scholarly journals Game with a random second player and its application to the problem of optimal fare choice

2021 ◽  
Vol 57 ◽  
pp. 170-180
Author(s):  
G.A. Timofeeva ◽  
D.S. Zavalishchin
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Optimal Strategies ◽  
Random Parameter ◽  
Decision Makers ◽  
Stackelberg Equilibrium ◽  
Deterministic Solution ◽  
Mathematical Formalization ◽  
Probabilistic Solution ◽  
Mode Of Transport

The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of decision makers. The strategies of the players that ensure the Stackelberg equilibrium are studied. The strategy of the second player is formalized as a probabilistic solution to an optimization problem with an objective function depending on a continuously distributed random parameter. In many cases, the choice of optimal strategies takes place in conditions when there are many decision makers, and each of them chooses a decision based on his (her) criterion. The mathematical formalization of such problems leads to the study of probabilistic solutions to problems with an objective function depending on a random parameter. In particular, probabilistic solutions are used for mathematical describing the passenger's choice of a mode of transport. The problem of optimal fare choice for a new route based on a probabilistic model of passenger preferences is considered. In this formalization, the carrier that sets the fare is treated as the first player; the set of passengers is treated as the second player. The second player's strategy is formalized as a probabilistic solution to an optimization problem with a random objective function. A model example is considered.

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.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

ROBUST INTERVAL-BASED MINIMAX-REGRET ANALYSIS METHOD FOR FILTER MANAGEMENT OF FLUID POWER SYSTEM

2013 ◽  
Vol 30 (06) ◽  
pp. 1350021
Author(s):  
SONGLIN NIE ◽  
HUI JI ◽  
YEQING HUANG ◽  
ZHEN HU ◽  
YONGPING LI
Keyword(s):  
Power System ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Fluid Power ◽  
Maintenance Cost ◽  
Minimax Regret ◽  
Fluid Power System ◽  
System Maintenance ◽  
Management Alternatives

Fluid contamination is one of the main reasons for the wear failure and the related downtime in a hydraulic power system. Filters play an important role in controlling the contamination effectively, increasing the reliability of the system, and maintaining the system economically. Due to the uncertainties of system parameters, the complicated relationship among components, as well as the lack of effective approach, managing filters is becoming one of the biggest challenges for engineers and decision makers. In this study, a robust interval-based minimax-regret analysis (RIMA) method is developed for the filter management in a fluid power system (FPS) under uncertainty. The RIMA method can handle the uncertainties existed in contaminant ingressions of the system and contaminant holding capacity of filters without making assumption on probabilistic distributions for random variables. Through analyzing the system cost of all possible filter management alternatives, an interval element regret matrix can be obtained, which enables decision makers to identify the optimal filter management strategy under uncertainty. The results of a case study indicate that the reasonable solutions generated can help decision makers understand the consequence of short-term and long-term decisions, identify optimal strategies for filter allocation and selection with minimized system-maintenance cost and system-failure risk.

scholarly journals Nonnegative Signal Decomposition with Supervision

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Teng Li ◽  
Huan Chang ◽  
Jun Wu
Keyword(s):  
Objective Function ◽  
Image Classification ◽  
Pattern Classification ◽  
Optimization Problem ◽  
Real Data ◽  
Classification Performance ◽  
Signal Decomposition ◽  
Weak Supervision ◽  
Training Samples ◽  
Novel Algorithm

This paper presents a novel algorithm to numerically decompose mixed signals in a collaborative way, given supervision of the labels that each signal contains. The decomposition is formulated as an optimization problem incorporating nonnegative constraint. A nonnegative data factorization solution is presented to yield the decomposed results. It is shown that the optimization is efficient and decreases the objective function monotonically. Such a decomposition algorithm can be applied on multilabel training samples for pattern classification. The real-data experimental results show that the proposed algorithm can significantly facilitate the multilabel image classification performance with weak supervision.

Multi-Attribute Group Decision Making Method for Preference Conflicting with Heterogeneous Information

2018 ◽  
Vol 7 (4) ◽  
pp. 1-14 ◽  
Author(s):  
Kai-Rong Liang
Keyword(s):  
Decision Making ◽  
Objective Function ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Heterogeneous Information ◽  
Multi Objective ◽  
Attribute Weights ◽  
Relative Closeness ◽  
Decision Making Model

The aim of this article is to propose a multi-objective decision-making method for researching and solving multi-attribute heterogeneous group decision-making problems. This is in the case that the characters of the decision information and decision makers' preferences are heterogeneous, and the weight information is incomplete. In this method, the multi-objective decision-making model, which considers the alternatives decision relative closeness and the preference of heterogeneous degree of decision makers in the objective function, is put forward. In addition, this article uses the minimax method to derive the multi-objective decision-making model and obtain the attribute weights and decision makers weights, and then the optimal scheme is established. Finally, an illustrative example shows the effectiveness of the proposed method.

scholarly journals Optimal design of a DC MHD pump by simulated annealing method

2014 ◽  
Vol 11 (2) ◽  
pp. 339-350
Author(s):  
Khadidja Bouali ◽  
Fatima Kadid ◽  
Rachid Abdessemed
Keyword(s):  
Simulated Annealing ◽  
Optimal Design ◽  
Objective Function ◽  
Design Problem ◽  
Design Methodology ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Simulated Annealing Method ◽  
Direct Interpretation ◽  
Annealing Method

In this paper a design methodology of a magnetohydrodynamic pump is proposed. The methodology is based on direct interpretation of the design problem as an optimization problem. The simulated annealing method is used for an optimal design of a DC MHD pump. The optimization procedure uses an objective function which can be the minimum of the mass. The constraints are both of geometrics and electromagnetic in type. The obtained results are reported.

scholarly journals Table cartogram generation as an optimization problem

2019 ◽  
Vol 1 ◽  
pp. 1-2 ◽  
Author(s):  
Mao Li ◽  
Ryo Inoue
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Optimization Problem ◽  
Data Representation ◽  
Linear Least Squares ◽  
Original Table ◽  
Outer Border ◽  
Limited Degree ◽  
The Difference ◽  
Operation Results

<p><strong>Abstract.</strong> A table cartogram, visualization of table-form data, is a rectangle-shaped table in which each cell is transformed to express the magnitude of positive weight by its area while maintaining the adjacency relationship of cells in the original table. Winter (2011) applies an area cartogram generation method of Gastner and Newman (2004) for their generation, and Evans et al. (2018) proposes a new geometric procedure. The rows and columns on a table cartogram should be easily recognized by readers, however, no methods have focused to enhance the readability. This study proposes a method that defines table cartogram generation as an optimization problem and attempts to minimize vertical and horizontal deformation. Since the original tables are comprised of regular quadrangles, this study uses quadrangles to express cells in a table cartogram and fixes the outer border to attempt to retain the shape of a standard table.</p><p>This study proposes a two-step approach for table cartogram generation with cells that begin as squares and with fixed outer table borders. The first step only adjusts the vertical and horizontal borders of cells to express weights to the greatest possible degree. All cells maintain their rectangular shape after this step, although the limited degree of freedom of this operation results in low data representation accuracy. The second step adapts the cells of the low-accuracy table cartogram to accurately fit area to weight by relaxing the constraints on the directions of borders of cells. This study utilizes an area cartogram generation method proposed by Inoue and Shimizu (2006), which defines area cartogram generation as an optimization problem. The formulation with vertex coordinate parameters consists of an objective function that minimizes the difference between the given data and size of each cell, and a regularization term that controls the changes of bearing angles. It is formulated as non-linear least squares, and is solved through the iteration of linear least squares by linearizing the problem at the coordinates of vertices and updating the estimated coordinates until the value of the objective function becomes small enough.</p>

scholarly journals Optimizing community detection in social networks using antlion and K-median

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Amany A. Naem ◽  
Neveen I. Ghali
Keyword(s):  
Social Networks ◽  
Objective Function ◽  
Community Detection ◽  
Optimization Problem ◽  
Real Life ◽  
Optimization Methods ◽  
Population Based ◽  
Detection Problem ◽  
Network Communities ◽  
Antlion Optimization

Antlion Optimization (ALO) is one of the latest population based optimization methods that proved its good performance in a variety of applications. The ALO algorithm copies the hunting mechanism of antlions to ants in nature. Community detection in social networks is conclusive to understanding the concepts of the networks. Identifying network communities can be viewed as a problem of clustering a set of nodes into communities. k-median clustering is one of the popular techniques that has been applied in clustering. The problem of clustering network can be formalized as an optimization problem where a qualitatively objective function that captures the intuition of a cluster as a set of nodes with better in ternal connectivity than external connectivity is selected to be optimized. In this paper, a mixture antlion optimization and k-median for solving the community detection problem is proposed and named as K-median Modularity ALO. Experimental results which are applied on real life networks show the ability of the mixture antlion optimization and k-median to detect successfully an optimized community structure based on putting the modularity as an objective function.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

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