Study On Differential Evolution Algorithms Orientating Analysis And Design Of Mechanisms

The theoretical research on advanced mechanisms and machine sciences is thefoundation of manufacture and the source for inventing modern mechanical produces.Therefore, it is scientific significance and engineering application worth to studydeeply the advanced mechanism and machine theory which includes two primarycontents, i.e., mechanism analysis and design. However, the most problems in thesefields are nonlinear. Thus, establishing model and solving approach for the nonlinearproblem is one of basic and key issues for the theoretical research on advancedmechanisms.It is primarily studied that the nonlinear problems in mechanisms are addressed bymodern computational intelligence approaches. Taking the kinematic analysis anddesign of linkages, and the discrete optimization design of gear mechanisms, etc., asresearch objectives, this work studies the constructing methods of mathematicalmodels and the solving strategies based on differential evolutionary (DE) algorithms.Orientating the above nonlinear problems in the mechanisms, the work develops fourimproved DE algorithms which are implemented to solve continuous and discreteoptimization problems in mechanism analysis and design. Principal contents of theresearch are described as follows.Firstly the strict mathematical defines are proposed to depict the operators and thepopulation states of a standard DE algorithm. Based on these defines, the one-steptransformation probabilities are calculated for mutation, cross, and selection operators.In the meantime, the convergence of a standard DE algorithm is analyzed by using theMarkov chain theory. It is proved that a standard DE algorithm is neither globallyconvergent nor locally convergent. The analytic conclusions are helpful to guide theresearch on improved algorithms and their engineering applications.In order to preserve diversity of the population, this study develops a modified DEalgorithm, namely adaptive chaotic DE algorithm (ACDE), for solving unconstrainedoptimization problems (UOPs), which hybridizes the classified mutation strategiesand the chaotic escape operators to improve its performance. Furthermore, it isconcluded by using the probability theory that the developed ACDE algorithm isglobally convergent. The unconstrained optimization models are constructed toformulate the displacement analysis problems for planar multi-bar linkages and spatialparallel robot mechanisms. Then, the ACDE algorithm is implemented to solve these optimization problems. The results of numerical examples show that forwardpositional solutions to mechanisms can be precisely found by the ACDE algorithmand they have well stability.Orientating constrained optimization problems (COPs), this work presents animproved DE algorithm, called bi-group constrained DE algorithm (BCDE), in whichan adaptive penalty function approach is incorporated into the proposed bi-group DEalgorithm to enhance its performance. The sketchy and refined search methods aresuggested to solve the optimization design problems of approximate kinematicsynthesis for hinged four-bar linkages, which are all nonlinear. Firstly, the sketchysearch technique based on the BCDE algorithm is utilized to find optimal solutions toapproximate kinematic synthesis. Afterwards, in the neighbor of a sketchy solution,refined search technique is implemented to minimize the maximum error.Experimental results indicate that the performance of BCDE algorithm is better thancompared algorithms and it has well robustness.A discrete DE (DDE) algorithm is proposed for constrained discrete optimizationproblems (CDOPs) in mechanisms. It is studied that a novel measure, termed as aquasi re-averaging gene distance for a population, is utilized to evaluate the diversityof the population and chaotic immigration operators depend on this measure.Orientating the mentioned CDOPs in mechanisms, this study develops a hybrid DDE(HDDE) algorithm in which adaptive penalty function techniques and chaoticimmigration operators are incorporated into the proposed DDE algorithm. Finally, thenovel HDDE algorithm is used to solve CDOPs of optimal design for gearmechanisms and obtained results demonstrate that the performance of novel algorithmis better than compared algorithms.This study suggests an evolutionary algorithm for solving constrained multi-objective optimization problems (CMOPs), called sector-sampling-based constrainedmulti-objective differential evolution (SS-CMODE) algorithm, which borrows thesector sampling technique, and combines the bi-subgroup differential evolutionaryalgorithm with secondary mutation operators and the constraint handling approach.Firstly, this work constructs constrained multi-objective optimization models for thecrank-rocker linkage, the macro-scaled clamp mechanism, and the two-stage helicalcylindrical gear mechanism. Consequently, the SS-CMODE algorithm is utilized tosolve these CMOPs and is able to find a set of Pareto optimal solutions which aresatisfied with the constraint functions and are decided by researchers, engineers and technicians as alternative solutions.A novel strategy is presented to construct and solve the models of nonlinearcontinuous and discrete problems for advanced mechanisms. The achievement of thisdissertation has important theoretical significance and engineering application valuefor enriching the solving theory and approaches of numerical problems for advancedmechanisms and extending the application fields of computational intelligencetechniques for mechanisms.