Numerical Probabilistic Approach for Optimization Problems

2016 ◽  
pp. 43-53 ◽  
Author(s):  
Boris Dobronets ◽  
Olga Popova
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach

scholarly journals A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ehtasham ul Haq ◽  
Ishfaq Ahmad ◽  
Ibrahim M. Almanjahie
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Diversity ◽  
Test Problems ◽  
Crossover Operator ◽  
Local Optima ◽  
Mutation Operators ◽  
Multiple Comparison Test ◽  
Power Mutation ◽  
Real Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

scholarly journals Probabilistic approach in solving an optimization problem with application to in physical and technical systems

2021 ◽  
Vol 2131 (2) ◽  
pp. 022125
Author(s):  
N A Saifutdinova
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Probabilistic Approach ◽  
Optimization Models ◽  
Optimal Value ◽  
Stochastic Parameters ◽  
Technical Systems ◽  
Distribution Type ◽  
Nonlinear Objective Function

Abstract The article considers some optimization models with a nonlinear objective function and constraints in the form of equalities and inequalities. The model is considered in two forms – deterministic and stochastic, which allows it to be used to solve various optimization problems in physical and technical systems. The presented stochastic model is based on the inclusion of stochastic parameters into the well-known Cobb-Douglas function. The influence of stochastic variables on the optimal value of the objective function, depending on their distribution type, is analyzed.

Sensitivity Analysis of Cylinder Head Fatigue Life Prediction Using Statistical Models

2014 ◽  
Author(s):  
Christoph Szasz ◽  
Sven Lauer
Keyword(s):  
Sensitivity Analysis ◽  
Cylinder Head ◽  
Information Quality ◽  
Development Process ◽  
Optimization Problems ◽  
Combustion Engine ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Variable Loading ◽  
Worst Case

For the efficient virtual development of combustion engine cylinder heads in terms of high cycle fatigue (HCF) it is highly important to have a reliable development process that represents reality in the best possible way. Most of today’s standard HCF procedures are capable of delivering high quality results for a specific load combination. However, loads are usually subject to variation. This is also valid for loads the cylinder head is subjected to. Assembly loads and operating loads considered during the virtual development process are widely determined by the production process which again is subject to variation due to certain tolerances, wear of the tooling equipment etc. As it is highly important to ensure the fatigue design of a cylinder head, there is the need for new analysis models capable of capturing every possible load variation. Within the framework of this paper the influence of different variable loading parameters on the cylinder head HCF margin of a heavy duty diesel engine will be discussed. A design of experiments (DoE) analysis is used together with the 3-d finite element method (FEM) for the investigations. Furthermore a methodology for the probabilistic assessment of the cylinder head HCF margin based on stochastic loading data is introduced. At the same time an effective methodology for the identification of the worst case boundary conditions for HCF analysis will be presented. With the presented probabilistic method it is possible to achieve a highly accurate prediction of the HCF design margin. Due to the probabilistic approach a better understanding of the entire system is possible, as the interaction between input and output parameters can be illustrated. Therefore HCF optimization problems can be encountered more effectively. Furthermore the presented methodology can be used for error estimation of analysis results and assessment of the result sensitivity. Thus, a borderline layout of the cylinder head can be achieved. Also the minimum input information quality, which is required for a profound HCF analysis, can be assessed by using the sensitivity analysis presented. Therefore the proposed methods enable a fast and reliable development of cylinder heads and other combustion engine components.

Probabilistic approach for shape optimization problems in contact mechanics

2010 ◽  
Vol 43 (1) ◽  
pp. 99-106
Author(s):  
Nikolai V. Banichuk ◽  
Francesco Ragnedda ◽  
Mauro Serra
Keyword(s):  
Shape Optimization ◽  
Contact Mechanics ◽  
Optimization Problems ◽  
Probabilistic Approach

Dynamic Swarm Artificial Bee Colony Algorithm

2012 ◽  
Vol 3 (4) ◽  
pp. 19-33 ◽  
Author(s):  
Harish Sharma ◽  
Jagdish Chand Bansal ◽  
K. V. Arya ◽  
Kusum Deep
Keyword(s):  
Global Optimization ◽  
Real World ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Based ◽  
Test Problems ◽  
Local Optima ◽  
Bee Colony

Artificial Bee Colony (ABC) optimization algorithm is relatively a simple and recent population based probabilistic approach for global optimization. ABC has been outperformed over some Nature Inspired Algorithms (NIAs) when tested over test problems as well as real world optimization problems. This paper presents an attempt to modify ABC to make it less susceptible to stick at local optima and computationally efficient. In the case of local convergence, addition of some external potential solutions may help the swarm to get out of the local valley and if the algorithm is taking too much time to converge then deletion of some swarm members may help to speed up the convergence. Therefore, in this paper a dynamic swarm size strategy in ABC is proposed. The proposed strategy is named as Dynamic Swarm Artificial Bee Colony algorithm (DSABC). To show the performance of DSABC, it is tested over 16 global optimization problems of different complexities and a popular real world optimization problem namely Lennard-Jones potential energy minimization problem. The simulation results show that the proposed strategies outperformed than the basic ABC and three recent variants of ABC, namely, the Gbest-Guided ABC, Best-So-Far ABC and Modified ABC.

scholarly journals Cemracs 2017: numerical probabilistic approach to MFG

2019 ◽  
Vol 65 ◽  
pp. 84-113
Author(s):  
Andrea Angiuli ◽  
Christy V. Graves ◽  
Houzhi Li ◽  
Jean-François Chassagneux ◽  
François Delarue ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Continuation Method ◽  
Large Population ◽  
Probabilistic Approach ◽  
Mean Field ◽  
Picard Iteration ◽  
Mean Field Games ◽  
Benchmark Problems ◽  
Control Problems ◽  
Great Success

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.

Comparison of Meta-heuristic Algorithms on Benchmark Functions

2019 ◽  
Vol 2 (3) ◽  
pp. 508-517
Author(s):  
FerdaNur Arıcı ◽  
Ersin Kaya
Keyword(s):  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Time Interval ◽  
Bee Colony ◽  
Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC’17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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