Appropriate Combination of Crossover Operator and Mutation Operator in Genetic Algorithms for the Travelling Salesman Problem

Genetic algorithms(GAs)are very good metaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems.AsimpleGAbeginswith a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes.It uses a crossover operator to create better offspring chromosomes and thus,converges the population.Also,it uses a mutation operator to explore the unexplored areas by the crossover operator,and thus,diversifies the GA search space.A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution.However,appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem.In this present paper,we aim to study the benchmark traveling salesman problem(TSP).We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances.The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem.The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances.

Solving the Generalized Traveling Salesman Problem Using Sequential Constructive Crossover Operator in Genetic Algorithm

The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is highly expensive,we will develop genetic algorithms(GAs)to obtain heuristic solutions to the problem.In GAs,as the crossover is a very important process,the crossovermethods proposed for the traditional TSP could be adapted for the GTSP.The sequential constructive crossover(SCX)and three other operators are adapted to use in GAs to solve the GTSP.The effectiveness of GA using SCX is verified on some GTSP Library(GTSPLIB)instances first and then compared against GAs using the other crossover methods.The computational results show the success of the GA using SCX for this problem.Our proposed GA using SCX,and swap mutation could find average solutions whose average percentage of excesses fromthe best-known solutions is between 0.00 and 14.07 for our investigated instances.

SFGA-CPA: A Novel Screening Correlation Power Analysis Framework Based on Genetic Algorithm

Correlation power analysis(CPA)combined with genetic algorithms(GA)now achieves greater attack efficiency and can recover all subkeys simultaneously.However,two issues in GA-based CPA still need to be addressed:key degeneration and slow evolution within populations.These challenges significantly hinder key recovery efforts.This paper proposes a screening correlation power analysis framework combined with a genetic algorithm,named SFGA-CPA,to address these issues.SFGA-CPA introduces three operations designed to exploit CPA characteris-tics:propagative operation,constrained crossover,and constrained mutation.Firstly,the propagative operation accelerates population evolution by maximizing the number of correct bytes in each individual.Secondly,the constrained crossover and mutation operations effectively address key degeneration by preventing the compromise of correct bytes.Finally,an intelligent search method is proposed to identify optimal parameters,further improving attack efficiency.Experiments were conducted on both simulated environments and real power traces collected from the SAKURA-G platform.In the case of simulation,SFGA-CPA reduces the number of traces by 27.3%and 60%compared to CPA based on multiple screening methods(MS-CPA)and CPA based on simple GA method(SGA-CPA)when the success rate reaches 90%.Moreover,real experimental results on the SAKURA-G platform demonstrate that our approach outperforms other methods.

Genetic Crossover Operators for the Capacitated Vehicle Routing Problem

We study the capacitated vehicle routing problem(CVRP)which is a well-known NP-hard combinatorial optimization problem(COP).The aim of the problem is to serve different customers by a convoy of vehicles starting from a depot so that sum of the routing costs under their capacity constraints is minimized.Since the problem is very complicated,solving the problem using exact methods is almost impossible.So,one has to go for the heuristic/metaheuristic methods and genetic algorithm(GA)is broadly applied metaheuristic method to obtain near optimal solution to such COPs.So,this paper studies GAs to find solution to the problem.Generally,to solve a COP,GAs start with a chromosome set named initial population,and then mainly three operators-selection,crossover andmutation,are applied.Among these three operators,crossover is very crucial in designing and implementing GAs,and hence,numerous crossover operators were developed and applied to different COPs.There are two major kinds of crossover operators-blind crossovers and distance-based crossovers.We intend to compare the performance of four blind crossover and four distance-based crossover operators to test the suitability of the operators to solve the CVRP.These operators were originally proposed for the standard travelling salesman problem(TSP).First,these eight crossovers are illustrated using same parent chromosomes for building offspring(s).Then eight GAs using these eight crossover operators without any mutation operator and another eight GAs using these eight crossover operators with a mutation operator are developed.These GAs are experimented on some benchmark asymmetric and symmetric instances of numerous sizes and various number of vehicles.Our study revealed that the distance-based crossovers are much superior to the blind crossovers.Further,we observed that the sequential constructive crossover with and without mutation operator is the best one for theCVRP.This estimation is validated by Student’s t-test at 95%confidence level.We further determined a comparative rank of the eight crossovers for the CVRP.

Genetic Algorithm for the Thermal Stresses Optimum Design ofFunctionally Gradient Material Plate

Based on the thermal stress distribution for functionally gradient material (FGM) plates, a Genetic Algorithm (GA) method for the thermal stresses optimum design of FGM plate with computer technologies is given. The minimum thermal stresses combination distribution for FGM is obtained.

A REAL-VALUED GENETIC ALGORITHM FOR OPTIMIZATION PROBLEM WITH CONTINUOUS VARIABLES

A real valued genetic algorithm(RVGA) for the optimization problem with continuous variables is proposed. It is composed of a simple and general purpose dynamic scaled fitness and selection operator, crossover operator, mutation operators and adaptive probabilities for these operators. The algorithm is tested by two generally used functions and is used in training a neural network for image recognition. Experimental results show that the algorithm is an efficient global optimization algorithm.

An Improved Genetic Algorithm with Quasi-Gradient Crossover

The convergence of genetic algorithm is mainly determined by its core operation crossover operation. When the objective function is a multiple hump function, traditional genetic algorithms are easily trapped into local optimum, which is called premature conver- gence. In this paper, we propose a new genetic algorithm with improved arithmetic crossover operation based on gradient method. This crossover operation can generate offspring along quasi-gradient direction which is the Steepest descent direction of the value of objective function. The selection operator is also simplified, every individual in the population is given an opportunity to get evolution to avoid complicated selection algorithm. The adaptive mutation operator and the elitist strategy are also applied in this algorithm. The case 4 indicates this algorithm can faster converge to the global optimum and is more stable than the conventional genetic algorithms.

Application of Genetic Algorithm in Estimation of Gyro Drift Error Model

Extended Kalman Filter(EKF)algorithm is widely used in parameter estimation for nonlinear systems.The estimation precision is sensitively dependent on EKF’s initial state covariance matrix and state noise matrix.The grid optimization method is always used to find proper initial matrix for off-line estimation.However,the grid method has the draw back being time consuming hence,coarse grid followed by a fine grid method is adopted.To further improve efficiency without the loss of estimation accuracy,we propose a genetic algorithm for the coarse grid optimization in this paper.It is recognized that the crossover rate and mutation rate are the main influencing factors for the performance of the genetic algorithm,so sensitivity experiments for these two factors are carried out and a set of genetic algorithm parameters with good adaptability were selected by testing with several gyros’experimental data.Experimental results show that the proposed algorithm has higher efficiency and better estimation accuracy than the traversing grid algorithm.

Three-Objective Programming with Continuous Variable Genetic Algorithm

The subject area of multiobjective optimization deals with the investigation of optimization problems that possess more than one objective function. Usually, there does not exist a single solution that optimizes all functions simultaneously;quite the contrary, we have solution set that is called nondominated set and elements of this set are usually infinite. It is from this set decision made by taking elements of nondominated set as alternatives, which is given by analysts. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for linear and nonlinear three objective optimization problems. In this paper a continuous variable genetic algorithm is used to find approximate near optimal solution set. Objective functions are considered as fitness function without modification. Initial solution was generated within box constraint and solutions will be kept in feasible region during mutation and recombination.

Using Genetic Algorithms for Solving the Comparison-Based Identification Problem of Multifactor Estimation Model

In this paper the statement and the methods for solving the comparison-based structure-parametric identification problem of multifactor estimation model are addressed. A new method that combines heuristics methods with genetic algorithms is proposed to solve the problem. In order to overcome some disadvantages of using the classical utility functions, the use of nonlinear Kolmogorov-Gabor polynomial, which contains in its composition the first as well as higher characteristics degrees and all their possible combinations is proposed in this paper. The use of nonlinear methods for identification of the multifactor estimation model showed that the use of this new technique, using as a utility function the nonlinear Kolmogorov-Gabor polynomial and the use of genetic algorithms to calculate the weights, gives a considerable saving in time and accuracy performance. This method is also simpler and more evident for the decision maker (DM) than other methods.

An Improved Real-Coded Genetic Algorithm and Its Application

Real-coded genetic algorithm（RGA）usually meets the demand of consecutive space problem.However,compared with simple genetic algorithm（SGA）RGA also has the inherent disadvantages such as prematurity and slow convergence when the solution is close to the optimum solution.This paper presents an improved real-coded genetic algorithm to increase the computation efficiency and avoid prematurity,especially in the optimization of multi-modal function.In this method,mutation operation and crossover operation are improved.Examples are given to demonstrate its com p utation efficiency and robustness.

On Some Basic Concepts of Genetic Algorithms as a Meta-Heuristic Method for Solving of Optimization Problems

The genetic algorithms represent a family of algorithms using some of genetic principles being present in nature, in order to solve particular computational problems. These natural principles are: inheritance, crossover, mutation, survival of the fittest, migrations and so on. The paper describes the most important aspects of a genetic algorithm as a stochastic method for solving various classes of optimization problems. It also describes the basic genetic operator selection, crossover and mutation, serving for a new generation of individuals to achieve an optimal or a good enough solution of an optimization problem being in question.

An improved genetic algorithm for searching for pollution sources

As an optimization method that has experienced rapid development over the past 20 years, the genetic algorithm has been successfully applied in many fields, but it requires repeated searches based on the characteristics of high-speed computer calculation and conditions of the known relationship between the objective function and independent variables. There are several hundred generations of evolvement, but the functional relationship is unknown in pollution source searches. Therefore, the genetic algorithm cannot be used directly. Certain improvements need to be made based on the actual situation, so that the genetic algorithm can adapt to the actual conditions of environmental problems, and can be used in environmental monitoring and environmental quality assessment. Therefore, a series of methods are proposed for the improvement of the genetic algorithm： （1） the initial generation of individual groups should be artificially set and move from lightly polluted areas to heavily polluted areas; （2） intervention measures should be introduced in the competition between individuals; （3） guide individuals should be added; and （4） specific improvement programs should be put forward. Finally, the scientific rigor and rationality of the improved genetic algorithm are proven through an example.

A NEW OPTIMIZATION ALGORITHM BASED ON THE PRINCIPLE OF EVOLUTION

A new genetic algorithm is proposed for the optimization problem of real-valued variable functions. A new robust and adaptive fitness scaling is presented by introducing the median of the population in exponential transformation. For float-point represented chromosomes, crossover and mutation operators are given. Convergence of the algorithm is proved. The performance is tested by two generally used functions. Hybrid algorithm which takes the BP algorithm as a mutation operator is used to train a neural network for image recognition. Experimental results show that the proposed algorithm is an efficient global optimization algorithm.

An adaptive genetic algorithm for solving bilevel linear programming problem

Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

基于Petri网和改进遗传算法的多资源调度问题

针对混流装配线工序加工资源需求多样、工艺复杂、装配工期长等问题,采用Petri网和改进遗传算法对该问题进行优化求解。建立混流装配线赋时库所Petri网(timed place Petri net, TPPN)调度模型,基于模型激发序列,采用基于工序的编码方式进行染色体编码;采用精英保留策略选择优异个体,改进遗传算法的交叉、变异操作,用改进后的遗传算法求解混流装配线调度问题。通过对比案例及实例数据计算结果验证了方案的有效性。

基于改进遗传算法的柔性作业车间调度研究

针对柔性作业车间的多目标调度问题,文章建立以最大完工时间、能耗为目标的数学模型,提出一种多目标的改进遗传算法的求解方法。首先,在交叉算子中使用均匀交叉法,采用了基于邻域的变异算子。其次,针对交叉变异算子进行了非均匀改进,旨在增加算法搜索能力。通过动态调整非均匀交叉和非均匀变异的概率,提高搜索空间覆盖率,避免陷入局部最优解。最后,采用基准算例Kacem测试集进行测试。实验证明,该改进算法有效地解决了同时考虑最大完工时间和能耗的多目标调度问题,取得了显著的改善效果。

基于遗传-灰狼算法的水肥一体化控制系统研究

变量施肥是精准农业的重要组成部分,非线性、大惯性和参数时变性是影响水肥一体化控制系统精度和稳态性能的关键因素。PID控制算法因其简单方便而被人们广泛应用于工农业领域中,但往往很难达到理想的控制效果。灰狼优化算法(Gray Wolf Optimization Algorithm, GWO)是一种参数设置少且收敛性能好的群体智能优化算法,但在迭代过程中容易陷入局部最优解。为此,通过在标准GWO算法中引入遗传交叉和变异算子,结合佳点集方法,提出一种改进的新型灰狼智能优化算法(Genetic–Grey Wolf Optimization algorithm, GGWO),并将改进的遗传-灰狼优化算法应用于水肥一体化控制系统的PID控制中。以液肥控制系统为研究对象,建立相应的负反馈控制系统数学模型,分别采用常规PID控制、基于GWO的PID控制以及基于GGWO的PID等3种不同控制方法并用MatLab对其进行仿真,并对比分析了各控制方法下的系统性能指标。仿真结果表明:基于GGWO的PID控制在系统的上升时间、调节时间和适应值等性能指标上都优于其它两种控制方法,在系统的精度、均匀性、鲁棒性和稳态性能上实现了更好的控制效果,不仅满足了精准农业的作业要求,而且为后续研究打下了基础。

基于改进遗传算法优化BP网络的密度预测

为了能利用工艺参数实时预测药柱密度并提高密度预测精度,提出采用改进遗传算法优化BP网络(improved genetic algorithm backpropagation neural network,IGA-BPNN)的炸药密度预测模型。通过动态调整GA的交叉概率和变异概率,确定BPNN权重和阈值的最优值,构建IGA-BP预测模型,利用采集的工艺参数,基于所构建模型进行炸药密度预测。实验结果表明:改进的GA对交叉率和变异率做出了更好的调整,能快速搜寻BPNN的最优权重和阈值,提高炸药压制密度的预测精度。

GA and PSO culled hybrid technique for economic dispatch problem with prohibited operating zones

This paper presents an efficient and reliable genetic algorithm (GA) based particle swarm optimization (PSO) tech- nique (hybrid GAPSO) for solving the economic dispatch (ED) problem in power systems. The non-linear characteristics of the generators, such as prohibited operating zones, ramp rate limits and non-smooth cost functions of the practical generator operation are considered. The proposed hybrid algorithm is demonstrated for three different systems and the performance is compared with the GA and PSO in terms of solution quality and computation efficiency. Comparison of results proved that the proposed algo- rithm can obtain higher quality solutions efficiently in ED problems. A comprehensive software package is developed using MATLAB.