An ε-domination based two-archive 2 algorithm for many-objective optimization

The two-archive 2 algorithm(Two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA) and convergence archive(CA).However,the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems.The traditional algorithm even cannot converge due to the weak selection pressure.Meanwhile,Two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the algorithm.To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions,an ε-domination based Two_Arch2 algorithm(ε-Two_Arch2) for many-objective problems(MaOPs) is proposed in this paper.In ε-Two_Arch2,to decrease the computational complexity and speed up the convergence,a novel evolutionary framework with a fast update strategy is proposed;to increase the selection pressure,ε-domination is assigned to update the individuals in DA;to guarantee the uniform distribution of the solution,a boundary protection strategy based on I_(ε+) indicator is designated as two steps selection strategies to update individuals in CA.To evaluate the performance of the proposed algorithm,a series of benchmark functions with different numbers of objectives is solved.The results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with Two_Arch2.

图的全-Domination染色

图G的一个全-domination染色是图G的一个正常点染色,使得G的每个顶点v控制除了v以外的至少一个色类,并且每一个色类被G中至少一个顶点控制。图G的全-domination染色所需的最少颜色数称为G的全-domination色数,记为χ_(td)(G)。本文通过图构造的方法证明了对于任意的图G和任意固定的整数k≥1,决定χ_(td)(G)=k是否是NP-完全的,并研究了χ_(td)(G)和χ_(td)(G′)之间的关系,这里G′是G通过某种操作得到的图。

On the 2-Domination Number of Complete Grid Graphs

A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].

Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

Most multimodal multi-objective evolutionary algorithms(MMEAs)aim to find all global Pareto optimal sets(PSs)for a multimodal multi-objective optimization problem(MMOP).However,in real-world problems,decision makers(DMs)may be also interested in local PSs.Also,searching for both global and local PSs is more general in view of dealing with MMOPs,which can be seen as generalized MMOPs.Moreover,most state-of-theart MMEAs exhibit poor convergence on high-dimension MMOPs and are unable to deal with constrained MMOPs.To address the above issues,we present a novel multimodal multiobjective coevolutionary algorithm(Co MMEA)to better produce both global and local PSs,and simultaneously,to improve the convergence performance in dealing with high-dimension MMOPs.Specifically,the Co MMEA introduces two archives to the search process,and coevolves them simultaneously through effective knowledge transfer.The convergence archive assists the Co MMEA to quickly approach the Pareto optimal front.The knowledge of the converged solutions is then transferred to the diversity archive which utilizes the local convergence indicator and the-dominance-based method to obtain global and local PSs effectively.Experimental results show that Co MMEA is competitive compared to seven state-of-the-art MMEAs on fifty-four complex MMOPs.

一种基于正态分布交叉的ε-MOEA

实数编码的多目标进化算法常使用模拟二进制交叉(simulated binary crossover,称SBX)算子.通过对SBX以及进化策略中变异算子进行对比分析,并引入进化策略中的离散重组算子,提出了一种正态分布交叉(normal distribution crossover,称NDX)算子.首先在一维搜索空间实例中对NDX与SBX算子进行比较和分析,然后将NDX算子应用于Deb等人提出的稳态多目标进化算法ε-MOEA(ε-dominance based multiobjective evolutionary algorithm)中.采用NDX算子的ε-MOEA(记为ε-MOEA/NDX)算法在多目标优化标准测试集ZDT和DTLZ的10个函数上进行了实验比较.实验结果和分析表明,采用NDX的ε-MOEA所求得的Pareto最优解集质量明显优于经典算法ε-MOEA/SBX和NSGA-Ⅱ.

具有特定独立的罗马2-控制数的树

For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 for which f(u1)=f(u2)=1.A Roman{2}-dominating function f=(V0,V1,V2)is called independent if V1∪V2 is an independent set.The weight of an independent Roman{2}-dominating function f is the valueω(f)=Σv∈V f(v),and the independent Roman{2}-domination number i{R2}(G)is the minimum weight of an independent Roman{2}-dominating function on G.In this paper,we characterize all trees with i{R2}(T)=γ(T)+1,and give a linear time algorithm to compute the value of i{R2}(T)for any tree T.

Total [1,2]-domination in Graphs

A subset S V in a graph G =（V, E） is a total [1, 2]-set if, for every vertex v ∈ V, 1 ≤ ｜N（v）∩S｜ ≤2. The minimum cardinality of a total [1, 2]-set of G is called the total [1, 2]-domination number, denoted byγt[1,2]（G）.We establish two sharp upper bounds on the total [1,2]-domination number of a graph G in terms of its order and minimum degree, and characterize the corresponding extremal graphs achieving these bounds. Moreover,we give some sufficient conditions for a graph without total [1, 2]-set and for a graph with the same total[1, 2]-domination number, [1, 2]-domination number and domination number.

Improving the Efficiency of Multi-Objective Grasshopper Optimization Algorithm to Enhance Ontology Alignment

Ontology alignment is an essential and complex task to integrate heterogeneous ontology.The meta-heuristic algorithm has proven to be an effective method for ontology alignment.However,it only applies the inherent advantages of metaheuristics algorithm and rarely considers the execution efficiency,especially the multi-objective ontology alignment model.The performance of such multi-objective optimization models mostly depends on the well-distributed and the fast-converged set of solutions in real-world applications.In this paper,two multi-objective grasshopper optimization algorithms(MOGOA)are proposed to enhance ontology alignment.One isε-dominance concept based GOA(EMO-GOA)and the other is fast Non-dominated Sorting based GOA(NS-MOGOA).The performance of the two methods to align the ontology is evaluated by using the benchmark dataset.The results demonstrate that the proposed EMO-GOA and NSMOGOA improve the quality of ontology alignment and reduce the running time compared with other well-known metaheuristic and the state-of-the-art ontology alignment methods.

Dominant Skyline Query Processing over Multiple Time Series

Multiple time series （MTS）, which describes an object in multi-dimensions, is based on single time series and has been proved to be useful. In this paper, a new analytical method called α/β-Dominant-Skyline on MTS and a formal definition of the α/β-dominant skyline MTS are given. Also, three algorithms, called NL, BC and MFB, are proposed to address the α/β-dominant skyline queries over MTS. Finally experimental results on both synthetic and real data verify the correctness and effectiveness of the proposed method and algorithms.