CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

Novel electromagnetism-like mechanism method for multiobjective optimization problems

As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.

MODS： A Novel Metaheuristic of Deterministic Swapping for the Multi-Objective Optimization of Combinatorials Problems

This paper states a new metaheuristic based on Deterministic Finite Automata （DFA） for the multi - objective optimization of combinatorial problems. First, a new DFA named Multi - Objective Deterministic Finite Automata （MDFA） is defined. MDFA allows the representation of the feasible solutions space of combinatorial problems. Second, it is defined and implemented a metaheuritic based on MDFA theory. It is named Metaheuristic of Deterministic Swapping （MODS）. MODS is a local search strategy that works using a MDFA. Due to this, MODS never take into account unfeasible solutions. Hence, it is not necessary to verify the problem constraints for a new solution found. Lastly, MODS is tested using well know instances of the Bi-Objective Traveling Salesman Problem （TSP） from TSPLIB. Its results were compared with eight Ant Colony inspired algorithms and two Genetic algorithms taken from the specialized literature. The comparison was made using metrics such as Spacing, Generational Distance, Inverse Generational Distance and No-Dominated Generation Vectors. In every case, the MODS results on the metrics were always better and in some of those cases, the superiority was 100%.

A Multi-Objective Optimal Evolutionary Algorithm Based on Tree-Ranking

Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.

Solving Multi-Area Environmental/Economic Dispatch by Pareto-Based Chemical-Reaction Optimization Algorithm

In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a selfadaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore,a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.

Method of Searching for Earthquake Disaster Evacuation Routes Using Multi-Objective GA and GIS

This study treats the determination of routes for evacuation on foot in earthquake disasters as a multi-objective optimization problem, and aims to propose a method for quantitatively searching for evacuation routes using a multi-objective genetic algorithm (multi-objective GA) and GIS. The conclusions can be summarized in the following three points. 1) A GA was used to design and create an evacuation route search algorithm which solves the problem of the optimization of earthquake disaster evacuation routes by treating it as an optimization problem with multiple objectives, such as evacuation distance and evacuation time. 2) In this method, goodness of fit is set by using a Pareto ranking method to determine the ranking of individuals based on their relative superiorities and inferiorities. 3) In this method, searching for evacuation routes based on the information on present conditions allows evacuation routes to be derived based on present building and road locations.?Further, this method is based on publicly available information;therefore, obtaining geographic information similar to that of this study enables this method to be effective regardless of what region it is applied to, or whether the data regards the past or the future. Therefore, this method has high degree of spatial and temporal reproducibility.

A Novel Quantum - inspired Multi - Objective Evolutionary Algorithm Based on Cloud Theory

In the previous papers,Quantum-inspired multi-objective evolutionary algorithm(QMEA) was proved to be better than conventional genetic algorithms for multi-objective optimization problem.To improve the quality of the non-dominated set as well as the diversity of population in multi-objective problems,in this paper,a Novel Cloud -based quantum -inspired multi-objective evolutionary Algorithm(CQMEA) is proposed.CQMEA is proposed by employing the concept and principles of Cloud theory.The algorithm utilizes the random orientation and stability of the cloud model,uses a self-adaptive mechanism with cloud model of Quantum gates updating strategy to implement global search efficient.By using the self-adaptive mechanism and the better solution which is determined by the membership function uncertainly,Compared with several well-known algorithms such as NSGA-Ⅱ,QMEA.Experimental results show that(CQMEA) is more effective than QMEA and NSGA -Ⅱ.

面向多行程取送货车辆路径问题的混合NSGA-Ⅱ

针对多行程取送货车辆路径问题(VRP)收敛性与多样性相互制约的问题,提出一种融合自适应大邻域搜索(ALNS)算法和自适应邻域选择(ANS)的混合快速非支配排序遗传算法(NSGA-Ⅱ-ALNS-ANS)。首先,考虑初始解对算法收敛速度的影响,提出一种改进的后悔插入法以获得高质量初始解;其次,结合取送货问题特性,设计多组破坏和修复算子,以及多种邻域结构,提高算法的全局搜索能力和局部搜索能力;最后,设计基于随机采样的最佳拟合下降(BFD)算法与高效的可行解评价标准,生成路径分配方案。采用不同规模的标准公开算例进行仿真实验,与模因算法(MA)相比,所提算法的最优解质量提升了27%。实验结果表明,所提算法可快速得到满足多重约束的高质量车辆多行程路径分配方案,并在收敛性与多样性上优于对比算法。

车联网边缘计算场景下基于改进型NSGA-Ⅱ算法的边缘服务器部署决策

车联网环境下,边缘服务器的放置位置与部署数量直接影响到边缘计算的效率。由于在宏基站或基站上部署大型边缘服务器的成本较高,可以在微基站上部署一个小型边缘服务器作为补充,并通过优化大型边缘服务器的放置位置来降低成本。为了最小化边缘服务器的部署代价和服务延迟、最大化运营商的收入和服务器负载均衡度,把边缘服务器放置问题与车联网用户应用服务放置问题联合建模为一个多目标优化问题,并提出了基于改进型NSGA-Ⅱ算法的放置方案。实验结果表明,提出的边缘服务器放置方案能够降低约44%的边缘服务器部署成本,降低约14.2%的时延,提升24.2%的运营商收入,具有较好的应用价值。

约束多目标优化问题的一类内-外混合罚函数方法

该文提出一种内-外混合罚函数方法求解具有等式和不等式约束的多目标优化问题.其中罚函数由目标函数,内点罚函数和可行集外点罚函数构成.在适当的条件下,借助具有单调性的辅助函数,证明了算法所生成的迭代序列收敛于问题的Pareto最优解或弱Pareto最优解.同时给出了三个数值实验来验证算法的可行性.最后将算法应用于解决多指标交通网络最小费用流问题,并与线性加权法进行比较,结果表明该算法在时间成本上具有明显的优势.

A new evolutionary algorithm for constrained optimization problems

To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.

基于改进的NSGA-II纺织生产车间柔性作业车间调度问题算法的研究

在纺织生产线调度领域,传统的人工调度方式已难以满足当前对高效利用机器和提升生产效率的迫切需求。鉴于此,本文建立了以最小化最大完工时间和机器总负载为优化目标的多目标柔性作业车间调度问题(flexible job shop scheduling problem,FJSP)数学模型,并提出了一种改进的NSGA-II算法(INSGA-II)用于求解。本文的主要特点是:(1)该算法采用基于工序和机器的两层编码方法;(2)采用混合种群初始化策略,目的是提高种群的初始质量;(3)设计了一种基于迭代次数的变领域搜索策略,在减少无效搜索的同时提高了局部搜索能力。本文在MK01-MK09和abz05-abz09的测试集上,将所提出的算法与其他算法(MOEA/D、MOEA/DD和NSGA-II)进行对比,并通过对14个标准算例的分析,证明了改进个NSGA-II算法在求解FJSP问题中的有效性。

基于改进NSGA-II算法的装配式建筑施工调度优化

针对以往装配式建筑调度研究主要基于每项活动只有确定的活动时间和一种执行模式,而实际调度过程中存在不确定的活动时间和多种执行模式,建立多目标多模式资源约束下的模糊工期调度模型,提出一种改进的非支配排序遗传算法(INSGA-II)来求解(时间−成本)双目标优化模型。该算法根据活动的优先级关系进行种群初始化和交叉操作,同时提出新的包含活动列表、模式列表和资源列表的3段编码。最后,通过装配式建筑施工现场实际案例分析和算法性能对比,证明本文构建的调度模型和算法设计能有效地解决多模式资源约束下的模糊工期调度模型,为施工调度计划的设计提供科学的思路和方法。

考虑负效应的垃圾回收两级选址-路径模型与算法

针对生活垃圾中转站和焚烧站的选址-路径问题(LRP),考虑经济目标和垃圾设施的负面影响,设计了与风向和距离有关的负效应分段函数,构建了两级多目标选址-路径(2E-MOLRP)模型,并提出了鲸鱼优化算法(WOA)和模拟退火(SA)算法结合的非支配算法WOA-SA。首先,结合随机方法与Clarke和Wright(CW)节约算法优化初始种群;其次,采用非线性动态惯性权重系数调整收敛速度;然后,设计WOA-SA的并行结构来增强全局搜索能力;最后,使用非支配排序法得到帕累托解集。对Prins和Barreto等35个基准案例以及天津市模拟案例进行分析。结果表明,WOA-SA可以找到20个基准案例的已知最优解(BKS),且对Prins和Barreto案例的求解结果与BSK差距的平均值分别为0.37%和0.08%,具有很好的收敛性和稳定性。将所提模型和算法应用于实例,给决策者提供了三种不同方案的负效应值及经济成本的方案,以支持不同偏好决策者选择,从而减少垃圾回收物流成本和设施对环境的负面影响。

Optimization methods for regularization-based ill-posed problems： a survey and a multi-objective framework

Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational regularizafion. Meanwhile, we also retrospect popular optimiza- tion approaches and regularization parameter choice meth- ods. In fact, the regularization problem is inherently a multi- objective problem. The traditional methods usually combine the fidelity term and the regularization term into a single- objective with regularization parameters, which are difficult to tune. Therefore, we propose a multi-objective framework for ill-posed problems, which can handle complex features of problem such as non-convexity, discontinuity. In this framework, the fidelity term and regularization term are optimized simultaneously to gain more insights into the ill-posed prob- lems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.

基于Kriging模型的改进型NSGA-Ⅲ解决昂贵优化问题

在许多实际的优化问题中,为了进行适应度评估,其物理实验或数值仿真代价高昂,这给大多数现有的多目标进化算法(EAs)带来了巨大挑战。因此,文中提出了一种基于克里金模型辅助的改进参考点引导进化的优化算法,用于解决昂贵的超多目标优化问题。具体而言,根据种群的空间分布特征,借助关联点的熵差信息筛选参考点引导进化,以达到探索与开发的平衡。所提出的代理辅助进化算法(SAEA)使用克里金法来逼近每个目标函数,而无需进行原始昂贵的函数评估从而降低了计算成本。模型管理中采用一种纯指标填充采样准则,借助收敛性、多样性指标确定适当采样策略并使用昂贵目标函数对采样解进行真实评估以提升种群收敛与算法优化的效率。对具有3个以上目标的80个DTLZ与WFG基准测试问题进行了对比研究,证明了此算法的有效性和可行性。

GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

Breeding Particle Swarm Optimization for Railways Rolling Stock Preventive Maintenance Scheduling

The goal of railway rolling stock maintenance and replacement approaches is to reduce overall cost while increasing reliability which is multi objective optimization problem and a proper predictive maintenance scheduling table should be adequately designed. We propose Breeding Particle Swarm Optimization (BPSO) model based on the concepts of Breeding Swarm and Genetic Algorithm (GA) operators to design this table. The practical experiment shows that our model reduces cost while increasing reliability compared to other models previously utilized.

考虑区域资源利用均衡的电动公交充电站选址及充电路径问题

在新基建助推区域平衡发展和低碳双重背景下,研究电动公交充电站选址及充电路径问题,以经济效益最大化和区域资源利用均衡为目标,考虑公交司机可能充电时机以及充电需求、运营时间、利用率等约束条件建立两阶段多目标决策模型,设计多重嵌套式遗传算法求解模型,并应用于算例检验模型可行性。结果表明:仅考虑经济效益目标会产生充电“拥挤”、路途过长等弊端,而本文模型能有效缩小区域间公交充电效率差异,提高全局资源利用均衡性;通过降低充电站容量可提高充电站利用率与经济效益,但区域资源利用均衡性会减弱,且充电站容量对公交充电路途所耗费时间的作用较为敏感;适当增加区域资源利用均衡目标的权重更有利于提高总体优化效果。研究结果可为公交充电站选址和路径规划提供决策支持。

具有紧时、高能耗特征的混合流水车间多目标调度优化问题

针对具有紧时、高能耗工序特征的混合流水车间调度问题,以优化产品暴露时间、最大完工时间和能源消耗为目标,建立混合流水车间调度模型,并提出一种改进的多目标粒子群算法进行有效求解。首先构建了基于ISDE指标的档案维护策略及局部邻域搜索策略,辅助算法跃出局部极值及减少生产阻塞。之后,提出一种基于模糊理论的决策分析方法选取最优调度方案。最后,通过仿真实验验证提出的多目标调度模型与算法的可行性和优越性。