Evolutionary Algorithms For Optimization Problems

In industrial production,logistics transportation,scientific research and daily life,people always seek the optimal solution to achieve certain goals.These problems have formed a wide variety of complicated optimization problems.According to the value range of their solutions,optimization problems can be divided into combinational optimization and function optimization.Because of large calculating quantity and solving difficulty of these problems,the traditional exact algorithms are not suitable to solve these problems.At this point,evolutionary algorithms derived from the wisdom of nature are proposed.These algorithms imitate population evolution,having the ability to search globally,and they do not depend on characteristics of problems,with a good generality.This paper will use different evolutionary algorithms to solve two kinds of optimization problems in real life: flowshop scheduling problems and function optimization problems.Flowshop scheduling is an important branch of combinatorial optimization problems.Among,the production mode of distributed assembly permutation flowshop scheduling problem(DAPFSP)is more complicated in the real production process.It consists of two stages: production and assembly.The first stage is production in factories;the second stage is to assemble jobs into final products.This paper applies local search to improve genetic algorithm for solving the problem.First,the mating pool is designed based on greedy strategy,to choose promising parents.To accelerate the convergence rate,this paper designs different crossover strategies for different sequences: sequences of product assembly and job assignment apply single-point crossover,sequences of job processing use crossover operator improved by greedy strategy.At last,local search strategies based on two neighborhood structures are incorporated to enhance the exploitation capability.After the exhaustive computation and statistical analysis,we can observe that the proposed methods are robust and outperform the existing algorithms.Function optimization has a wide range of application and has attracted many researchers to study.Cuckoo search(CS)is an innovative evolutionary algorithm designed for these problems.It is skilled in handling complex functions but has a slow convergence rate.On the other hand,covariance matrix adaption evolution strategy(CMA_ES)can converge quickly by self-adaptation of the mutation distribution and cumulation of the evolution path;however,it has a bad performance in complicated functions.Therefore,a hybridization of CS and CMA_ES,CS_CMA,is devised in this paper.A new population is initialized with previous evolutions in iteration.Covariance matrix of variable distribution and randomization are used to improve Levy Flight and biased random wal.First,a referenced vector(donor)is generated by improved Levy Flight;then,improved biased random walk uses donor and current population to generate offsprings.At last,selection operator is applied to generate the next generation.During the evolutionary process,parameters are adjusted via successful values self-adaptively.To demonstrate the capability of CS_CMA,experiments were done through 7 high-dimensional functions from CEC2008 and an engineering optimization problem from CEC2011,and comparative results prove that CS_CMA is superior to other contestant algorithms.