Differential Evolution Algorithm For Engineering Structural Optimization And Design

In practical engineering optimization design problems,we always counter this kind of optimization problems.The objective functions of these problems are discontinuity,non-differentiable and multiple local optima which are difficult to be solved by the traditional optimization theory and techniques based on gradient information,thus it is significant to develop new optimization techniques.Recently,owing to the advantages of evolutionary algorithms with self-adaptive,self-organizing,implicit parallelism,employing evolutionary algorithm to deal with this kind of problems has been obtained more and more attention.Most of intelligent evolutionary algorithms do not require the gradient information of objective and constraint functions and only demands the values of objective and constraints,so that it provides a new effective tool to solve this kind problem.Differential evolution is one of the population-based global algorithms and is easy to implent and robustness,so that it achieves more and more popularity in practical applications.The classical differential evolution is easy to search for local optimal and trap in premature convergence,so it is very urgent to improve and introduce new methodologies to develop new differential evolution variants.In this paper,two different differential evolution variants are proposed to solve unconstrain optimization problems after introducing two different strategies.Subsequently,an improved differential evolution algorithm is presented to deal with complicated constrain optimization problems.Finally,after introducing the interval uncertainty into the framework of differential evolution,two efficient algorthims are developed to solve the nonlinear interval optimization problem.As a result,the following studies are carried out in this dissertation:(1)A differential evolution based on intergeneration with fast-convergence performance is proposed.In order to increase the diversity of evolutionary population,the opposition learning strategy and traditional random stratetgy are similanetously utilized to generate initial population.The best individuals from two successive generations are employed to construct the search direction to conveniently generate better promising individuals to improve convergence.Two new inidivduals are generated to add into the evolutionary population at every several generations to avoiding locating in a local optimium.(2)An adaptive differential evolution algorithm with an aging leader and challengers mechanism is proposed to solve optimization problems.The aging mechanism is introduced into the framework of DE and defines the leader individual to lead the evolutionary population to generate promising offspring individuals.The lifespan of the leader adaptively increases or decreases according to its leadership ability which is benefical to generate better offspring and keep diversity.At the same time,a self-adaptive technique is employed to control its critical parameters.(3)An improved differential evolution with shrinking space technique and adaptive trade-off model is proposed to solve constrained optimization problems.Firstly,a new mutant strategy combined binominal crossover is constructed to generate new individuals according to the feasibility proportion of current population.Then the shrinking space technique is introduced to shrink the search region in order to speed up convergence.For the constraints,the adaptive trade-off model as one of the most important constraint-handling techniques is employed to select better individuals to retain into the next population which aims to search for feasible soultions.(4)An interval differential evolution algorithm based on interval possibility and interval preferential rule is proposed to deal with the nonlinear interval uncertain optimization problems.Based on the characteristics of evolutionary population,the main advantage of IDE is a direct optimization algorithm which avoids transforming the original uncertain problems into determinsictic ones to be solved.The interval possibility is utilized to quantitatively measure the possibility of an interval better than or worse than another one which is utilized to deal with constrain functions.Meanwhile,the interval preferential rule is proposed to choose the better individual from two ones into the next evolutionary population under considering interval uncertainty(5)Two effective nonlinear interval optimization algorithms based on interval and subinterval analysis technique are proposed.For the interval parameter with small uncertainty level,the Taylor expansion technique for the uncertain parameter is utilized and the uncertain optimization function is linealy expansed.For the interval parameter with large uncertainty,a subinterval decomposition analysis is developed to achieve the bounds of the objective and constraint functions caused by uncertainty.Hence,after this treatment,the traditional interval optimization is a single loop optimization process and its computation efficiency is improved greatly.