【作者】 陈淼；

【导师】 赵世杰；

【作者基本信息】 辽宁工程技术大学 ， 数学， 2024， 硕士

【摘要】 约束多目标优化问题(Constrained Multi-objective Optimization Problems,CMOPs)是科学与工程领域广泛存在的一类优化问题,如何高性能确定CMOPs问题的Pareto前沿面是其研究的重点和难点。进化算法是当前求解CMOPs问题的一类有效方法,但囿于传统精英引导机制易导致种群多样性降低并诱发算法陷入局部极值,特别是面对存在着许多狭小且不连通可行域的CMOPs问题时其性能表现愈发欠意,因此,需要研发适配于该类CMOPs问题的新型约束多目标进化算法。鉴于双存档策略可有效克服精英引导机制存在的低种群多样性问题,而双种群机制可特定性捕捉CMOPs问题的可行域边界信息,故适定性改进并交互双存档策略与双种群机制,提出两种新型约束多目标进化算法,以改善算法的种群多样性和CMOPs问题的优化性能。主要研究内容如下:(1)针对传统进化算法在求解具有狭小且不连通可行域CMOPs问题时,存在种群难以有效收敛到所有Pareto前沿面的现象,提出一种基于双存档非支配解维护与辅种群动态衰减的约束多目标进化算法。双存档非支配解维护策略中的两个存档分别存储主种群进化产生的非支配不可行解和辅种群进化产生的非支配解,以增强种群的多样性。此外,提出一种辅种群动态衰减策略。通过动态调控辅种群的种群规模,降低其计算资源的消耗。该策略为主种群提供更多计算资源去探索潜在的可行域,以提高种群的收敛性。实验结果表明,所提算法具有较优勘探狭小且不连通可行域的能力,可有效提高算法的收敛精度,在不同基准测试函数套件上均表现较强的竞争力。(2)为解决求解CMOPs问题时算法多样性丧失的缺陷,提出一种基于约束存档解阶变与辅种群环境选择顿停的约束多目标进化算法。在约束存档解阶变策略中进化前期强调解的多样性,故约束存档存储主种群进化产生的非支配不可行解;进化后期侧重解的可行性,因此,约束存档转为存储非支配可行解。同时,无约束存档持续存储辅种群进化产生的非支配解以增强种群多样性,进而改善种群多样性低问题。此外,提出一种辅种群环境选择顿停策略以避免在进化后期辅种群对主种群协佐作用小的问题。该策略中,辅种群在进化后期停止进化并采用前期进化中的最优种群信息指导进化。实验结果表明,所提算法在求解不同基准测试函数套件上相较对比算法具有一定的竞争力。所提出的两种新型约束多目标进化算法能够较好地动态寻得复杂CMOPs问题的潜在可行域并表现出相对更优的分布均匀性。研究成果不仅有效延拓了约束多目标进化算法的理论体系,而且可迁移应用于高维、大规模型CMOPs问题,蕴含重要的理论与现实意义。该论文有图31幅,表26个,参考文献80篇。更多还原

【Abstract】 Constrained multi-objective optimization problems(CMOPs)are prevalent optimization issues in the fields of science and engineering,where the efficient determination of the Pareto front is both a critical research focus and a significant challenge.Evolutionary algorithms have emerged as a potent solution for tackling CMOPs.However,they are limited by the traditional elitist guidance mechanism,which can lead to diminished population diversity and trap the algorithm into local extrema.Particularly when faced with CMOPs that have many narrow and disconnected feasible regions,the performance becomes increasingly unsatisfactory.Therefore,there is a need to develop novel constrained multi-objective evolutionary algorithms that are suitable for this type of CMOPs.Given that the dual-archive strategy is leveraged to counteract the reduced diversity associated with elitist guidance mechanism,while the dual-population mechanism adeptly captures the boundary information of the feasible regions within CMOPs.So it is suitable to appropriately improve and interact the dual-archive strategy with the dual-population mechanism.This thesis introduces two novel constrained multi-objective evolutionary algorithms designed to enhance both the diversity of the population and the optimization performance for CMOPs.The main research contents are summarized as follows:(1)To address the challenge that traditional evolutionary algorithms struggle to effectively converge on all Pareto fronts,especially when dealing with CMOPs that have narrow and disconnected feasible regions,this thesis introduces a novel constrained multi-objective evolutionary algorithm with dual-archive non-dominance solution maintenance and auxiliarypopulation dynamic decay.The dual-archive separately store the non-dominated infeasible solutions generated during the evolution of the main population and the non-dominated solutions generated by the evolution of the auxiliary population,enhancing diversity.Additionally,auxiliarypopulation dynamic decay strategy is proposed,dynamically adjusting the population size of the auxiliary population,the consumption of computational resources is reduced.This strategy allow the main population to allocate more computational resources to explore potential feasible regions and improve population convergence.Experimental results demonstrate that the proposed algorithm exhibits excellent ability to explore narrow and disconnected feasible regions,significantly enhancing convergence precision and outperforming other algorithms on various benchmark test suites.(2)To tackle the issue of diversity loss in solving CMOPs,constrained multi-objective evolutionary algorithm with constrained-archive solution phase-transition and auxiliarypopulation environment selection pause-termination is proposed.During constrained-archive solution phase-transition strategy,the diversity of solutions is emphasized in the early generation of evolution,thus the constrained archive stores non-dominated infeasible solutions generated by the evolution of the main population.As the evolution shifts to emphasizing the feasibility of solutions,the role of the constrained archive transitions from storing non-dominated infeasible solutions to storing non-dominated feasible solutions.The unconstrained archive continuously stores non-dominated solutions generated by the evolution of the auxiliary population to strengthen population diversity and thus enhance the issue of low population diversity.Furthermore,auxiliary-population environment selection pause-termination strategy is proposed to avoid the problem of limited assistance provided by the auxiliary population to the main population in the last generation of evolution.In this strategy,the auxiliary population pauses evolution in the last generation and adopts the optimal population information from earlier evolution to guide its further evolution.Experimental results demonstrate that the proposed algorithm exhibits a certain level of competitiveness compared to other algorithms when solving different benchmark test function suites.The proposed two novel constrained multi-objective evolutionary algorithms can dynamically find the potential feasible region of complex CMOPs and show relatively better distribution uniformity.The research results not only effectively extend the theoretical system of constrained multi-objective evolutionary algorithm,but also can be applied to high-dimensional and large-scale CMOPs,which has important theoretical and practical significance.The thesis has 31 pictures,26 tables,and 80 references.更多还原