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.     

随机混流U型拆卸线平衡排序问题多目标进化算法优化

针对混流U型拆卸线平衡排序问题,考虑拆卸时间不确定,建立了该问题最小拆卸线平均闲置率、尽早拆卸危害和高需求零部件、最小化平均方向改变次数的多目标优化模型,并提出一种基于分解和动态邻域搜索的混合多目标进化算法(Hybrid Multi-objective Evolutionary Algorithm Based on Decomposition, HMOEA/D)。该算法通过采用弹性任务分配策略、动态邻域结构和动态调整权重以保证解的可行性并搜索得到分布较好的非劣解集。最后,仿真求解实验设计技术(DOE)生成的测试算例,结果表明HMOEA/D较其它算法能得到更接近Pareto最优、分布更好的近似解集。     

求解混合流水线调度问题的离散人工蜂群算法

本文给出了一种离散的人工蜂群算法(HDABC)用于求解混合流水车间调度(HFS)问题。采用工件排序的编码方式,并设计了四种邻域结构。雇佣蜂依次分派到解集中每个解,采用结合问题特征的局部搜索策略完成挖掘搜索工作。跟随蜂随机选择两个解并挑选较优者作为当前解,完成进一步的探优过程。侦察蜂采用三种策略跳出局部极小。通过34个同构并行机HFS问题和2个异构并行机HFS实际调度问题的实验,并与当前文献中的典型算法对比,验证了本文提出的算法无论在算法时间还是在求解质量上,都具备良好的性能。     

Synchronous and asynchronous Pareto-based multi-objective Artificial Bee Colony algorithms

Pareto-based multi-objective optimization algorithms prefer non-dominated solutions over dominated solutions and maintain as much as possible diversity in the Pareto optimal set to represent the whole Pareto-front. This paper proposes three multi-objective Artificial Bee Colony (ABC) algorithms based on synchronous and asynchronous models using Pareto-dominance and non-dominated sorting: asynchronous multi-objective ABC using only Pareto-dominance rule (A-MOABC/PD), asynchronous multi-objective ABC using non-dominated sorting procedure (A-MOABC/NS) and synchronous multi-objective ABC using non-dominated sorting procedure (S-MOABC/NS). These algorithms were investigated in terms of the inverted generational distance, hypervolume and spread performance metrics, running time, approximation to whole Pareto-front and Pareto-solutions spaces. It was shown that S-MOABC/NS is more scalable and efficient compared to its asynchronous counterpart and more efficient and robust than A-MOABC/PD. An investigation on parameter sensitivity of S-MOABC/NS was presented to relate the behavior of the algorithm to the values of the control parameters. The results of S-MOABC/NS were compared to some state-of-the art algorithms. Results show that S-MOABC/NS can provide good approximations to well distributed and high quality non-dominated fronts and can be used as a promising alternative tool to solve multi-objective problems with the advantage of being simple and employing a few control parameters.     

A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution. Additionally, a strategy based on subpopulations is implemented to avoid the direct computation of descent directions for the entire population. The evaluation of the proposed algorithm is performed on a set of benchmark test problems allowing a comparison with the most representative state-of-the-art multiobjective algorithms. The results show that the proposed approach is highly competitive in terms of the quality of non-dominated solutions and robustness.     

基于一类新方向的宽邻域路径跟踪内点算法

基于一类带有参数theta的新方向, 提出了求解单调线性互补问题的宽邻 域路径跟踪内点算法, 且当theta=1时即为经典牛顿方向. 当取theta为与问题规模 n无关的常数时, 算法具有O(nL)迭代复杂性, 其中L是输入数据的长度, 这与经典宽邻 域算法的复杂性相同; 当取theta=\sqrt{n/\beta\tau}时, 算法具有O(\sqrt{n}L)迭代复杂性, 这里的\beta, \tau是邻域参数, 这与窄邻域算法的复杂性相同. 这是首次研究包括经典宽邻域路径跟踪算法的一类内点算法, 给出了统一的算法框架和收敛性分析方法.     

Parallel local search

We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of hyper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.     

椭圆曲线素阶群上的离散对数求解

该文对解椭圆曲线上离散对数的Pollard ρ算法和并行碰撞搜索算法分别建立了它 们的图论模型和分析了碰撞技巧,比较了两个算法,进而提出了设计迭代函数的准则并 给出一个改进的并行碰撞算法.     

多目标0-1规划问题的元胞狼群优化算法研究

针对多目标0-1规划问题,首先基于元胞自动机原理和人工狼群智能算法,提出一种元胞狼群优化算法,该算法将元胞机的演化规则与嚎叫信息素更新规则、人工狼群更新规则进行组合,采用元胞及其邻居来增强搜索过程的多样性和分布性,使人工头狼在元胞空间搜索的过程中,增强了人工狼群算法的全局搜索能力,并获得更多的全局非劣解;其次结合多目标0-1规划模型对元胞狼群算法进行了详细的数学描述,定义了人工狼群搜索空间、移动算子、元胞演化规则和非劣解集更新规则,并给出了元胞狼群算法的具体实现步骤;最后通过MATLAB软件对3个典型的多目标0-1规划问题算例进行解算,并将解算结果与其它人工智能算法的结果进行比较,结果表明:元胞狼群算法在多目标0-1规划问题求解方面可获得更多的非劣解集和更优的非劣解,并具有较快的收敛速度和较好的全局寻优能力。     

Multiple-objective heuristics for scheduling unrelated parallel machines

This research proposes two heuristics and a Genetic Algorithm (GA) to find non-dominated solutions to multiple-objective unrelated parallel machine scheduling problems. Three criteria are of interest, namely: makespan, total weighted completion time, and total weighted tardiness. Each heuristic seeks to simultaneously minimize a pair of these criteria; the GA seeks to simultaneously minimize all three. The computational results show that the proposed heuristics are computationally efficient and provide solutions of reasonable quality. The proposed GA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.     

带有资源转移时间的RCPSP资源流模型及算法

本文在传统资源受限项目调度问题(resource-constrained project scheduling problem, RCPSP)中引入资源转移时间,为有效获得问题的最优解,采用资源流编码方式表示可行解,建立了带有资源转移时间的RCPSP资源流优化模型,目标为最小化项目工期。根据问题特征设计了改进的资源流重构邻域算子,分别设计了改进的禁忌搜索算法和贪心随机自适应禁忌搜索算法求解模型。数据实验结果表明,相较于现有文献中的方法,所提两种算法均可针对更多的项目实例求得最优解,并且得到最优解的时间更短,求解效率更高。此外,分析了算法在求解具有不同特征的项目实例时的性能,所得结果为项目经理结合项目特征评价算法适用性提供了指导。     

整数线性规划投资组合模型的直接搜索算法求解

利用松弛最优邻近解临域整数点搜索法作过滤条件,建立求解整数规划的新方法——直接搜索算法,利用直接搜索算法并借助Matlab软件求解整数线性规划投资组合模型.数值结果表明了模型的建立与提出方法的有效性.     

Balancing global and local search in parallel efficient global optimization algorithms

Most parallel efficient global optimization (EGO) algorithms focus only on the parallel architectures for producing multiple updating points, but give few attention to the balance between the global search (i.e., sampling in different areas of the search space) and local search (i.e., sampling more intensely in one promising area of the search space) of the updating points. In this study, a novel approach is proposed to apply this idea to further accelerate the search of parallel EGO algorithms. In each cycle of the proposed algorithm, all local maxima of expected improvement (EI) function are identified by a multi-modal optimization algorithm. Then the local EI maxima with value greater than a threshold are selected and candidates are sampled around these selected EI maxima. The results of numerical experiments show that, although the proposed parallel EGO algorithm needs more evaluations to find the optimum compared to the standard EGO algorithm, it is able to reduce the optimization cycles. Moreover, the proposed parallel EGO algorithm gains better results in terms of both number of cycles and evaluations compared to a state-of-the-art parallel EGO algorithm over six test problems.     

Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NP-complete problem, and existing exact algorithms can solve only small size problems. Currently, the best available heuristic procedures for the CMST problem are tabu search algorithms due to Amberg et al. and Sharaiha et al. These algorithms use two-exchange neighborhood structures that are based on exchanging a single node or a set of nodes between two subtrees. In this paper, we generalize their neighborhood structures to allow exchanges of nodes among multiple subtrees simultaneously; we refer to such neighborhood structures as multi-exchange neighborhood structures. Our first multi-exchange neighborhood structure allows exchanges of single nodes among several subtrees. Our second multi-exchange neighborhood structure allows exchanges that involve multiple subtrees. The size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors. Our approach, which is based on the cyclic transfer neighborhood structure due to Thompson and Psaraftis and Thompson and Orlin transforms a profitable exchange into a negative cost subset-disjoint cycle in a graph, called an improvement graph, and identifies these cycles using variants of shortest path label-correcting algorithms. Our computational results with GRASP and tabu search algorithms based on these neighborhood structures reveal that (i) for the unit demand case our algorithms obtained the best available solutions for all benchmark instances and improved some; and (ii) for the heterogeneous demand case our algorithms improved the best available solutions for most of the benchmark instances with improvements by as much as 18%. The running times our multi-exchange neighborhood search algorithms are comparable to those taken by two-exchange neighborhood search algorithms. Received: September 1998 / Accepted: March 2001?Published online May 18, 2001     

含不相关机的动态可重入柔性流水车间问题的混合DABC-GA算法

为了改善生产线的物流平衡和加强阶段间的时间衔接,扩展一般可重入柔性流水车间调度理论,以最小化总加权完工时间为目标,研究了每阶段含不相关并行机的动态可重入柔性流水车间问题,工件在各阶段的加工时间取决于加工它的机器。鉴于所研究问题为NP-hard问题,首先,建立整数规划模型;其次,设计元胞矩阵编码方案,提出融合离散人工蜂群算法和遗传算法的一种混合算法以获得问题的近优解;最后,为了评估混合算法的性能,将所提出算法和一些元启发式算法进行了不同规模问题的对比测试,实验结果说明了所提算法的有效性。     

A graph partitioning heuristic for the parallel pseudo-exhaustive logical test of VLSI combinational circuits

The logical test of integrated VLSI circuits is one of the main phases of their design and fabrication. The pseudo-exhaustive approach for the logical test of integrated circults consists in partitioning the original circuits to be tested into non-overlapping subcircuits with a small, bounded number of subcircuits, which are then exhaustively tested in parallel. In this work, we present an approximate algorithm for the problem of partitioning integrated combinational circuits, based on the tabu search metaheuristic. The proposed algorithm presents several original features, such as: the use of a reduced neighborhood, obtained from moves involving only a subset of boundary nodes; complex moves which entail several resulting moves, although the variations in the cost function are easily computable; a bi-criteria cost function combining the number of subcircuits and the number of cuts, which simultaneously adds a diversification strategy to the search; and the use of a bin-packing heuristic as a post-optimization step. The behavior of the proposed algorithm was evaluated through its application to a set of benchmark circuits. The computational results have been compared with those obtained by the other algorithms in the literature, with significant improvements. The average reduction rates have been of the order of 30% in the number of subcircuits in the partition, and of the order of 40% in the number of cuts.     

A hybrid method for solving multi-objective global optimization problems

Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of optimums, which constitute the so called Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, most problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. The objective of this work is to compare the performance of a new hybrid method here proposed, with several well-known multi-objective evolutionary algorithms (MOEA). The main attraction of these methods is the integration of selection and diversity maintenance. Since it is very difficult to describe exactly what a good approximation is in terms of a number of criteria, the performance is quantified with adequate metrics that evaluate the proximity to the global Pareto-front. In addition, this work is also one of the few empirical studies that solves three-objective optimization problems using the concept of global Pareto-optimality.     

Multi-Objective Biclustering: When Non-dominated Solutions are not Enough

The biclustering technique was developed to avoid some of the drawbacks presented by standard clustering techniques, such as their impossibility of finding correlating data under a subset of features, and, consequently, to allow the extraction of more accurate information from datasets. Given that biclustering requires the optimization of at least two conflicting objectives (residue and volume) and that multiple independent solutions are desirable as the outcome, a few multi-objective evolutionary algorithms for biclustering were proposed in the literature. However, these algorithms only focus their search in the generation of a global set of non-dominated biclusters, which may be insufficient for most of the problems as the coverage of the dataset can be compromised. In order to overcome such problem, a multi-objective artificial immune system capable of performing a multipopulation search, named MOM-aiNet, was proposed. In this work, the MOM-aiNet algorithm will be described in detail, and an extensive set of experimental comparisons will be performed, with the obtained results of MOM-aiNet being confronted with those produced by the popular CC algorithm, by another immune-inspired approach for biclustering (BIC-aiNet), and by the multi-objective approach for biclustering proposed by Mitra & Banka.     

预制构件流水车间订单接受与调度的集成优化

针对预制构件生产管理过程中订单工期紧和生产能力不足的问题,在充分考虑中断和不可中断工序,串行和并行工序等复杂工况特点的基础上,以最大化净利润为目标,建立了一种订单接受与调度集成优化模型。鉴于问题的NP难性和模型的高度非线性,通过集成问题性质、构造启发式、邻域搜索和破坏-构造机制,提出了一种混合加速迭代贪婪搜索框架。其中,在调度构造阶段,为提高算法求解质量和搜索效率,设计了两种融合订单插入操作性质的加速构造策略。计算结果显示,与混合遗传禁忌搜索算法,遗传算法以及禁忌搜索算法相比,本文所提算法具有更好的求解质量和搜索效率。同时验证了所提出的加速构造策略能够有效减少算法运行时间。该研究有望显著提高预制生产企业净利润和客户满意度。     

Generating efficient schedules for identical parallel machines involving flow-time and tardy jobs

This paper considers the problem of generating a set of efficient (non-dominated) schedules on identical parallel machines involving total flow-time and total number of tardy jobs. In view of the NP-hard nature of this problem, heuristic algorithms are proposed for its solution. Two evaluation methods that provide a scheme by which multiple non-dominated sets can be compared are described and used to compare the performance of the proposed algorithms. Results of several experiments demonstrate the capability of the proposed algorithms and evaluation methodologies to address the problem at hand.