scholarly journals On Submodular Search and Machine Scheduling

2019 ◽  
Vol 44 (4) ◽  
pp. 1431-1449 ◽  
Author(s):  
Robbert Fokkink ◽  
Thomas Lidbetter ◽  
László A. Végh
Keyword(s):  
Total Curvature ◽  
Optimal Strategies ◽  
Concave Function ◽  
Scheduling Theory ◽  
Finite Set ◽  
Full Solution ◽  
Supermodular Function ◽  
Zero Sum ◽  
The Cost ◽  
Completion Times

Suppose that some objects are hidden in a finite set S of hiding places that must be examined one by one. The cost of searching subsets of S is given by a submodular function, and the probability that all objects are contained in a subset is given by a supermodular function. We seek an ordering of S that finds all the objects with minimal expected cost. This problem is NP-hard, and we give an efficient combinatorial 2-approximation algorithm, generalizing analogous results in scheduling theory. We also give a new scheduling application where a set of jobs must be ordered subject to precedence constraints to minimize the weighted sum of some concave function of the completion times of subsets of jobs. We go on to give better approximations for submodular functions with low total curvature, and we give a full solution when the problem is what we call series-parallel decomposable. Next, we consider a zero-sum game between a cost-maximizing hider and a cost-minimizing searcher. We prove that the equilibrium mixed strategies for the hider are in the base polyhedron of the cost function, suitably scaled, and we solve the game in the series-parallel decomposable case, giving approximately optimal strategies in other cases.

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

scholarly journals Modelling of the Impact of National Standardization on Duopolistic Competition in the Civil Aircraft Market

2020 ◽  
Vol 17 (4) ◽  
pp. 859-873
Author(s):  
E. V. Varyukhina ◽  
◽  
V. V. Klochkov ◽  
Keyword(s):  
Market Competition ◽  
Civil Aviation ◽  
Aviation Industry ◽  
Equilibrium Degree ◽  
Aviation Noise ◽  
Market Shares ◽  
Civil Aircraft ◽  
Zero Sum ◽  
The Cost ◽  
The Impact

The purpose of this study is to analyze standards as one of the main tools of protectionism in global markets of industrial goods. We use standards for modeling of market competition and adapt this approach for civil aviation markets. The role of local noise standards in civil aircraft markets is discussed. Imposition of more stringent aviation noise standards is modelled in the form of a two-person non-zero-sum game. Players are aircraft corporations that conduct research and development to reduce noise and lobby for stricter regulations in their controlled markets. The model can be used to predict that tighter aviation noise standards will be imposed and to justify the strategy of Russian aviation industry and science. The proposed approach can be adapted for other industries with strict regulations (in terms of safety, ecology). Such estimation allows us to assess whether it is in the country’s interests to participate in the standards race or not. It is shown that the equilibrium degree of standards tightening is higher if the players’ market shares are close to equal or individual players have advantages in the cost of production and/or product improvement is highly likely due to the company’s R&D progress.

OPTIMAL ENERGY DESIGN AND RETROFIT RECOMMENDATIONS FOR THE TURKISH BUILDING SECTOR

2021 ◽  
Vol 16 (1) ◽  
pp. 61-90
Author(s):  
Selçuk Sayin ◽  
Godfried Augenbroe
Keyword(s):  
Energy Saving ◽  
Large Scale ◽  
Optimal Strategies ◽  
Energy Performance ◽  
Optimization Approach ◽  
Investment Strategies ◽  
Single Family ◽  
Building Sector ◽  
Design Standards ◽  
The Cost

ABSTRACT This paper introduces methodologies and optimal strategies to reduce the energy consumption of the building sector with the aim to reduce global energy usage of a given .region or country. Many efforts are underway to develop investment strategies for large-scale energy retrofits and stricter energy design standards for existing and future buildings. This paper presents a study that informs these strategies in a novel way. It introduces support for the cost-optimized retrofits of existing, and design improvements of new buildings in Turkey with the aim to offer recommendations to individual building owners as well as guidance to the market. Three building types, apartment, single-family house and office are analyzed with a novel optimization approach. The energy performance of each type is simulated in five different climate regions of Turkey and four different vintages. For each vintage, the building is modelled corresponding to local Turkish regulations that applied at the time of construction. Optimum results are produced for different goals in terms of energy saving targets. The optimization results reveal that a 50% energy saving target is attainable for the retrofit and a 40% energy saving target is attainable for new design improvements for each building type in all climate regions.

Democratic Sovereignty and Transnational Law

2017 ◽  
pp. 21-46
Author(s):  
Seyla Benhabib
Keyword(s):  
Human Rights ◽  
International Treaties ◽  
International Human Rights ◽  
Legal Norms ◽  
Global Constitutionalism ◽  
International Human ◽  
The One ◽  
Human Rights Norms ◽  
Zero Sum ◽  
The Cost

Critics of legal cosmopolitanism and global constitutionalism have often pointed to an alleged zero-sum conflict between democratic sovereignty and a particular class of international legal norms: those pertaining to human rights. It is undeniable that there exist tensions between the application of, and compliance with, human rights norms in domestic contexts, on the one hand, and international treaties and covenants, on the other. Benhabib develops a conceptual and empirical model for understanding these tensions not as a zero-sum game, but rather as a process of dialectical norm-enhancement and interpretation. Her thesis is that compliance with international human rights norms does not come at the cost of, but rather reinforces, democratic sovereignty.

scholarly journals Simplified Sensorless Current Predictive Control of Synchronous Reluctance Motor Using Online Parameter Estimation

Energies ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 492 ◽  
Author(s):  
Ahmed Farhan ◽  
Mohamed Abdelrahem ◽  
Amr Saleh ◽  
Adel Shaltout ◽  
Ralph Kennel
Keyword(s):  
Parameter Estimation ◽  
Predictive Control ◽  
Operating Conditions ◽  
Parameter Mismatch ◽  
Speed Controller ◽  
Synchronous Reluctance Motor ◽  
Reluctance Motor ◽  
Finite Set ◽  
Insufficient Response ◽  
The Cost

In this paper, a simplified efficient method for sensorless finite set current predictive control (FSCPC) for synchronous reluctance motor (SynRM) based on extended Kalman filter (EKF) is proposed. The proposed FSCPC is based on reducing the computation burden of the conventional FSCPC by using the commanded reference currents to directly calculate the reference voltage vector (RVV). Therefore, the cost function is calculated for only three times and the necessity to test all possible voltage vectors will be avoided. For sensorless control, EKF is composed to estimate the position and speed of the rotor. Whereas the performance of the proposed FSCPC essentially necessitates the full knowledge of SynRM parameters and provides an insufficient response under the parameter mismatch between the controller and the motor, online parameter estimation based on EKF is combined in the proposed control strategy to estimate all parameters of the machine. Furthermore, for simplicity, the parameters of PI speed controller and initial values of EKF covariance matrices are tuned offline using Particle Swarm Optimization (PSO). To demonstrate the feasibility of the proposed control, it is implemented in MATLAB/Simulink and tested under different operating conditions. Simulation results show high robustness and reliability of the proposed drive.

PIVOTING ALGORITHMS FOR SOME CLASSES OF STOCHASTIC GAMES: A SURVEY

2001 ◽  
Vol 03 (02n03) ◽  
pp. 253-281 ◽  
Author(s):  
S. R. MOHAN ◽  
S. K. NEOGY ◽  
T. PARTHASARATHY
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Linear Complementarity ◽  
Dual Simplex Method ◽  
Special Cases ◽  
Dual Simplex ◽  
Finite Step ◽  
Zero Sum

In this paper, we survey the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies of the players for special cases of nonzero-sum stochastic games, using finite-step algorithms based on pivoting. Examples of finite-step pivoting algorithms are the various simplex-type algorithms, such as the primal simplex or dual simplex method for solving the linear programming problem or Lemke's or Lemke-Howson's algorithm for solving the linear complementarity problem. Also included are Lemke-type algorithms for solving various generalisations of the linear complementarity problem. The survey also includes a few new results and observations.

Dual-Issue Final-Offer Arbitration: Invariance of Pure Optimal Strategies Under Lp Metrics

2019 ◽  
Vol 21 (04) ◽  
pp. 1950011
Author(s):  
Brian R. Powers
Keyword(s):  
Normal Distribution ◽  
Optimal Strategies ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal ◽  
Final Offer ◽  
Pure Strategies ◽  
Zero Sum

We consider a final-offer arbitration problem between two players with two quantitative issues in dispute. We model the problem as a zero-sum game where the arbiter’s opinion is drawn from a bivariate normal distribution and derive the only possible pure strategies regardless of the choice of [Formula: see text] metric used by the arbiter.

scholarly journals Solving the Asymmetry Multi-Objective Optimization Problem in PPPs under LPVR Mechanism by Bi-Level Programing

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1667
Author(s):  
Feiran Liu ◽  
Jun Liu ◽  
Xuedong Yan
Keyword(s):  
Optimization Problem ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Present Value ◽  
Public And Private ◽  
The Public ◽  
Multi Objective ◽  
The Cost

Optimizing the cost and benefit allocation among multiple players in a public-private partnership (PPP) project is recognized to be a multi-objective optimization problem (MOP). When the least present value of revenue (LPVR) mechanism is adopted in the competitive procurement of PPPs, the MOP presents asymmetry in objective levels, control variables and action orders. This paper characterizes this asymmetrical MOP in Stackelberg theory and builds a bi-level programing model to solve it in order to support the decision-making activities of both the public and private sectors in negotiation. An intuitive algorithm based on the non-dominated sorting genetic algorithm III (NSGA III) framework is designed to generate Pareto solutions that allow decision-makers to choose optimal strategies from their own criteria. The effectiveness of the model and algorithm is validated via a real case of a highway PPP project. The results reveal that the PPP project will be financially infeasible without the transfer of certain amounts of exterior benefits into supplementary income for the private sector. Besides, the strategy of transferring minimum exterior benefits is more beneficial to the public sector than to users.

Optimal strategies in a risk selection investment model

2000 ◽  
Vol 32 (02) ◽  
pp. 518-539
Author(s):  
David Assaf ◽  
Yuliy Baryshnikov ◽  
Wolfgang Stadje
Keyword(s):  
Optimal Strategies ◽  
Concave Function ◽  
Investment Model ◽  
Interarrival Time ◽  
Objective Functions ◽  
Constant Rate ◽  
Optimal Value ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Interarrival Times

We study the following stochastic investment model: opportunities occur randomly over time, following a renewal process with mean interarrival time d, and at each of them the decision-maker can choose a distribution for an instantaneous net gain (or loss) from the set of all probability measures that have some prespecified expected value e and for which his maximum possible loss does not exceed his current capital. Between the investments he spends money at some constant rate. The objective is to avoid bankruptcy as long as possible. For the case e>d we characterize a strategy maximizing the probability that ruin never occurs. It is proved that the optimal value function is a concave function of the initial capital and uniquely determined as the solution of a fixed point equation for some intricate operator. In general, two-point distributions suffice; furthermore, we show that the cautious strategy of always taking the deterministic amount e is optimal if the interarrival times are hyperexponential, and, in the case of bounded interarrival times, is optimal ‘from some point on’, i.e. whenever the current capital exceeds a certain threshold. In the case e = 0 we consider a class of natural objective functions for which the optimal strategies are non-stationary and can be explicitly determined.

A hide–search game

1981 ◽  
Vol 18 (3) ◽  
pp. 628-640 ◽  
Author(s):  
Eduardo J. Subelman
Keyword(s):  
Optimal Strategies ◽  
Linear Program ◽  
The Other ◽  
Efficient Computation ◽  
Search Game ◽  
Expected Time ◽  
Zero Sum

We consider a game in which one player hides a ball in one of n boxes and the other player is allowed to search for it. There are known probabilities that the searcher will overlook the ball if he searches the correct box. The hider wishes to minimize and the searcher to maximize the probability that the ball will be found in m or fewer searches. We exhibit a procedure which allows efficient computation of optimal strategies for both players without solving the game as a linear program. The results are extended to a non-zero-sum game where the searcher's objective is to minimize the expected time until the ball is found.

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