scholarly journals Stackelberg Population Dynamics: A Predictive-Sensitivity Approach

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 88
Author(s):  
Eduardo Mojica-Nava ◽  
Fredy Ruiz
Keyword(s):  
Population Dynamics ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Social Systems ◽  
Energy Resource ◽  
Bilevel Optimization ◽  
Stackelberg Equilibrium ◽  
Coordination Problem ◽  
Gradient Descent Algorithm ◽  
Population Equilibrium

Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play. In general, this problem can be modeled as a leader–follower Stackelberg equilibrium problem using a mathematical program with equilibrium constraints. We propose two interconnected dynamical systems to dynamically solve a bilevel optimization problem between a leader and follower population in a single time scale by a predictive-sensitivity conditioning interconnection. For the leader’s optimization problem, we developed a gradient descent algorithm based on the total derivative, and for the followers’ optimization problem, we used the population dynamics framework to model a population of interacting strategic agents. We extended the concept of the Stackelberg population equilibrium to the differential Stackelberg population equilibrium for population dynamics. Theoretical guarantees for the stability of the proposed Stackelberg population learning dynamics are presented. Finally, a distributed energy resource coordination problem is solved via pricing dynamics based on the proposed approach. Some simulation experiments are presented to illustrate the effectiveness of the framework.

scholarly journals A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 377
Author(s):  
Nimit Nimana
Keyword(s):  
Fixed Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Splitting Method ◽  
Optimal Solution ◽  
Bilevel Optimization ◽  
Convergence Properties ◽  
Nonlinear Operators ◽  
Convex Optimization Problems ◽  
Feasible Points

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

Multiple optimization and segmentation technique (MOST) for large-scale bilevel life cycle optimization

2011 ◽  
Vol 38 (3) ◽  
pp. 263-271 ◽  
Author(s):  
Tarek Hegazy ◽  
Ahmed Elhakeem
Keyword(s):  
Life Cycle ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Scale Problem ◽  
Segmentation Technique ◽  
Building Components ◽  
Life Cycle Optimization ◽  
New Formulation

This paper introduces a new formulation for large-scale combinatorial bilevel optimization problems that involve integer, discrete, two-level decisions. The most vivid example where the new technique most applies is the life cycle optimization needed to allocate repair types and repair timings to a number of infrastructure assets (e.g., building components). Combining these decisions into a single optimization for hundreds of assets simultaneously makes the optimization problem complex and prohibitive. For such a large-scale problem, a multiple optimization and segmentation technique (MOST) is proposed to handle the optimization one level at a time through a series of small-size optimizations that can be solved easily. The performance of MOST has been validated on various problem sizes and proved to be innovative and can handle thousands of variables simultaneously.

scholarly journals Proximal Gradient Method for Solving Bilevel Optimization Problems

2020 ◽  
Vol 25 (4) ◽  
pp. 66
Author(s):  
Seifu Endris Yimer ◽  
Poom Kumam ◽  
Anteneh Getachew Gebrie
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Split Feasibility Problem ◽  
Bilevel Optimization ◽  
Feasibility Problem ◽  
Proximal Gradient Method ◽  
Level Problem ◽  
Upper Level ◽  
The Split Feasibility Problem

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.

A microbial treatment population dynamics optimization approach

2021 ◽  
pp. 1-15
Author(s):  
Jinding Gao
Keyword(s):  
Population Dynamics ◽  
Information Exchange ◽  
Information Diffusion ◽  
Optimization Problems ◽  
Microbial Control ◽  
Function Optimization ◽  
Optimization Approach ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Number Of Individuals

In order to solve some function optimization problems, Population Dynamics Optimization Algorithm under Microbial Control in Contaminated Environment (PDO-MCCE) is proposed by adopting a population dynamics model with microbial treatment in a polluted environment. In this algorithm, individuals are automatically divided into normal populations and mutant populations. The number of individuals in each category is automatically calculated and adjusted according to the population dynamics model, it solves the problem of artificially determining the number of individuals. There are 7 operators in the algorithm, they realize the information exchange between individuals the information exchange within and between populations, the information diffusion of strong individuals and the transmission of environmental information are realized to individuals, the number of individuals are increased or decreased to ensure that the algorithm has global convergence. The periodic increase of the number of individuals in the mutant population can greatly increase the probability of the search jumping out of the local optimal solution trap. In the iterative calculation, the algorithm only deals with 3/500∼1/10 of the number of individual features at a time, the time complexity is reduced greatly. In order to assess the scalability, efficiency and robustness of the proposed algorithm, the experiments have been carried out on realistic, synthetic and random benchmarks with different dimensions. The test case shows that the PDO-MCCE algorithm has better performance and is suitable for solving some optimization problems with higher dimensions.

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

scholarly journals Use of a spatially explicit individual-based model to predict population trajectories and habitat connectivity for a reintroduced ursid

Oryx ◽  
2021 ◽  
pp. 1-10
Author(s):  
Desiree Andersen ◽  
Yoonjung Yi ◽  
Amaël Borzée ◽  
Kyungmin Kim ◽  
Kwang-Seon Moon ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Radio Telemetry ◽  
Suitable Habitat ◽  
Large Carnivores ◽  
Environmental Interactions ◽  
Dispersal Capability ◽  
The Republic ◽  
Suitable Habitats ◽  
Mixed Modelling ◽  
Population Equilibrium

Abstract Reintroductions of large carnivore species present unique opportunities to model population dynamics as populations can be monitored from the beginning of a reintroduction. However, analysis of the population dynamics of such reintroduced populations is rare and may be limited in incorporating the complex movements and environmental interactions of large carnivores. Starting in 2004, Asiatic black bears Ursus thibetanus were reintroduced and tracked in the Republic of Korea, along with their descendants, using radio telemetry, yielding 33,924 tracking points over 12 years. Along with information about habitat use, landscape, and resource availability, we estimated the population equilibrium and dispersal capability of the reintroduced population. We used a mixed modelling approach to determine suitable habitat areas, population equilibria for three different resources-based scenarios, and least-cost pathways (i.e. corridors) for dispersal. Our population simulations provided a mean population equilibrium of 64 individuals at the original reintroduction site and a potential maximum of 1,438 individuals in the country. The simulation showed that the bear population will disperse to nearby mountainous areas, but a second reintroduction will be required to fully restore U. thibetanus. Northern suitable habitats are currently disconnected and natural re-population is unlikely to happen unless supported. Our methodologies and findings are also relevant for determining the outcome and trajectories of reintroduced populations of other large carnivores.

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.

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

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