Expert Systems and Mathematical Optimization Approaches on Physical Layout Optimization Problems

2000 ◽  
pp. 168-173
Author(s):  
Julio C. G. Pimentel ◽  
Yosef Gavriel ◽  
Éber A. Schmitz
Keyword(s):  
Expert Systems ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Layout Optimization ◽  
Physical Layout

scholarly journals On implicit variables in optimization theory

2021 ◽  
Vol Volume 2 (Original research articles) ◽  
Author(s):  
Matúš Benko ◽  
Patrick Mehlitz
Keyword(s):  
Optimization Problems ◽  
Constraint Qualifications ◽  
Optimization Theory ◽  
Mathematical Optimization ◽  
General Setting ◽  
Necessary Optimality Conditions ◽  
Detailed Comparison ◽  
Mordukhovich Stationarity ◽  
Stationarity Conditions ◽  
The One

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory. Comment: 34 pages

Mathematical Optimization by Using Particle Swarm Optimization, Genetic Algorithm, and Differential Evolution and Its Similarities

2021 ◽  
pp. 1-34
Author(s):  
Shailendra Aote ◽  
Mukesh M. Raghuwanshi
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Mathematical Optimization ◽  
Evolutionary Computing ◽  
Swarm Optimization

To solve the problems of optimization, various methods are provided in different domain. Evolutionary computing (EC) is one of the methods to solve these problems. Mostly used EC techniques are available like Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolution (DE). These techniques have different working structure but the inner working structure is same. Different names and formulae are given for different task but ultimately all do the same. Here we tried to find out the similarities among these techniques and give the working structure in each step. All the steps are provided with proper example and code written in MATLAB, for better understanding. Here we started our discussion with introduction about optimization and solution to optimization problems by PSO, GA and DE. Finally, we have given brief comparison of these.

scholarly journals Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

2019 ◽  
Author(s):  
Liang Wang ◽  
Xue Zhang ◽  
Filippo Zaniboni ◽  
Eugenio Oñate ◽  
Stefano Tinti
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Element Formulation ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Landslide Modeling ◽  
Element Method

AbstractNotwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

scholarly journals Multifeature Extreme Ordinal Ranking Machine for Facial Age Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhao ◽  
Han Wang ◽  
Guang-Bin Huang
Keyword(s):  
Age Estimation ◽  
Optimization Problems ◽  
State Of The Art ◽  
Mathematical Optimization ◽  
The State ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Training Process ◽  
Ordinal Ranking ◽  
Facial Age

Recently the state-of-the-art facial age estimation methods are almost originated from solving complicated mathematical optimization problems and thus consume huge quantities of time in the training process. To refrain from such algorithm complexity while maintaining a high estimation accuracy, we propose a multifeature extreme ordinal ranking machine (MFEORM) for facial age estimation. Experimental results clearly demonstrate that the proposed approach can sharply reduce the runtime (even up to nearly one hundred times faster) while achieving comparable or better estimation performances than the state-of-the-art approaches. The inner properties of MFEORM are further explored with more advantages.

Models and algorithms for fair layout optimization problems

2008 ◽  
Vol 179 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Albert E. Fernandes Muritiba ◽  
Manuel Iori ◽  
Silvano Martello ◽  
Marcos J. Negreiros Gomes
Keyword(s):  
Optimization Problems ◽  
Layout Optimization

scholarly journals Nonconvex and game theory optimization for resource allocation in wireless communications

2021 ◽  
Author(s):  
Kandasamy Illanko
Keyword(s):  
Wireless Communication ◽  
Power Allocation ◽  
Communication Systems ◽  
Optimization Problem ◽  
Polynomial Complexity ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mathematical Optimization ◽  
Simultaneous Optimization ◽  
Theoretical Development

Designing wireless communication systems that efficiently utilize the resources frequency spectrum and electric power, leads to problems in mathematical optimization. Most of these optimization problems are difficult to solve because the objective functions are nonconvex. While some problems remain unsolved, the solutions proposed in the literature for the others are of somewhat limited use because the algorithms are either unstable or have too high a computational complexity. This dissertation presents several stable algorithms, most of which have polynomial complexity, that solve five different nonconvex optimization problems in wireless communication. Two centralized and two distributed algorithms deal with the power allocation that maximizes the throughput in the Gaussian interference channel (GIC)with various constraints. The most valuable of these algorithms, the one with the minimum rate constraints became possible after a significant theoretical development in the dissertation that proves that the throughput of the GIC has a new generalized convex structure called invexity. The fifth algorithm has linear complexity, and finds the power allocation that maximizes the energy efficiency (EE) of OFDMA transmissions, for a given subchannel assignment. Some fundamental results regarding the power allocation are then used in the genetic algorithm for determining the subchannel allocation that maximizes the EE. Pricing for channel subleasing for ad-hoc wireless networks is considered next. This involves the simultaneous optimization of many functions that are interconnected through the variables involved. A composite game, a strategic game within a Stackelberg game, is used to solve this optimization problem with polynomial complexity. For each optimization problem solved, numerical results obtained using simulations that support the analysis and demonstrate the performance of the algorithms are presented.

scholarly journals A Comparative Study on Bio-Inspired Algorithms in Layout Optimization of Construction Site Facilities

2018 ◽  
Vol 20 (2) ◽  
pp. 102 ◽  
Author(s):  
Doddy Prayogo ◽  
Jessica Chandra Sutanto ◽  
Hieronimus Enrico Suryo ◽  
Samuel Eric
Keyword(s):  
Optimization Problems ◽  
Transportation Cost ◽  
Layout Optimization ◽  
Symbiotic Organisms Search ◽  
Bee Colony ◽  
Site Layout ◽  
Critical Attention ◽  
Engineering Problems ◽  
Symbiotic Organisms ◽  
Planning Problems

A good arrangement of site layout on a construction project is a fundamental component of the project’s efficiency. Optimization on site layout is necessary in order to reduce the transportation cost of resources or personnel between facilities. Recently, the use of bio-inspired algorithms has received considerable critical attention in solving the engineering optimization problem. These methods have consistently provided better performance than traditional mathematical-based methods to a variety of engineering problems. This study compares the performance of particle swarm optimization (PSO), artificial bee colony (ABC), and symbiotic organisms search (SOS) algorithms in optimizing site layout planning problems. Three real-world case studies of layout optimization problems have been used in this study. The results show that SOS has a better performance in comparison to the other algorithms. Thus, this study provides useful insights to construction practitioners in the industry who are involved in dealing with optimization problems

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