Research On Single-objective And Multi-objective Dynamic Optimization Methods Based On Evolutionary Computation

Dynamic optimization problems (DOPs) are often encountered in areas such as chemical engineering, aerospace industry, and biological engineering. Due to its abilities to improve product quality, reduce production costs and ensure the safety of operation, research on dynamic optimization methods has attracted a wide of attention from the academia and engineering. However, the challenge of dynamic optimization study lies in the following two aspects:(1) Real-world DOPs are often characterized by multi-peak, multi-variables, multi-constraints, and explicit mathematical descriptions are often unavailable; therefore, traditional dynamic optimization methods sometimes cannot deal with these problems; (2) Multiple conflict objectives often exist in real-world DOPs, which poses greater challenges for the solutions of DOPs. Evolutionary computational methods are population-based stochastic search techniques inspired by nature. They have unique advantages for DOPs characterized by multi-peak, discontinuity, without explicit mathematical descriptions, and especially multi-objective. Therefore, this dissertation aims at developing new methods for DOPs with single-objectives and multi-objectives based on evolutionary computational methods, within the framework of control vector parameterizations (CVP). The main contributions are summarized as follows:(1) Hybrid gradient particle swarm optimization for single-objective DOPsMost of evolutionary computational methods own weaknesses of low precision and slow convergence speed when solving DOPs. Therefore, aiming at alleviating these weaknesses, hybrid gradient particle swarm optimization (HGPSO) is presented to deal with DOPs, which combines the advantages of particle swarm optimization (PSO) and the gradient-based algorithm. HGPSO employs a two-stage search framework, i.e., it first adopts PSO with local ring topology to detect the area of global optimal solution, and gradient-based algorithm is then used to perform a fast local research. HGPSO owns the global search ability of PSO and fast local search ability of gradient-based algorithm. By integrated with CVP approach, HGPSO is applied to solve five DOPs with different characteristics such as singular, multi-peak and multi-variables. The simulation results demonstrated the superiority of HGPSO in terms of solution accuracy and computational cost, compared with two PSO variants and other methods in the literature.(2) Non-uniform discretization-based CVP approach for single-objective DOPsTo overcome the defects such as low control precision and inflexible discretization in traditional uniform discretization-based CVP (udCVP), a novel non-uniform discretization-based CVP (ndCVP) approach is proposed, aiming at achieving high control precision with a small number of control intervals. In ndCVP, the incremental time parameters are encoded along with the control parameters into the individual to be optimized. The coding method of ndCVP can avoid handling complex ordinal constraints. It is also proved that ndCVP is a natural generalization of udCVP. By combining ndCVP approach and HGPSO algorithm, a new dynamic optimization method named ndCVP-HGPSO is presented. Its applications to four single-objective DOPs shows that ndCVP-HGPSO can adjust the time intervals in the optimization processes in compliance with the shapes of the optimal control trajectories; therefore ndCVP-HGPSO can achieve better results with a small number of control intervals. Moreover, ndCVP-HGPSO is compared with udCVP-HGPSO to show its advantages.(3) Ranking-based differential evolution algorithms for constrained single-objective DOPsRecent study indicates that differential evolution (DE) lacks sufficient selection pressure when handling complex real-world optimization problems, therefore, ranking-based differen-tial evolution (DE-RMO) algorithms are presented to solve the constrained single-objective DOPs, which consider both the search efficiency of the optimization process and the feasibility of the final optimal solutions. Firstly, ranking-based mutation operator (RMO) based on a constraint-handling mechanism named superiority of feasible solutions (SFS), are devised for DE-RMO algorithms, in which better individuals have larger selection probabilities to produce offspring. Then, with the introduction of state constrained variables, the path constraints are converted into the terminal constraints to calculate the overall constraint violation, and the SFS mechanism is employed to handle the constraints. Three ranking-based constrained DEs and their corresponding non-ranking DEs are evaluated by solving four constrained DOPs. Simulation results reveal the effectiveness and efficiencies of the proposed algorithms.(4) Ranking-based multi-objective differential evolution for multi-objective DOPsMulti-objective differential evolution (MODE) also has weaknesses of lacking sufficient selection pressure when handling real-world optimization problems. Therefore, a new algorithm named MODE with ranking-based mutation operator (MODE-RMO) is proposed for multi-objective optimization problems, and its application for multi-objective DOPs is also discussed. Firstly, ranking-based mutation operator is extended for multi-objective optimization by incorporating fast nondominated sorting and crowding distance. Then, MODE-RMO is put forward by embedding ranking-based mutation operator into the MODE algorithm. Simulation results on ten multi-objective benchmark functions demonstrate that the ranking-based mutation operator can enhance the performance of MODE by accelerating the convergence rate. Finally, by combining with CVP approach, MODE-RMO is applied to solve three multi-objective DOPs taken from literature. The MODE-RMO algorithm obtains satisfactory Pareto optimal front, and provides a variety of Pareto optimal controls for designers.(5) Multi-objective differential evolution with ensemble of parameters and mutation strategies for constrained multi-objective DOPsTo enhance the robustness of MODE for multi-objective DOPs, a new adaptive MODE algorithm named MODE with ensemble of parameters and mutation strategies (EPSMODE) is proposed, which used a multi-parameters and multi-strategies ensemble method to select proper control parameters and mutation strategies during the evolution. EPSMODE approach employs an ensemble of parameter values and mutation strategies, and these parameter values and mutation strategies compete to produce offspring based on Pareto domination mechanisms. Moreover, Deb’s constrained domination principle is used to handle the constraints. EPSMODE is evaluated in eleven constrained multi-objective benchmark functions, and compared with GDE3 and NSGA-Ⅱ. Simulation results demonstrate that EPSMODE is a very competitive algorithm. Moreover, by combining with the CVP approach, EPSOMODE is applied to solve two constrained multi-objective DOPs. The satisfactory Pareto optimal fronts are obtained, and all Pareto optimal controls are feasible.