Asymptotic convergence of genetic algorithms

1998 ◽  
Vol 30 (02) ◽  
pp. 521-550 ◽  
Author(s):  
Raphaël Cerf
Keyword(s):  
Genetic Algorithms ◽  
Population Size ◽  
Fitness Function ◽  
Evolutionary Process ◽  
Asymptotic Convergence ◽  
Homogeneous Case ◽  
Selection Scheme ◽  
Convergence Results ◽  
Asymptotic Dynamics ◽  
Simple Selection

We study a markovian evolutionary process which encompasses the classical simple genetic algorithm. This process is obtained by randomly perturbing a very simple selection scheme. Using the Freidlin-Wentzell theory, we carry out a precise study of the asymptotic dynamics of the process as the perturbations disappear. We show how a delicate interaction between the perturbations and the selection pressure may force the convergence toward the global maxima of the fitness function. We put forward the existence of a critical population size, above which this kind of convergence can be achieved. We compute upper bounds of this critical population size for several examples. We derive several conditions to ensure convergence in the homogeneous case and these provide the first mathematically well-founded convergence results for genetic algorithms.

Asymptotic convergence of genetic algorithms

1998 ◽  
Vol 30 (2) ◽  
pp. 521-550 ◽  
Author(s):  
Raphaël Cerf
Keyword(s):  
Genetic Algorithms ◽  
Population Size ◽  
Fitness Function ◽  
Evolutionary Process ◽  
Asymptotic Convergence ◽  
Homogeneous Case ◽  
Selection Scheme ◽  
Convergence Results ◽  
Asymptotic Dynamics ◽  
Simple Selection

We study a markovian evolutionary process which encompasses the classical simple genetic algorithm. This process is obtained by randomly perturbing a very simple selection scheme. Using the Freidlin-Wentzell theory, we carry out a precise study of the asymptotic dynamics of the process as the perturbations disappear. We show how a delicate interaction between the perturbations and the selection pressure may force the convergence toward the global maxima of the fitness function. We put forward the existence of a critical population size, above which this kind of convergence can be achieved. We compute upper bounds of this critical population size for several examples. We derive several conditions to ensure convergence in the homogeneous case and these provide the first mathematically well-founded convergence results for genetic algorithms.

scholarly journals Analysis of Selection Methods Used in Genetic Algorithms

2021 ◽  
Vol 4 ◽  
pp. 29-43
Author(s):  
Nataliya Gulayeva ◽  
Artem Ustilov
Keyword(s):  
Growth Rate ◽  
Genetic Algorithms ◽  
Selection Pressure ◽  
Fitness Function ◽  
Selection Method ◽  
Initial Population ◽  
Reproduction Rate ◽  
Selection Methods ◽  
Selection Scheme ◽  
Fitness Value

This paper offers a comprehensive review of selection methods used in the generational genetic algorithms.Firstly, a brief description of the following selection methods is presented: fitness proportionate selection methods including roulette-wheel selection (RWS) and its modifications, stochastic remainder selection with replacement (SRSWR), remainder stochastic independent selection (RSIS), and stochastic universal selection (SUS); ranking selection methods including linear and nonlinear rankings; tournament selection methods including deterministic and stochastic tournaments as well as tournaments with and without replacement; elitist and truncation selection methods; fitness uniform selection scheme (FUSS).Second, basic theoretical statements on selection method properties are given. Particularly, the selection noise, selection pressure, growth rate, reproduction rate, and computational complexity are considered. To illustrate selection method properties, numerous runs of genetic algorithms using the only selection method and no other genetic operator are conducted, and numerical characteristics of analyzed properties are computed. Specifically, to estimate the selection pressure, the takeover time and selection intensity are computed; to estimate the growth rate, the ratio of best individual copies in two consecutive populations is computed; to estimate the selection noise, the algorithm convergence speed is analyzed based on experiments carried out on a specific fitness function assigning the same fitness value to all individuals.Third, the effect of selection methods on the population fitness distribution is investigated. To do this, there are conducted genetic algorithm runs starting with a binomially distributed initial population. It is shown that most selection methods keep the distribution close to the original one providing an increased mean value of the distribution, while others (such as disruptive RWS, exponential ranking, truncation, and FUSS) change the distribution significantly. The obtained results are illustrated with the help of tables and histograms.

scholarly journals Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 115
Author(s):  
Andriy Chaban ◽  
Marek Lis ◽  
Andrzej Szafraniec ◽  
Radoslaw Jedynak
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Fitness Function ◽  
Least Square ◽  
Distributed Parameter ◽  
Parameter Method ◽  
Analytical Mechanics ◽  
Parameter System ◽  
Rotational Systems ◽  
Elastic Elements

Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

scholarly journals Adaptive Gene Level Mutation

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 16
Author(s):  
Jalal Al-afandi ◽  
Horváth András
Keyword(s):  
Genetic Algorithms ◽  
Stochastic Optimization ◽  
Specific Problem ◽  
Traditional Approach ◽  
Fitness Function ◽  
Optimization Methods ◽  
Analytic Solutions ◽  
Problem Representation ◽  
Travelling Salesman ◽  
Gene Level

Genetic Algorithms are stochastic optimization methods where solution candidates, complying to a specific problem representation, are evaluated according to a predefined fitness function. These approaches can provide solutions in various tasks even, where analytic solutions can not be or are too complex to be computed. In this paper we will show, how certain set of problems are partially solvable allowing us to grade segments of a solution individually, which results local and individual tuning of mutation parameters for genes. We will demonstrate the efficiency of our method on the N-Queens and travelling salesman problems where we can demonstrate that our approach always results faster convergence and in most cases a lower error than the traditional approach.

The Nesting of Two-Dimensional Shapes Using Genetic Algorithms

1995 ◽  
Vol 209 (2) ◽  
pp. 115-124 ◽  
Author(s):  
H S Ismail ◽  
K K B Hon
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spatial Constraints ◽  
Global Optimal ◽  
Optimum Solution ◽  
Rapid Conversion

The general two-dimensional cutting stock problem is concerned with the optimum layout and arrangement of two-dimensional shapes within the spatial constraints imposed by the cutting stock. The main objective is to maximize the utilization of the cutting stock material. This paper presents some of the results obtained from applying a combination of genetic algorithms and heuristic approaches to the nesting of dissimilar shapes. Genetic algorithms are stochastically based optimization approaches which mimic nature's evolutionary process in finding global optimal solutions in a large search space. The paper discusses the method by which the problem is defined and represented for analysis and introduces a number of new problem-specific genetic algorithm operators that aid in the rapid conversion to an optimum solution.

Assembly Planning: A Genetic Approach

1998 ◽  
Author(s):  
Shiang-Fong Chen
Keyword(s):  
Genetic Algorithms ◽  
Fitness Function ◽  
Assembly Planning ◽  
Genetic Approach ◽  
Genetic Operators ◽  
Complex Problems ◽  
All Solutions ◽  
Assembly Problem ◽  
Optimal Assembly

Abstract The difficulty of an assembly problem is the inherent complexity of possible solutions. If the most suitable plan is selected after all solutions are found, it will be very time consuming and unrealistic. Motivated by the success of genetic algorithms (GAs) in solving combinatorial and complex problems by examining a small number of possible candidate solutions, GAs are employed to find a near-optimal assembly plan for a general environment. Five genetic operators are used: tree crossover, tree mutation, cut-and-paste, break-and-joint, and reproduction. The fitness function can adapt to different criteria easily. This assembly planner can help an inexperienced technician to find a good solution efficiently. The algorithm has been fully implemented. One example product is given to show the applications and results.

scholarly journals Strategic Team AI Path Plans: Probabilistic Pathfinding

2008 ◽  
Vol 2008 ◽  
pp. 1-6 ◽  
Author(s):  
Tng C. H. John ◽  
Edmond C. Prakash ◽  
Narendra S. Chaudhari
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Computer Games ◽  
Fitness Function ◽  
New Method ◽  
High Quality ◽  
Plan Generation ◽  
Novel Method ◽  
Games And Simulations

This paper proposes a novel method to generate strategic team AI pathfinding plans for computer games and simulations using probabilistic pathfinding. This method is inspired by genetic algorithms (Russell and Norvig, 2002), in that, a fitness function is used to test the quality of the path plans. The method generates high-quality path plans by eliminating the low-quality ones. The path plans are generated by probabilistic pathfinding, and the elimination is done by a fitness test of the path plans. This path plan generation method has the ability to generate variation or different high-quality paths, which is desired for games to increase replay values. This work is an extension of our earlier work on team AI: probabilistic pathfinding (John et al., 2006). We explore ways to combine probabilistic pathfinding and genetic algorithm to create a new method to generate strategic team AI pathfinding plans.

scholarly journals Application of the genetic algorithm to the task of compiling the curriculum

2018 ◽  
Author(s):  
V. A. Turchina ◽  
D. O. Tanasienko
Keyword(s):  
Higher Education ◽  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Necessary Conditions ◽  
Fitness Function ◽  
Educational Process ◽  
Heuristic Methods ◽  
Educational Groups ◽  
The Individual ◽  
Negative Property

One of the main tasks in organizing the educational process in higher education is the drawing up of a schedule of classes. It reflects the weekly student and faculty load. At the same time, when compiling, there are a number of necessary conditions and a number of desirable. The paper considers seven required and four desirable conditions. In this paper, one of the well-known approaches that can be used in drawing up a curriculum is consid-ered. The proposed scheme of the genetic algorithm, the result of which is to obtain an approximate solution to the problem of scheduling with the need to further improve it by other heuristic methods. To solve the problem, an island model of the genetic algorithm was selected and its advantages were considered. In the paper, the author's own structure of the individual, which includes chromosomes in the form of educational groups and genes as a lesson at a certain time, is presented and justified. The author presents his own implementations of the genetic algorithms. During the work, many variants of operators were tested, but they were rejected due to their inefficiency. The biggest problem was to maintain the consistency of information encoded in chromosomes. Also, two post-steps were added: to try to reduce the number of teacher conflict conflicts and to normalize the schedule - to remove windows from the schedule. The fitness function is calculated according to the following principles: if some desired or desired property is present in the individual, then a certain number is deducted from the individual's assessment, if there is a negative property, then a certain number is added to the assessment. Each criterion has its weight, so the size of the fine or rewards may be different. In this work, fines were charged for non-fulfillment of mandatory conditions, and rewards for fulfilling the desired

scholarly journals PENENTUAN PARAMETER LEARNING RATE SELAMA PEMBELAJARAN JARINGAN SYARAF TIRUAN BACKPROPAGATION MENGGUNAKAN ALGORITMA GENETIKA

2020 ◽  
Vol 14 (2) ◽  
pp. 202-212
Author(s):  
Ade chandra Saputra
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Fitness Function ◽  
Learning Rate ◽  
Local Minima ◽  
Rate Parameter ◽  
Neural Network Learning ◽  
Value Of Learning ◽  
Backpropagation Learning

One of the weakness in backpropagation Artificial neural network(ANN) is being stuck in local minima. Learning rate parameter is an important parameter in order to determine how fast the ANN Learning. This research is conducted to determine a method of finding the value of learning rate parameter using a genetic algorithm when neural network learning stops and the error value is not reached the stopping criteria or has not reached the convergence. Genetic algorithm is used to determine the value of learning rate used is based on the calculation of the fitness function with the input of the ANN weights, gradient error, and bias. The calculation of the fitness function will produce an error value of each learning rate which represents each candidate solutions or individual genetic algorithms. Each individual is determined by sum of squared error value. One with the smallest SSE is the best individual. The value of learning rate has chosen will be used to continue learning so that it can lower the value of the error or speed up the learning towards convergence. The final result of this study is to provide a new solution to resolve the problem in the backpropagation learning that often have problems in determining the learning parameters. These results indicate that the method of genetic algorithms can provide a solution for backpropagation learning in order to decrease the value of SSE when learning of ANN has been static in large error conditions, or stuck in local minima

Evaluating Genetic Algorithms on Welding Sequence Optimization With Respect to Dimensional Variation and Cycle Time

2011 ◽  
Author(s):  
Johan Segeborn ◽  
Johan S. Carlson ◽  
Kristina Wa¨rmefjord ◽  
Rikard So¨derberg
Keyword(s):  
Genetic Algorithms ◽  
Significant Influence ◽  
Cycle Time ◽  
Spot Welding ◽  
Fitness Function ◽  
Welding Robot ◽  
Single Criterion ◽  
Welding Sequence ◽  
Dimensional Variation ◽  
Welding Sequences

Spot welding is the predominant joining method in car body assembly. Spot welding sequences have a significant influence on the dimensional variation of resulting assemblies and ultimately on overall product quality. It also has a significant influence on welding robot cycle time and thus ultimately on manufacturing cost. In this work we evaluate the performance of Genetic Algorithms, GAs, on multi-criteria optimization of welding sequence with respect to dimensional assembly variation and welding robot cycle time. Reference assemblies are fully modelled in 3D including detailed fixtures, welding robots and weld guns. Dimensional variation is obtained using variation simulation and part measurement data. Cycle time is obtained using automatic robot path planning. GAs are not guaranteed to find the global optimum. Besides exhaustive calculations, there is no way to determine how close to the actual optimum a GA trial has reached. Furthermore, sequence fitness evaluations constitute the absolute majority of optimization computation running time and do thus need to be kept to a minimum. Therefore, for two industrial reference assemblies we investigate the number of fitness evaluations that is required to find a sequence that is optimal or a near-optimal with respect to the fitness function. The fitness function in this work is a single criterion based on a weighted and normalized combination of dimensional variation and cycle time. Both reference assemblies involves 7 spot welds which entails 7!=5040 possible welding sequences. For both reference assemblies, dimensional variation and cycle time is exhaustively calculated for all 5040 possible sequences, determining the optimal sequence, with respect to the fitness function, for a fact. Then a GA that utilizes Random Key Encoding is applied on both cases and the performance is recorded. It is found that in searching through about 1% of the possible sequences, optimum is reached in about half of the trials and 80–90% of the trials reach the ten best sequences. Furthermore the optimum of the single criterion fitness function entails dimensional variation and cycle time fairly close to their respective optimum. In conclusion, this work indicates that genetic algorithms are highly effective in optimizing welding sequence with respect to dimensional variation and cycle time.

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