A Rigorous Complexity Analysis of the (1 + 1) Evolutionary Algorithm for Separable Functions with Boolean Inputs

1998 ◽  
Vol 6 (2) ◽  
pp. 185-196 ◽  
Author(s):  
Stefan Droste ◽  
Thomas Jansen ◽  
Ingo Wegener
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Randomized Algorithms ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Mutation Rates ◽  
Crossover Operator ◽  
Separable Functions ◽  
Run Time

Evolutionary algorithms (EAs) are heuristic randomized algorithms which, by many impressive experiments, have been proven to behave quite well for optimization problems of various kinds. In this paper a rigorous theoretical complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs is given. Different mutation rates are compared, and the use of the crossover operator is investigated. The main contribution is not the result that the expected run time of the (1 + 1) evolutionary algorithm is Θ(n ln n) for separable functions with n variables but the methods by which this result can be proven rigorously.

scholarly journals Implementation of new hybrid evolutionary algorithm with fuzzy logic control approach for optimization problems

2021 ◽  
Vol 6 (4 (114)) ◽  
pp. 6-14
Author(s):  
Maan Afathi
Keyword(s):  
Fuzzy Logic ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Fuzzy Logic Control ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Function Optimization ◽  
Evolutionary Computations ◽  
Hybrid Evolutionary Algorithm ◽  
Logic Control

The main purpose of using the hybrid evolutionary algorithm is to reach optimal values and achieve goals that traditional methods cannot reach and because there are different evolutionary computations, each of them has different advantages and capabilities. Therefore, researchers integrate more than one algorithm into a hybrid form to increase the ability of these algorithms to perform evolutionary computation when working alone. In this paper, we propose a new algorithm for hybrid genetic algorithm (GA) and particle swarm optimization (PSO) with fuzzy logic control (FLC) approach for function optimization. Fuzzy logic is applied to switch dynamically between evolutionary algorithms, in an attempt to improve the algorithm performance. The HEF hybrid evolutionary algorithms are compared to GA, PSO, GAPSO, and PSOGA. The comparison uses a variety of measurement functions. In addition to strongly convex functions, these functions can be uniformly distributed or not, and are valuable for evaluating our approach. Iterations of 500, 1000, and 1500 were used for each function. The HEF algorithm’s efficiency was tested on four functions. The new algorithm is often the best solution, HEF accounted for 75 % of all the tests. This method is superior to conventional methods in terms of efficiency

scholarly journals An Empirical Investigation on Evolutionary Algorithm Evolving Developmental Timings

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1866
Author(s):  
Kei Ohnishi ◽  
Kouta Hamano ◽  
Mario Koeppen
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Search Strategy ◽  
Empirical Investigation ◽  
Optimization Problems ◽  
Machine Learning Technique ◽  
Model Based ◽  
Fitness Value ◽  
Learning Technique ◽  
The Difference

Recently, evolutionary algorithms that can efficiently solve decomposable binary optimization problems have been developed. They are so-called model-based evolutionary algorithms, which build a model for generating solution candidates by applying a machine learning technique to a population. Their central procedure is linkage detection that reveals a problem structure, that is, how the entire problem consists of sub-problems. However, the model-based evolutionary algorithms have been shown to be ineffective for problems that do not have relevant structures or those whose structures are hard to identify. Therefore, evolutionary algorithms that can solve both types of problems quickly, reliably, and accurately are required. The objective of the paper is to investigate whether the evolutionary algorithm evolving developmental timings (EDT) that we previously proposed can be the desired one. The EDT makes some variables values more quickly converge than the remains for any problems, and then, decides values of the remains to obtain a higher fitness value under the fixation of the variables values. In addition, factors to decide which variable values converge more quickly, that is, developmental timings are evolution targets. Simulation results reveal that the EDT has worse performance than the linkage tree genetic algorithm (LTGA), which is one of the state-of-the-art model-based evolutionary algorithms, for decomposable problems and also that the difference in the performance between them becomes smaller for problems with overlaps among linkages and also that the EDT has better performance than the LTGA for problems whose structures are hard to identify. Those results suggest that an appropriate search strategy is different between decomposable problems and those hard to decompose.

Composite Evolutionary Algorithm for Constrained Optimization

2012 ◽  
Vol 220-223 ◽  
pp. 2846-2851
Author(s):  
Si Lian Xie ◽  
Tie Bin Wu ◽  
Shui Ping Wu ◽  
Yun Lian Liu
Keyword(s):  
Evolutionary Algorithms ◽  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Selection Criteria ◽  
Optimization Problems ◽  
Experimental Results ◽  
Constrained Optimization Problems ◽  
Mutation Operators ◽  
Single Operator ◽  
Algorithm Framework

Evolutionary algorithms are amongst the best known methods of solving difficult constrained optimization problems, for which traditional methods are not applicable. Due to the variability of characteristics in different constrained optimization problems, no single evolutionary with single operator performs consistently over a range of problems. We introduce an algorithm framework that uses multiple search operators in each generation. A composite evolutionary algorithm is proposed in this paper and combined feasibility rule to solve constrained optimization problems. The proposed evolutionary algorithm combines three crossover operators with two mutation operators. The selection criteria based on feasibility of individual is used to deal with the constraints. The proposed method is tested on five well-known benchmark constrained optimization problems, and the experimental results show that it is effective and robust

HYBRID-FITNESS FUNCTION EVOLUTIONARY ALGORITHM BASED ON SIMPLEX CROSSOVER AND PSO MUTATION FOR CONSTRAINED OPTIMIZATION PROBLEMS

2009 ◽  
Vol 23 (01) ◽  
pp. 115-127 ◽  
Author(s):  
YIBO HU
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Penalty Function ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Fitness Function ◽  
Benchmark Problems ◽  
Crossover Operator ◽  
Hybrid Fitness ◽  
Constrained Optimization Problems

For constrained optimization problems, evolutionary algorithms often utilize a penalty function to deal with constraints, even if it is difficult to control the penalty parameters. To overcome this shortcoming, this paper presents a new penalty function which has no parameter and can effectively handle constraint first, after which a hybrid-fitness function integrating this penalty function into the objective function is designed. The new fitness function can properly evaluate not only feasible solution, but also infeasible one, and distinguish any feasible one from an infeasible one. Meanwhile, a new crossover operator based on simplex crossover operator and a new PSO mutation operator are also proposed, which can produce high quality offspring. Based on these, a new evolutionary algorithm for constrained optimization problems is proposed. The simulations are made on ten widely used benchmark problems, and the results indicate the proposed algorithm is effective.

Parallel Evolutionary Algorithm for Computationally Expensive Single Criteria Design Optimization

2014 ◽  
Vol 555 ◽  
pp. 586-592
Author(s):  
Stanisław Krenich
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Design Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Computation Method ◽  
Mechanism Optimization ◽  
Parallel Evolutionary Algorithms ◽  
Parallel Evolutionary Algorithm ◽  
Method Analysis

The paper presents an approach to design optimization using parallel evolutionary algorithms. The only use of a simple evolutionary algorithm in order to generate the optimal solution for complex problems can be ineffective due to long calculation time. Thus a tournament evolutionary algorithm (EA) and a parallel computation method are proposed and used. The proposed EA does not require an analysis of the optimization model for each potential solution from evolutionary populations. The second element of the method consists in parallel running of evolutionary algorithms using multi-threads approach. The experiments were carried out for many different single design optimization problems and two of them are presented in the paper. The first problem considers a task of robot gripper mechanism optimization and the second one deals with the optimization of a shaft based on Finite Element Method analysis. From the generated results it is clear that proposed approach is a very effective tool for solving fairly complicated tasks considering both the accuracy and the time of calculation.

A many-objective evolutionary algorithm based on vector angle distance scaling

2021 ◽  
Vol 40 (5) ◽  
pp. 10285-10306
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Adaptive Strategy ◽  
Great Success ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value ◽  
Vector Angle

In the past two decades, multi-objective evolutionary algorithms (MOEAs) have achieved great success in solving two or three multi-objective optimization problems. As pointed out in some recent studies, however, MOEAs face many difficulties when dealing with many-objective optimization problems(MaOPs) on account of the loss of the selection pressure of the non-dominant candidate solutions toward the Pareto front and the ineffective design of the diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm based on vector guidance. In this algorithm, the value of vector angle distance scaling(VADS) is applied to balance convergence and diversity in environmental selection. In addition, tournament selection based on the aggregate fitness value of VADS is applied to generate a high quality offspring population. Besides, we adopt an adaptive strategy to adjust the reference vector dynamically according to the scales of the objective functions. Finally, the performance of the proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 52 instances of 13 MaOPs with diverse characteristics. Experimental results show that the proposed algorithm performs competitively when dealing many-objective with different types of Pareto front.

A Quantum-Inspired Evolutionary Algorithm with Elite Group Guided

2015 ◽  
Vol 738-739 ◽  
pp. 323-333 ◽  
Author(s):  
Sheng Xiang ◽  
Yi Gang He
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Knapsack Problems ◽  
Elite Group ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Number Of Individuals

To improve the performance of quantum-inspired evolutionary algorithms (QIEAs), a new kind of QIEAs——elite group guided QIEA (EQIEA) are proposed through introducing an elite group guidance updating approach to solve knapsack problems. In EQIEA, the elite group at each iteration is composed of a certain number of individuals with better fitness values in the current population; all the individuals in the elite group cooperate together to affect quantum-inspired gates to produce off spring. Knapsack problems, a class of well-known NP-complete combinatorial optimization problems, are used to conduct experiments. The choices of parameters in EQIEA are discussed in an empirical way. Extensive experiments show that the EQIEA outperform six variants of QIEAs recently reported in the literature in terms of the quality of solutions. This paper also analyzes the convergence of EQIEA and the six variants of QIEAs. Experimental results show that EQIEA has better convergence than the six variants of QIEAs.

Hybrid Dynamical Evolutionary Algorithm and Time Complexity Analysis

2012 ◽  
Vol 263-266 ◽  
pp. 2344-2348
Author(s):  
Hui Ying Li ◽  
Yi Lai Zhang ◽  
Xing Xu
Keyword(s):  
Evolutionary Algorithm ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Function Optimization ◽  
Numerical Function ◽  
Similar Time ◽  
Local Optima ◽  
Minimization Problems ◽  
Dynamical Evolutionary Algorithm

The dynamical evolutionary algorithm (DEA) is a new evolutionary algorithm based on the theory of statistical mechanics, however, DEA converges slowly and often converge at local optima for some function optimization problems. In this paper, a hybrid dynamical evolutionary algorithm (HDEA) with multi-parent crossover and differential evolution mutation is proposed for accelerating convergence velocity and easily escaping suboptimal solutions. Moreover, the population of HDEA is initialized by chaos. In order to confirm the effectiveness of our algorithm, HDEA is applied to solve the typical numerical function minimization problems. The computational complexity of HDEA is analyzed, and the experimental results show that HDEA outperforms the DEA in the aspect of convergence velocity and precision, even the two algorithms have the similar time complexity.

scholarly journals An Opposition-Based Evolutionary Algorithm for Many-Objective Optimization with Adaptive Clustering Mechanism

2019 ◽  
Vol 2019 ◽  
pp. 1-27
Author(s):  
Wan Liang Wang ◽  
Weikun Li ◽  
Yu Le Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Test Problems ◽  
Adaptive Clustering ◽  
Opposition Based Learning ◽  
Environmental Selection ◽  
Large Numbers ◽  
Complex Optimization ◽  
Nondominated Sorting

Balancing convergence and diversity has become a key point especially in many-objective optimization where the large numbers of objectives pose many challenges to the evolutionary algorithms. In this paper, an opposition-based evolutionary algorithm with the adaptive clustering mechanism is proposed for solving the complex optimization problem. In particular, opposition-based learning is integrated in the proposed algorithm to initialize the solution, and the nondominated sorting scheme with a new adaptive clustering mechanism is adopted in the environmental selection phase to ensure both convergence and diversity. The proposed method is compared with other nine evolutionary algorithms on a number of test problems with up to fifteen objectives, which verify the best performance of the proposed algorithm. Also, the algorithm is applied to a variety of multiobjective engineering optimization problems. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in solving challenging real-world problems.

scholarly journals The Algorithm for Algorithms: An Evolutionary Algorithm Based on Automatic Designing of Genetic Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Dazhi Jiang ◽  
Zhun Fan
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Human Beings ◽  
Genetic Operators ◽  
Problem Space ◽  
Wide Range ◽  
Definition Of ◽  
Solution Accuracy

At present there is a wide range of evolutionary algorithms available to researchers and practitioners. Despite the great diversity of these algorithms, virtually all of the algorithms share one feature: they have been manually designed. A fundamental question is “are there any algorithms that can design evolutionary algorithms automatically?” A more complete definition of the question is “can computer construct an algorithm which will generate algorithms according to the requirement of a problem?” In this paper, a novel evolutionary algorithm based on automatic designing of genetic operators is presented to address these questions. The resulting algorithm not only explores solutions in the problem space like most traditional evolutionary algorithms do, but also automatically generates genetic operators in the operator space. In order to verify the performance of the proposed algorithm, comprehensive experiments on 23 well-known benchmark optimization problems are conducted. The results show that the proposed algorithm can outperform standard differential evolution algorithm in terms of convergence speed and solution accuracy which shows that the algorithm designed automatically by computers can compete with the algorithms designed by human beings.

Sign in / Sign up

Export Citation Format

Share Document