Research On Multi-objective Dynamic Differential Evolution And Its Applications

Multi-objective optimization problems are often encountered in many practice engineering applications and science researches, and it is one of class of very important but difficult complex problem to be solved. As stochastic optimization metaheuristics, evolutionary algorithms deal simultaneously with a set of possible solutions (the so-called population) which allows us to find several members of the Pareto optimal set in a single run of the algorithm. Consequently, Evolutionary multi-objective optimization (EMO) has now become a popular and useful field of research and application. Differential evolution (DE), as one of the most powerful stochastic real-parameter optimization algorithms in current use, is a natural candidate to be extended for multi-objective optimization. This dissertation mainly focuses on the researches of differential evolution with dynamic population updating stratey, and its extention for multi-objective optimization. Main results and contribu-tions of this dissertation are as follows:The research background of multi-objective differential evolution (MODE) is introduced firstly. Then, the relative definitions of multi-objective optimization (MO) are presented, and a breaf histrory of EMO and main multi-objective evolutionary algorithms (MOEAs) are introduced. Furthermore, a review of the basic concepts of DE and a survey of its application to multiobjective are also presented. Thereafhter, the hot and difficult problems in EMO are discussed and the research significance of this dissertation is also provided.In the view of slower convergence of original DE with static population updating structure, a dynamic population updating stratey is introduced and a novel dynamic differential evolution (DDE) is then proposed. Twenty-one Benchmark test functions are used to evaluate the effectiveness of the proposed DDE. Experiment results show that the dynamic population updating stratey greatly speeds up the DE’s convergence speed, but also increases the risk to premature convergence in some extent for the DEs with ’best’ mutation strategy. Therefore, to keep the balance between the global explora-tion and local exploitation, an adaptive mutation operator combined with the advantages of strategies of DDE/rand/1/bin and DDE/best/2/bin is proposed. The effectiveness of the modified version is validated by using twenty-one classical Benchmark functions and a specific2D IIR filter design problem. An approach called MOSADDE to extend the stragety of DDE/rand/1/bin to solve multi-objective optimization problems with an external elitist archive is presented. To preserve the diversity of the Pareto optimality, a more accurate crowding measure method namely crowding entropy is proposed. Moreover, to improve the robustness of DDE, a control parameter self-adaptive strategy is introduced. Therefore, the user does not need to guess the good values for F and CR, which are problem dependent. The proposed approach was validated using eighteen standard test problems currently adopted in the evolutionary multi-objective optimization community. The experiment results and no-parametric statistical results associated indicate that MOSADDE is able to maintain a better spread of solutions and converge in the obtained Pareto-optimal front compared to three representative multi-objective evolutionary algorithms NSGA-Ⅱ, SPEA2and MOPSO.To further improve the convergence properties of MOSADDE, based on the stratey of DDE/best/2/bin, an improved version MOSADDE-Ⅱ is proposed. The random initialization based parameter self-adaptive strategy in MOSADDE is replaced by a new parameter self-adaptive strategy with self-learning ability. Moreover, in order to preserve a set of nondominated solutions widely distributed along the Pareto front, especially along the Pareto front of high-dimension problem, a progressive comparison truncate operator based on normalized nearest neighbor distance is proposed in the MOSADDE-Ⅱ. This density estimation method is able to accurately reflect the crowding degree for problems with objective functions range between values of different orders of magnitude. The proposed approach was validated using twenty-seven standard test problems currently adopted in the evolutionary multi-objective optimization community.Based on the previous static MODDE, an approach for the dynamic multi-objective optimization is presented by introducing environment detecting operator and diversity maintaining strategy for inintial population in new enviroment. The effect-iveness of the dynamic multi-objective dynamic differential evolution (dMODDE) is validated against various dynamic MOEAs upon seven Bechmark problems with different characteristics in Pareto optimal front. Experiment results show that the proposed dMODDE is able to well track the Pareto front as it changes with time in dynamic environments.Based on the nondominate sorting strategy, a multi-objective dynamic differential evolution algorithm for the bi-level multi-objective optimization problems (BLMOP) is proposed. For the characteristics of BLMOPs, a special evolutionary population structure is designed for the bi-level multi-objective dynamic differential evolution (BLMODDE) algorithm. The effectiveness of the BLMODDE is examined on several updated test problems. Experiment results demonstrate that the proposed BLMODDE is able to maintain a good spread of solutions and converge to the Pareto-optimal front of problems. It is suggested that the proposed approach is promising for dealing with BLMOPs.The application of the MOSADDE-II for the simultaneous optimization of component sizing and control strategy in parallel hybrid electric vehicles (HEVs) is described. Based on an electric assist control strategy, the HEV optimal design problem is formulated as a nonlinear constrained multiobjective problem with competing and noncommensurable objectives of fuel consumption (FC), CO emission, HC emission, and NOx emission. The driving performance requirements are considered constraints. Moreover, fuzzy set theory is employed to extract the best compromise solution. The optimization process is performed over three typical driving cycles including FTP, ECE+EUDC and UDDS that currently used in United States and European community. The results demonstrate the capability of the proposed approach to generate well-distributed Pareto optimal solutions of the HEV multi-objective optimization design problem. The comparison with reported results of GA based weighting sum approaches and NSGA-Ⅱ reveals the superiority of the proposed approach and confirms its potential for optimal HEV design.To further demonstrate effectiveness of the MOSADDE-Ⅱ for engineering optimization design, it is used for the Environmental/Economic power Dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives. Several optimization runs of the proposed approach have been carried out on the IEEE30-and118-bus test system. The comparison with reported results of other MOEAs reveals the superiority of the proposed approach and confirms its potential for solving other power systems multi-objective optimization problems.Finally, the main innovations of the dissertation are summarized, and then the fields for further research are prospected.