基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)作为一种重要的多目标优化方法,已经成功地应用于解决各种多目标优化问题。然而,MOEA/D算法在解决具有高维目标和复杂帕累托前沿(Pare...基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)作为一种重要的多目标优化方法,已经成功地应用于解决各种多目标优化问题。然而,MOEA/D算法在解决具有高维目标和复杂帕累托前沿(Pareto frontier,PF)的问题时,容易陷入局部最优并难以获得可行解。本文提出一种改进的MOEA/D算法,包括3个优化策略:首先,使用拉丁超立方抽样方法代替随机方法初始化种群,得到分布均匀的初始种群,同时对权重向量关联解的策略进行优化;其次,提出一种稀疏度函数,用于计算种群中个体的稀疏度并维护外部种群;最后,提出了自适应调整权向量的方法,用于引导种群收敛到帕累托前沿,并且有效平衡种群的多样性和收敛性。将提出算法和4种对比算法在DTLZ和WFG系列问题以及多目标旅行商问题(multi-objective travel salesman problem,MOTSP)上进行对比实验,实验结果表明本文提出自适应调整权重向量的多目标进化(MOEA/D with cosine similarity adaptive weight adjustment,MOEA/D-CSAW)算法在处理具有复杂帕累托前沿和高维多目标的问题时,算法的综合性能要优于对比算法。展开更多
多目标车间布局优化是现代制造业发展的必然趋势。通过综合考虑生产效率、成本控制、工作环境和员工满意度等多方面因素,制定科学合理的布局方案,将有助于提升企业的整体竞争力和可持续发展能力。然而,传统的多目标进化算法在布局优化...多目标车间布局优化是现代制造业发展的必然趋势。通过综合考虑生产效率、成本控制、工作环境和员工满意度等多方面因素,制定科学合理的布局方案,将有助于提升企业的整体竞争力和可持续发展能力。然而,传统的多目标进化算法在布局优化解决方案的融合性和多样性方面面临着巨大的挑战。本文提出了一种基于柔性隔间结构的空间进化算法(ISEA)来求解具有多目标的设施布局问题。首先,创建了空间配置库,并使用进化操作(选择、交叉和变异)来产生新的配置,通过引入配置组半径d来控制ISEA中解的收敛性。其次,将最近和最远候选解方法与快速非主导排序相结合,选择帕累托最优解,以保证所得解的多样性。实验在8个不同的代表性实例和3个参数指标上进行了实验。与现有的MOEAs相比,ISEA能够找到更好的结果并具有更好的性能。数值实验验证了ISEA求解多目标布局优化问题的有效性。Multi-objective workshop layout optimization is the inevitable trend of the development of modern manufacturing industry. Making a scientific and reasonable layout plan by comprehensively considering many factors such as production efficiency, cost control, working environment and employee satisfaction will help to enhance the overall competitiveness and sustainable development ability of enterprises. However, the traditional multi-objective evolutionary algorithm faces great challenges in the integration and diversity of layout optimization solutions. In this paper, a spatial evolution algorithm (ISEA) based on flexible compartment structure is proposed to solve the facility layout problem with multiple objectives. Firstly, the spatial configuration library is created, and new configurations are generated by evolutionary operations (selection, crossover and mutation). The convergence of solutions in ISEA is controlled by introducing the radius d of configuration group. Secondly, the nearest and farthest candidate solution method is combined with fast non-dominant sorting to select Pareto optimal solution to ensure the diversity of the obtained solutions. Experiments were carried out on 8 different representative examples and 3 parameters. Compared with existing MOEAs, ISEA can find better results and has better performance. Numerical experiments verify the effectiveness of ISEA in solving multi-objective layout optimization problems.展开更多
文摘多目标车间布局优化是现代制造业发展的必然趋势。通过综合考虑生产效率、成本控制、工作环境和员工满意度等多方面因素,制定科学合理的布局方案,将有助于提升企业的整体竞争力和可持续发展能力。然而,传统的多目标进化算法在布局优化解决方案的融合性和多样性方面面临着巨大的挑战。本文提出了一种基于柔性隔间结构的空间进化算法(ISEA)来求解具有多目标的设施布局问题。首先,创建了空间配置库,并使用进化操作(选择、交叉和变异)来产生新的配置,通过引入配置组半径d来控制ISEA中解的收敛性。其次,将最近和最远候选解方法与快速非主导排序相结合,选择帕累托最优解,以保证所得解的多样性。实验在8个不同的代表性实例和3个参数指标上进行了实验。与现有的MOEAs相比,ISEA能够找到更好的结果并具有更好的性能。数值实验验证了ISEA求解多目标布局优化问题的有效性。Multi-objective workshop layout optimization is the inevitable trend of the development of modern manufacturing industry. Making a scientific and reasonable layout plan by comprehensively considering many factors such as production efficiency, cost control, working environment and employee satisfaction will help to enhance the overall competitiveness and sustainable development ability of enterprises. However, the traditional multi-objective evolutionary algorithm faces great challenges in the integration and diversity of layout optimization solutions. In this paper, a spatial evolution algorithm (ISEA) based on flexible compartment structure is proposed to solve the facility layout problem with multiple objectives. Firstly, the spatial configuration library is created, and new configurations are generated by evolutionary operations (selection, crossover and mutation). The convergence of solutions in ISEA is controlled by introducing the radius d of configuration group. Secondly, the nearest and farthest candidate solution method is combined with fast non-dominant sorting to select Pareto optimal solution to ensure the diversity of the obtained solutions. Experiments were carried out on 8 different representative examples and 3 parameters. Compared with existing MOEAs, ISEA can find better results and has better performance. Numerical experiments verify the effectiveness of ISEA in solving multi-objective layout optimization problems.
