamukti Banjaran Project is one of the projects implemented by one of the companies engaged in telecommunications. In its implementation, each project including Shift to The Front II Komplek Sukamukti Banjaran has a time limit specified in the contract. Project scheduling is an important role in predicting both the cost and time in a project. Every project should be able to complete the project before or just in the time specified in the contract. Delay in a project can be anticipated by accelerating the duration of completion by using the crashing method with the application of linear programming. Linear programming will help iteration in the calculation of crashing because if linear programming not used, iteration will be repeated. The objective function in this scheduling is to minimize the cost. This study aims to find a trade-off between the costs and the minimum time expected to complete this project. The acceleration of the duration of this study was carried out using the addition of 4 hours of overtime work, 3 hours of overtime work, 2 hours of overtime work, and 1 hour of overtime work. The normal time for this project is 35 days with a service fee of Rp. 52,335,690. From the results of the crashing analysis, the alternative chosen is to add 1 hour of overtime to 34 days with a total service cost of Rp. 52,375,492. This acceleration will affect the entire project because there are 33 different locations worked on Shift to The Front II and if all these locations can be accelerated then the duration of completion of the entire project will be effective

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

scholarly journals Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yaoxin Li ◽  
Jing Liu ◽  
Guozheng Lin ◽  
Yueyuan Hou ◽  
Muyun Mou ◽  
...  
Keyword(s):  
Objective Function ◽  
Statistical Physics ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Independent Set ◽  
Computational Social Science ◽  
Maximization Problem ◽  
Maximum Independent Set ◽  
Gradient Descent Algorithm

AbstractIn computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

Comparison of SVC and TCSC Installation in Transmission Line with Loss Minimization and Cost of Installation via Particle Swarm Optimization

2015 ◽  
Vol 785 ◽  
pp. 495-499
Author(s):  
Siti Amely Jumaat ◽  
Ismail Musirin
Keyword(s):  
Particle Swarm Optimization ◽  
Transmission Line ◽  
Objective Function ◽  
Transmission Loss ◽  
Particle Swarm ◽  
Static Var Compensator ◽  
Loss Minimization ◽  
Swarm Optimization ◽  
The Cost ◽  
Thyristor Controlled Series Compensator

The paper presents a comparison of performance Static Var Compensator (SVC) and Thyristor Controlled Series Compensator (TCSC) with objective function to minimize the transmission loss, improve the voltage and monitoring the cost of installation. Simulation performed on standard IEEE 30-Bus RTS and indicated that EPSO a feasible to achieve the objective function.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals Optimized Placement of Connecting the Distributed Generationswork Stand Alone to Improve the Distribution Systems Reliability

2013 ◽  
Vol 64 (2) ◽  
pp. 76-83
Author(s):  
Hamed Hashemi-Dezaki ◽  
Ali Agheli ◽  
Behrooz Vahidi ◽  
Hossein Askarian-Abyaneh
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
System Reliability ◽  
Distribution Systems ◽  
Analytical Approach ◽  
Distributed Generations ◽  
Joint Point ◽  
Cost Of Energy ◽  
Optimum Solution ◽  
The Cost

The use of distributed generations (DGs) in distribution systems has been common in recent years. Some DGs work stand alone and it is possible to improve the system reliability by connecting these DGs to system. The joint point of DGs is an important parameter in the system designing. In this paper, a novel methodology is proposed to find the optimum solution in order to make a proper decision about DGs connection. In the proposed method, a novel objective function is introduced which includes the cost of connector lines between DGs and network and the cost of energy not supplied (CENS) savings. Furthermore, an analytical approach is used to calculate the CENS decrement. To solve the introduced nonlinear optimization programming, the genetic algorithm (GA) is used. The proposed method is applied to a realistic 183-bus system of Tehran Regional Electrical Company (TREC). The results illustrate the effectiveness of the method to improve the system reliability by connecting the DGs work stand alone in proper placements.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

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