煤炭码头船货匹配下泊位动态分配多目标优化模型及算法

本文针对输出型煤炭码头船货匹配下泊位动态分配问题,构建了堆场-取装线-泊位-船舶联合分配优化数学模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,综合考虑船舶、泊位、堆场、取装线、煤种、航道开放时间和装船作业规则等要素,以船舶在港时间最短和作业效率最大为目标建立了相应的多约束多目标优化模型。然后,综合多目标优化、遗传算法以及仿真推演技术,设计了相应的遗传算法求解,包括:组合式编码、采用仿真推演策略的解码方法,追加了具有合法性检查的染色体生成算法,设计了采用多种策略的遗传操作等。最后实例表明,本算法的执行效率高而且优化效果好。     

基于油耗的带有车容限制弧路径问题的模型及优化

提出了一种基于油耗的带有车容限制的弧路径问题(Capacitated Arc RoutingProblem,CARP),建立了以降低油耗为目标的问题模型,构造了相应的遗传算法.基于标准测试问题,同传统以距离为优化目标的遗传算法求得的油耗进行比较,实验结果表明,此算法可以快速、有效的求得以油耗为优化目标的CARP问题的优化解,为实际中降低车辆运输服务成本提供了较好方案.     

不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化

项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。     

主通道位置不固定的设施布局问题多目标优化模型及算法

以物流中心设施布局问题为对象,提出了考虑出入口及主通道位置不固定情况下的设施布局问题的多目标优化模型并设计了其改进的遗传算法。首先,以物料搬运成本最小、活动关系密切度最大和面积利用率最大为目标,构建了考虑出入口位置不固定条件下的具有I型主通道的设施布局多目标优化数学模型。然后,设计了一种改进的遗传算法,包括:改进的编码、解码方法,追加了解码修正操作,基于惩罚函数策略的适应度函数等。实例测试表明,本算法的执行效率高而且结果稳定,优化效果好,布局结果紧凑适用。     

改进的生成树遗传算法及其在物流配送成本优化中的应用

针对物流配送成本优化问题的特点,建立了数学模型,并对基本的生成树遗传算法进行了改进,同时详细阐述了改进的生成树编码的遗传算法在物流配送成本优化问题中的运用等关键技术.最后根据此算法设计了一个物流配送优化系统,解决了一个物流配送成本优化问题,效果良好.此系统对于中小型物流公司设计最优物流策略和降低物流成本有着很大的应用前景.     

煤炭码头卸车调度问题多目标优化模型及算法

本文针对煤炭码头卸车调度问题,提出了相应的多约束多目标优化模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,本文考虑列车、煤种、场存、设备、翻堆线和卸车作业过程等约束条件,以卸车效率最大和列车在港时间最短为目标,构建了煤炭码头卸车调度问题多目标数学模型。然后,综合运筹学、遗传算法以及仿真技术,给出了煤炭码头卸车调度问题遗传算法详细设计,包括组合式编码和仿真推演解码方法,染色体生成算法,适应度函数设计,以及采用多种策略的遗传操作及修正等,并列出了算法步骤。实例测试表明,本算法的执行效率高而且优化效果好,结果适用。     

改进的NSGA-Ⅱ算法研究风力机叶片多目标优化

将一种采用精英控制策略和动态拥挤方法用于快速非支配排序遗传算法（NSGA-Ⅱ）,并应用到风力机叶片的优化研究中,获得了一种新颖的风力机叶片多目标优化设计方法．作为应用算例,以设计风速下的功率系数最大和叶片质量最小为优化目标,用该方法设计了5 MW大型风力机叶片．优化结果表明,此算法在处理风力机多目标优化问题取得了良好的效果,给出的是一个Pareto最优解集,而不是传统优化方法追求的单个最优解,为风力机多目标优化设计提供新的思路和通用的算法．     

基于分享学习和柯西变异的多目标人工蜂群算法

提出一种基于分享学习和柯西变异的多目标人工蜂群算法.该算法在基本人工蜂群算法中引入精英策略,即蜜蜂在更新食物源过程中,在随机选择邻居的同时,将全局最好个体以及外部档案中所有个体的平均位置作为分享学习的对象.在每次迭代结束后,对外部档案中排名位于前5%的个体进行柯西扰动,以增加解的多样性,并使得算法在求解复杂多目标优化问题时有能力跳出局部最优.在一些测试函数上的实验结果表明提出的新算法在求解多目标优化问题时,与某些经典算法相比具有一定的优越性.     

面向多目标优化的一种混合进化算法

针对多目标优化问题,设计一种基于量子计算和非支配排序遗传算法相结合的智能算法进行求解,综合量子算法和非支配排序遗传算法的优点,在局部搜索和全局搜索之间进行权衡。混合算法采用量子比特对问题的解进行编码,基于量子旋转门算子、分散交叉算子以及高斯变异算子对种群进行更新。进行局部深入搜索时,用一个解在目标空间中跟理想点的距离来评价该解的优劣;进行全局搜索时,基于非支配排序遗传算法中的有效前沿的划分和解之间的拥挤距离来评价某个解。最后,在经典的测试函数ZDT5上对所提混合算法进行了测试。通过对比分析若干项针对有效解集的评价指标,该混合算法在跟最优有效前沿的逼近程度以及有效解集分布的均匀程度上均优于目前得到广泛应用的非支配排序遗传算法。     

具有模糊目标的多目标双矩阵对策集结与求解

针对不确定性多冲突环境,建立了多个具有模糊目标的多目标双矩阵对策的综合集结模型.在假定局中人各模糊目标的隶属函数为线性函数的情形下,基于总体模糊目标的可达度,给出了纳什均衡解的定义,并应用粒子群优化算法对集结模型求解.最后,给出一个军事例子说明了模型的实用有效性和粒子群优化算法求解的高效性.     

An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results.     

Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

Heuristic approaches to determine base-stock levels in a serial supply chain with a single objective and with multiple objectives

This paper deals with the problem of determination of installation base-stock levels in a serial supply chain. The problem is treated first as a single-objective inventory-cost optimization problem, and subsequently as a multi-objective optimization problem by considering two cost components, namely, holding costs and shortage costs. Variants of genetic algorithms are proposed to determine the best base-stock levels in the single-objective case. All variants, especially random-key gene-wise genetic algorithm (RKGGA), show an excellent performance, in terms of convergence to the best base-stock levels across a variety of supply chain settings, with minimum computational effort. Heuristics to obtain base-stock levels are proposed, and heuristic solutions are introduced in the initial population of the RKGGA to expedite the convergence of the genetic search process. To deal with the multi-objective supply-chain inventory optimization problem, a simple multi-objective genetic algorithm is proposed to obtain a set of non-dominated solutions.     

A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design

Multi-objective particle swarm optimization (MOPSO) is an optimization technique inspired by bird flocking, which has been steadily gaining attention from the research community because of its high convergence speed. On the other hand, in the face of increasing complexity and dimensionality of today’s application coupled with its tendency of premature convergence due to the high convergence speeds, there is a need to improve the efficiency and effectiveness of MOPSO. In this paper a competitive and cooperative co-evolutionary approach is adapted for multi-objective particle swarm optimization algorithm design, which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co-evolution of competing and cooperating species. The competitive and cooperative co-evolution model helps to produce the reasonable problem decompositions by exploiting any correlation, interdependency between components of the problem. The proposed competitive and cooperative co-evolutionary multi-objective particle swarm optimization algorithm (CCPSO) is validated through comparisons with existing state-of-the-art multi-objective algorithms using established benchmarks and metrics. Simulation results demonstrated that CCPSO shows competitive, if not better, performance as compared to the other algorithms.     

基于遗传算法的固定起讫点危险品配送路线优化

为科学选择危险品配送路线,保障运输安全,将传统TSP(Travelling SalesmanProblem)问题加以推广和延伸,建立以路段交通事故率、路侧人口密度、环境影响因子和路段运输费用为指标的固定起讫点危险品配送路线优化模型.以遗传算法基本框架为基础,引入新的遗传算子,构建了可用于实现模型的多目标遗传算法.实例仿真表明,所建模型和算法在求解固定起讫点危险品配送路线优化问题中有较好的实用性.     

An improved NSGA-III algorithm based on elimination operator for many-objective optimization

Due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance schemes in the environmental selection, the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to handle many-objective optimization problems. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the uniformly distributed reference points to significantly promote population diversity, but the convergence based on the Pareto-dominance relation could still be enhanced. For this purpose, an improved NSGA-III algorithm based on elimination operator (NSGA-III-EO) is proposed. In the proposed algorithm, the elimination operator first identifies the reference point with maximum niche count and then employs the penalty-based boundary intersection distance to rank the individuals associated with it. To this end, the selection scheme is used to remove the worse individuals rather than to select the superior individuals. The proposed NSGA-III-EO is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art MOEAs. Additionally, it is also tested on constrained problems having a large number of objectives and shows good performance.     

Improving the non-dominated sorting genetic algorithm using a gene-therapy method for multi-objective optimization

The non-dominate sorting genetic algorithmic-II (NSGA-II) is an effective algorithm for finding Pareto-optimal front for multi-objective optimization problems. To further enhance the advantage of the NSGA-II, this study proposes an evaluative-NSGA-II (E-NSGA-II) in which a novel gene-therapy method incorporates into the crossover operation to retain superior schema patterns in evolutionary population and enhance its solution capability. The merit of each select gene in a crossover chromosome is estimated by exchanging the therapeutic genes in both mating chromosomes and observing their fitness differentiation. Hence, the evaluative crossover operation can generate effective genomes based on the gene merit without explicitly analyzing the solution space. Experiments for nine unconstrained multi-objective benchmarks and four constrained problems show that E-NSGA-II can find Pareto-optimal solutions in all test cases with better convergence and diversity qualities than several existing algorithms.     

FEMOEA: a fast and efficient multi-objective evolutionary algorithm

A multi-objective evolutionary algorithm which can be applied to many nonlinear multi-objective optimization problems is proposed. Its aim is to quickly obtain a fixed size Pareto-front approximation. It adapts ideas from different multi-objective evolutionary algorithms, but also incorporates new devices. In particular, the search in the feasible region is carried out on promising areas (hyperspheres) determined by a radius value, which decreases as the optimization procedure evolves. This mechanism helps to maintain a balance between exploration and exploitation of the search space. Additionally, a new local search method which accelerates the convergence of the population towards the Pareto-front, has been incorporated. It is an extension of the local optimizer SASS and improves a given solution along a search direction (no gradient information is used). Finally, a termination criterion has also been proposed, which stops the algorithm if the distances between the Pareto-front approximations provided by the algorithm in three consecutive iterations are smaller than a given tolerance. To know how far two of those sets are from each other, a modification of the well-known Hausdorff distance is proposed. In order to analyze the algorithm performance, it has been compared to the reference algorithms NSGA-II and SPEA2 and the state-of-the-art algorithms MOEA/D and SMS-EMOA. Several quality indicators have been considered, namely, hypervolume, average distance, additive epsilon indicator, spread and spacing. According to the computational tests performed, the new algorithm, named FEMOEA, outperforms the other algorithms.     

METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.