一类新型动态多目标鲁棒进化优化方法

传统动态多目标优化问题（Dynamic multi-objective optimization problems,DMOPs）的求解方法,通常需要在新环境下,通过重新激发寻优过程,获得适应该环境的Pareto最优解.这可能导致较高的计算代价和资源成本,甚至无法在有限时间内执行该优化解.由此,提出一类寻找动态鲁棒Pareto最优解集的进化优化方法.动态鲁棒Pareto解集是指某一时刻下的Pareto较优解可以以一定稳定性阈值,逼近未来多个连续动态环境下的真实前沿,从而直接作为这些环境下的Pareto解集,以减小计算代价.为合理度量Pareto解的环境适应性,给出了时间鲁棒性和性能鲁棒性定义,并将其转化为两类鲁棒优化模型.引入基于分解的多目标进化优化方法和无惩罚约束处理方法,构建了动态多目标分解鲁棒进化优化方法.特别是基于移动平均预测模型实现了未来动态环境下适应值的多维时间序列预测.基于提出的两类新型性能评价测度,针对8个典型动态测试函数的仿真实验,结果表明该方法得到满足决策者精度要求,且具有较长平均生存时间的动态鲁棒Pareto最优解.     

一种求解鲁棒优化问题的多目标进化方法

鲁棒优化问题（Robust Optimization Problem,ROP）是进化算法（Evolutionary Algorithms,EAs）研究的重要方面之一,对于许多实际工程优化问题,通常需要得到鲁棒最优解。利用多目标优化中的Pareto思想优化ROP的鲁棒性和最优性,将ROP转化为一个两目标的优化问题,一个目标为解的鲁棒性,一个目标为解的最优性。针对ROP与多目标优化的特点,利用动态加权思想,设计一种求解ROP的多目标进化算法。通过测试函数的实验仿真,验证了该方法的有效性。     

一种改进的鲁棒多目标优化方法

针对在解决某些复杂多目标优化问题过程中,所得到的Pareto最优解易受设计参数或环境参数扰动的影响,引入了鲁棒的概念并提出一种改进的鲁棒多目标优化方法,它利用了经典的基于适应度函数期望和方差方法各自的优势,有效地将两种方法结合在一起。为了实现该方法,给出一种基于粒子群优化算法的多目标优化算法。仿真实例结果表明,所给出的方法能够得到更为鲁棒的Pareto最优解。     

应急物流车辆调度多目标鲁棒优化研究

针对应急物流车辆调度问题中对于经济性、时效性、可靠性和鲁棒性的多种要求，考虑了含有时间窗、不确定需求、不确定行驶时间，以及路段含有失效风险的多目标鲁棒车辆路径优化问题，通过定义新的成本函数、满意度函数、风险度函数和鲁棒度函数作为四个优化目标来构建模型，并基于鲁棒优化理论将不确定模型转化为确定性鲁棒对应模型求解，为解决不确定环境下优化问题提供了新的思路。算法方面，主要基于SPEA2算法框架求解该多目标模型，针对算法缺陷提出多种改进策略，并通过对比实验证明了改进策略的有效性。     

基于坡度的鲁棒优化方法

提出一种基于坡度的鲁棒性评价指标, 通过三阶反距离平方权差分算法计算坡度, 以坡度指标来反映函数的变化趋势和平滑程度, 从而设计了一种求解鲁棒优化问题的多目标进化方法, 仿真实验证明其有效性。实验还表明该方法在解的分布性与区分度上更有优势。     

易腐品多周期闭环物流网络鲁棒优化模型

针对不同周期的易腐品需求与退货不确定性问题,构建了易腐品多周期闭环物流网络,并设计了对应的混合整数线性规划（MILP）模型,以实现最低系统总成本、最佳设施选址以及最优配送车辆运输路径的决策。为有效规避不确定参数的影响,采用基约束鲁棒方法,将模型中的部分清晰约束转换为鲁棒对应式。以上海市果蔬农产品企业为实例,通过遗传算法对模型进行求解。结果表明,相对单周期而言,多周期系统具有动态性、系统成本更低的优点,同时通过不确定预算参数的变化分析,验证了鲁棒模型的可行性与有效性,进而为不确定环境下构建多周期闭环物流网络及降低系统成本提供了借鉴。     

鲁棒线性优化问题研究综述

鲁棒优化（ＲＯ）是从计算复杂性的角度研究不确定优化模型鲁棒最优解的数学方法．从单阶段鲁棒优化和多阶段鲁棒优化两个方面对鲁棒线性优化（ＲＬＯ）理论的研究进展进行综述,前者的研究主要基于不同形式的不确定集合,后者的研究则基于前者的方法．研究多阶段不确定决策中决策变量受不确定参数实现值影响的情况,其核心是影响函数连续时的仿射可调鲁棒对应模型和函数离散时的有限适应性模型．最后对ＲＬＯ 的研究前景作了展望．     

基于进化算法的多目标优化方法

进化算法在解决多目标优化问题中有其特有的优势.首先对多目标优化问题进行了描述;然后结合研究现状讨论了目前几种主要的基于进化算法的多目标优化方法,以及它们的优缺点;最后给出了多目标进化优化算法的一些应用,以及进化多目标优化算法的未来发展方向.     

鲁棒多目标线性规划模型及混合遗传算法

针对目标函数系数和约束条件系数均在椭球扰动集下的不确定多目标线性规划, 提出了椭球扰动集下的鲁棒多目标线性规划问题。基于每个目标均需获得鲁棒解的假设下给出了定理及证明, 以此把原问题转换为具有二阶锥约束的确定性多目标优化问题。设计了一种混合策略求解算法, 整体流程采用多目标遗传算法, 局部采用SOCP优化软件Sedumi进行计算, 从而获得不确定多目标线性规划的鲁棒解集, 并通过数值算例验证了该算法的有效性。     

进化算法鲁棒最优解研究综述

在实际应用中,环境往往是不稳定的且易受到噪声的影响.因此,时于许多现实优化问题,一个鲁棒性好的解具有重要的意义.然而,以往关于进化算法(EAs)的研究主要集中在寻找全局最优解,解的鲁棒性却没有得到重视.从单目标鲁棒最优解、多目标鲁棒最优解及效率等方面较全面地分析了目前EAs搜索鲁棒最优解的研究现状.最后对相关研究工作做了展望.     

Solving a tri-objective supply chain problem with modified NSGA-II algorithm

In this paper, we propose the modification of an existing Multi-Objective Evolutionary Algorithm (MOEA) known as Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The proposed algorithm has been applied on a tri-objective problem for a two echelon serial supply chain. The objectives considered are: (1) minimization of the total cost of a two-echelon serial supply chain and (2) minimization of the variance of order quantity and (3) minimization of the total inventory. The variance of order quantity is an important factor to consider since the variance of order quantity is used to measure the bullwhip effect which is one of the performance measures of a supply chain. The supply chain under consideration is assumed to consist of buyers and supplier. The production process at the supplier is an imperfect production process and thus produces defective items. A percentage of defective items are sold at a secondary market and the remaining defective items are repaired. We have introduced a mutation algorithm which has been embedded in the proposed algorithm. Since the proposed mutation algorithm is performed over the entire population, thus the mutation algorithm has caused the modification of the parts of the original NSGA-II. The results of the modified algorithm have been compared with those of the original NSGA-II and SPEA2 (Strength Pareto Evolutionary Algorithm 2) evolutionary algorithms for varying values of probability of crossover. The experimental results show that the proposed algorithm performs significantly better than the original NSGA-II and SPEA2.     

基于改进SPEA2算法的火力分配问题

火力分配是战前任务规划的重要环节。考虑攻击效果、资源等约束条件,以攻击效益最大,武器消耗最小,自身损伤最小原则建立了火力分配多目标数学模型。针对传统方法在求解火力分配多目标优化问题时存在收敛效果差以及Pareto前端分布不均匀等不足,将近邻传播算法引入到SPEA2算法中,改进了SPEA2算法的多样性保持策略,优化了算法性能。实验结果表明：改进的SPEA2算法在解决多目标火力分配问题时,相较于标准SPEA2算法,具有收敛效果好,Pareto前端分布均匀的特性。通过实验,验证了模型的合理性和算法的可行性。     

Hybrid-Game Strategies for multi-objective design optimization in engineering

A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated.     

带时限的多出救点应急物资调度模型及算法

主要研究时间限制下的多出救点应急资源调度优化问题。针对传统优化算法搜索速度慢、易陷入局部最优解的缺点,提出一种新的基于高斯函数的混沌粒子群优化算法,该算法利用高斯函数的分布曲线特性和混沌的遍历性来增强粒子群优化算法的寻优能力。将该算法应用时间限制下的多出救点应急资源调度优化,建立了满足应急时间限制下系统总费用最小的数学模型,介绍了该算法的详细实现过程。算例通过和遗传算法和标准粒子群算法进行比较,证明了其搜索速度和寻优能力的优越性。     

Solution of multiobjective optimization problems: coevolutionary algorithm based on evolutionary game theory

When attempting to solve multiobjective optimization problems (MOPs) using evolutionary algorithms, the Pareto genetic algorithm (GA) has now become a standard of sorts. After its introduction, this approach was further developed and led to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to keep diversity. On the other hand, the scheme for solving MOPs presented by Nash introduced the notion of Nash equilibrium and aimed at solving MOPs that originated from evolutionary game theory and economics. Since the concept of Nash Equilibrium was introduced, game theorists have attempted to formalize aspects of the evolutionary equilibrium. Nash genetic algorithm (Nash GA) is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash equilibrium through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an evolutionary stable strategy (ESS). In this article, we find the ESS as a solution of MOPs using a coevolutionary algorithm based on evolutionary game theory. By applying newly designed coevolutionary algorithms to several MOPs, we can confirm that evolutionary game theory can be embodied by the coevolutionary algorithm and this coevolutionary algorithm can find optimal equilibrium points as solutions for an MOP. We also show the optimization performance of the co-evolutionary algorithm based on evolutionary game theory by applying this model to several MOPs and comparing the solutions with those of previous evolutionary optimization models. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003.     

改进量子遗传算法用于多峰值函数优化

传统遗传算法（SGA）在处理多峰值函数优化问题中存在局部收敛性的问题,最初的量子遗传算法（QGA）也存在这一问题。运用一种改进量子遗传算法（MQGA）,有效地解决了一些多峰值函数的优化问题。根据几个重要的测试函数进行仿真实验结果证明,与SGA和QGA相比,改进的量子遗传算法（MQGA）在一些多峰值优化问题中更具有效性和可行性。     

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.     

A parallel double-level multiobjective evolutionary algorithm for robust optimization

Robust optimization is a popular method to tackle uncertain optimization problems. However, traditional robust optimization can only find a single solution in one run which is not flexible enough for decision-makers to select a satisfying solution according to their preferences. Besides, traditional robust optimization often takes a large number of Monte Carlo simulations to get a numeric solution, which is quite time-consuming. To address these problems, this paper proposes a parallel double-level multiobjective evolutionary algorithm (PDL-MOEA). In PDL-MOEA, a single-objective uncertain optimization problem is translated into a bi-objective one by conserving the expectation and the variance as two objectives, so that the algorithm can provide decision-makers with a group of solutions with different stabilities. Further, a parallel evolutionary mechanism based on message passing interface (MPI) is proposed to parallel the algorithm. The parallel mechanism adopts a double-level design, i.e., global level and sub-problem level. The global level acts as a master, which maintains the global population information. At the sub-problem level, the optimization problem is decomposed into a set of sub-problems which can be solved in parallel, thus reducing the computation time. Experimental results show that PDL-MOEA generally outperforms several state-of-the-art serial/parallel MOEAs in terms of accuracy, efficiency, and scalability.