An LP-rounding 22-approximation for restricted maximum acyclic subgraph

In the classical Maximum Acyclic Subgraph problem (MAS), given a directed-edge weighted graph, we are required to find an ordering of the nodes that maximizes the total weight of forward-directed edges. MAS admits a 2-approximation, and this approximation is optimal under the Unique Game Conjecture.     

Genetic algorithm for the personnel assignment problem with multiple objectives

The assignment problem is a well-known graph optimization problem defined on weighted-bipartite graphs. The objective of the standard assignment problem is to maximize the summation of the weights of the matched edges of the bipartite graph. In the standard assignment problem, any node in one partition can be matched with any node in the other partition without any restriction. In this paper, variations of the standard assignment problem are defined with matching constraints by introducing structures in the partitions of the bipartite graph, and by defining constraints on these structures. According to the first constraint, the matching between the two partitions should respect the hierarchical-ordering constraints defined by forest and level graph structures produced by using the nodes of the two partitions respectively. In order to define the second constraint, the nodes of the partitions of the bipartite graph are distributed into mutually exclusive sets. The set-restriction constraint enforces the rule that in one of the partitions all the elements of each set should be matched with the elements of a set in the other partition. Even with one of these constraints the assignment problem becomes an NP-hard problem. Therefore, the extended assignment problem with both the hierarchical-ordering and set-restriction constraints becomes an NP-hard multi-objective optimization problem with three conflicting objectives; namely, minimizing the numbers of hierarchical-ordering and set-restriction violations, and maximizing the summation of the weights of the edges of the matching. Genetic algorithms are proven to be very successful for NP-hard multi-objective optimization problems. In this paper, we also propose genetic algorithm solutions for different versions of the assignment problem with multiple objectives based on hierarchical and set constraints, and we empirically show the performance of these solutions.     

Local branching-based algorithms for the disjunctively constrained knapsack problem

The disjunctively constrained knapsack problem (DCKP) is a variant of the well-known single constrained knapsack problem with special disjunctive constraints. This paper investigates the use of the local branching techniques for solving large-scale DCKP. Three versions of the algorithm are considered. The first version is based on the standard local branching which uses a starting solution provided by a specialized rounding solution procedure. The second version applies a two-phase solution procedure embedded in the local branching. For each subtree, the procedure serves to construct the set of objects containing the assigned variables and a second set including the free variables. The first set provides a partial local solution to the DCKP, whereas, for the second set, a truncated exact tree-search is applied for completing the partial local feasible solution. Finally, a diversification strategy is considered constituting the third version of the algorithm. All versions of the proposed algorithm are computationally analyzed on a set of benchmark instances of the literature and the obtained solutions are compared to those provided by existing algorithms. Encouraging results have been obtained.     

Modelling and managing disjunctions in scheduling problems

In this paper is presented a method for modelling and managing various constraints encountered in task scheduling problems. The approach aims at characterizing feasible schedules through the analysis of the set of constraints and their interaction, regardless of any optimization criteria. This analysis is achieved by a constraint propagation process on a constraint graph and produces both restricted domains for the decision variables and an updated formulation of the initial constraints. The graphs usually used to model temporal constraints seem to be limited because they only allow the representation of strict precedence relations between two tasks. In order to model a larger variety of temporal constraints, particularly any constraint that connects two events (start- or finish- time of a task), a model called a time-bound-on-node (TBON) graph is proposed in which each task is featured by two nodes. Then it becomes possible to handle constraints on task durations, due for example to flexibilities in resource utilization. This kind of graph is not new and has already been investigated in related works on project planning and Constraint Satisfaction Problems. But its processing and interpretation deserved to he developed, particularly for the present purpose, which is the search for the necessary conditions of feasibility. With respect to conjunctive temporal constraints, the analysis is achieved with a polynomial algorithm based on the longest path search on a conjunctive TBON graph, yielding the necessary and sufficient conditions of feasibility. Taking account of resource constraints leads to defining disjunctive constraints. To this end, disjunctive sets of arcs are introduced, making the TBON graph nonconjunctive. In this case, a complete characterization of feasibility cannot reasonably be faced, due to the combinatorial feature. Nevertheless, a polynomial algorithm that applies reduction and deletion rules on the nonconjunctive part of the graph is proposed to restart new propagations on the conjunctive part until all deductions have been made.     

Rough‐fuzzy quadratic minimum spanning tree problem

A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study, a bi‐objective rough‐fuzzy quadratic minimum spanning tree problem has been proposed for a connected graph, where the linear and the quadratic weights are represented as rough‐fuzzy variables. The proposed model is formulated by using rough‐fuzzy chance‐constrained programming technique. Subsequently, three related theorems are also proposed for the crisp transformation of the proposed model. The crisp equivalent models are solved with a classical multi‐objective solution technique, the epsilon‐constraint method and two multi‐objective evolutionary algorithms: (a) nondominated sorting genetic algorithm II (NSGA‐II) and (b) multi‐objective cross‐generational elitist selection, heterogeneous recombination, and cataclysmic mutation (MOCHC) algorithm. A numerical example is provided to illustrate the proposed model when solved with different methodologies. A sensitivity analysis of the example is also performed at different confidence levels. The performance of NSGA‐II and MOCHC are analysed on five randomly generated instances of the proposed model. Finally, a numerical illustration of an application of the proposed model is also presented in this study.     

大规模图上具有约束的多起点路径规划算法

路径规划查询是图数据上的一个基本问题,在众多的领域都有重要的应用价值。通常在实际问题中查询的路径是具有约束的,例如在外卖配送和共享出行问题中路径具有节点约束,其路径需要满足节点之间的先后关系约束。目前对于具有节点约束的路径查询问题,大多数的工作都在研究单起点的节点约束路径查询,但很难拓展到多起点节点约束问题中。因为具有节点约束的多起点路径查询问题是NP-hard的,所以该问题的大多数已有方法是使用贪心增量处理,但对于处理静态规则集拓展性不足。因此,提出了基于子路径的启发式算法和基于约束集拓展的精确算法,并在真实数据集上验证了算法的有效性。实验结果表明,启发式算法能够给出问题的精确解,而启发式算法能快速给出较好的近似解。     

Metric-topological maps from laser scans adjusted with incremental tree network optimizer

Several adaptations of maximum likelihood approaches to incremental map learning have been proposed recently. In particular, an incremental network optimizer based on stochastic gradient descent provides a fast and easy-to-implement solution to the problem. In this paper, we illustrate two map builders that process laser scans in order to extract the constraint network for the optimization algorithm. The first algorithm builds a map in the form of a collection of scans corresponding to a subset of the poses of a robot moving in the environment. Even though such a solution has the advantage of simplicity, it requires careful processing of data associations. After a preliminary selection of pose constraints candidates, a relative pose is computed through standard scan matching techniques. The second map builder stores a hybrid metric-topological representation: the map consists of a graph whose nodes contain local occupancy grid maps and whose edges are labeled with the relative pose between pairs of nodes. Each patch map summarizes the information of consecutive raw scans and such a richer representation better solves loop closure. Association between pairs of local maps is then performed and tested using correlation-based techniques. Our aim is to illustrate the effectiveness of a tree network optimizer integrated with simple methods for data association. Experiments reported in the paper show that a compact system integrating the optimizer and one of two versions of the map builder works reasonably well with commonly used benchmarks.     

A Generic Framework for Constrained Optimization Using Genetic Algorithms

In this paper, we propose a generic, two-phase framework for solving constrained optimization problems using genetic algorithms. In the first phase of the algorithm, the objective function is completely disregarded and the constrained optimization problem is treated as a constraint satisfaction problem. The genetic search is directed toward minimizing the constraint violation of the solutions and eventually finding a feasible solution. A linear rank-based approach is used to assign fitness values to the individuals. The solution with the least constraint violation is archived as the elite solution in the population. In the second phase, the simultaneous optimization of the objective function and the satisfaction of the constraints are treated as a biobjective optimization problem. We elaborate on how the constrained optimization problem requires a balance of exploration and exploitation under different problem scenarios and come to the conclusion that a nondominated ranking between the individuals will help the algorithm explore further, while the elitist scheme will facilitate in exploitation. We analyze the proposed algorithm under different problem scenarios using Test Case Generator-2 and demonstrate the proposed algorithm's capability to perform well independent of various problem characteristics. In addition, the proposed algorithm performs competitively with the state-of-the-art constraint optimization algorithms on 11 test cases which were widely studied benchmark functions in literature.     

含有析取语义循环的不变式生成改进方法

抽象解释为程序不变式的自动化生成提供了通用的框架,但是该框架下的大多数已有数值抽象域只能表达几何上是凸的约束集.因此,对于包含(所对应的约束集是非凸的)析取语义的特殊程序结构,采用传统数值抽象域会导致分析结果不精确.针对显式和隐式含有析取语义的循环结构,提出了基于循环分解和归纳推理的不变式生成改进方法,缓解了抽象解释分析中出现的语义损失问题.实验结果表明:相比已有方法,该方法能为这种包含析取语义的循环结构生成更加精确的不变式,并且有益于一些安全性质的推理.     

Deadline division-based heuristic for cost optimization in workflow scheduling

Cost optimization for workflow applications described by Directed Acyclic Graph (DAG) with deadline constraints is a fundamental and intractable problem on Grids. In this paper, an effective and efficient heuristic called DET (Deadline Early Tree) is proposed. An early feasible schedule for a workflow application is defined as an Early Tree. According to the Early Tree, all tasks are grouped and the Critical Path is given. For critical activities, the optimal cost solution under the deadline constraint can be obtained by a dynamic programming strategy, and the whole deadline is segmented into time windows according to the slack time float. For non-critical activities, an iterative procedure is proposed to maximize time windows while maintaining the precedence constraints among activities. In terms of the time window allocations, a local optimization method is developed to minimize execution costs. The two local cost optimization methods can lead to a global near-optimal solution. Experimental results show that DET outperforms two other recent leveling algorithms. Moreover, the deadline division strategy adopted by DET can be applied to all feasible deadlines.     

A constraint programming approach to the Chinese postman problem with time windows

The Chinese postman problem with time windows (CPPTW) is modelled as a constraint programme and results are reported for a set of test problems with up to 69 edges. Two different formulations are proposed. The first formulation approaches the problem directly and the second transforms the problem to an equivalent vehicle routing problem with time windows. The results demonstrate that optimal solutions can be obtained quickly when the time windows are tight. However, the results also show that as the time windows are made wider and the number of feasible solutions increases, these constraint programming formulations take significantly longer to find a provably optimal solution. The results also demonstrate how the size and density of the graph affects the computing time needed to find an optimal solution.     

A sound and complete chase procedure for constrained tuple-generating dependencies

We present a chase procedure for solving the implication problem of constrained tuple-generating dependencies (ctgds), a general class of database dependencies that is also able to handle data and predicates on interpreted domains. Current chase procedures for ctgds are sound but not complete, in the sense that they are unguaranteed to stop successfully whenever implication is true. The procedure we present is sound and complete, the first to our knowledge. It follows a linear reasoning over constraint domains that have the Independence of Negative Constraints property. We then soundly extend this procedure by a disjunctive reasoning over unrestricted constraint domains. To achieve these results, we used a different approach. Previous chases act like a closure operator, whereas we used a goal-directed design.     

求解存在运输空间约束多单元协作调度问题的拍卖算法

针对存在运输空间约束的多单元协作调度问题,提出合理的运输模式,建立非线性整数规划模型,对问题进行描述.通过拍卖的方式,将设备资源和运输资源分配给每一个工件,得到问题的可行解,并基于改进的(非)连通图对可行解进一步优化.通过拍卖方式,可以恰当地针对不同时间段的资源进行价值评估,从而提高资源的利用率,减少总的生产时间.拍卖过程分为两部分:车辆资源拍卖和设备资源拍卖.在整个拍卖过程中,车辆和设备分别扮演拍卖者,每个工件扮演竞拍者.通过对比实验,验证了所提出运输模式的合理性以及算法的有效性.     

Unified-memory-based hybrid processing for partition-oriented subgraph matching on GPU

World Wide Web - Subgraph isomorphism is a well known NP-hard problem that is to find all the matched subgraphs of a query graph in a large target graph. The state-of-the-art GPU-based solution is...     

Editing graphs to satisfy degree constraints: A parameterized approach

We study a wide class of graph editing problems that ask whether a given graph can be modified to satisfy certain degree constraints, using a limited number of vertex deletions, edge deletions, or edge additions. The problems generalize several well-studied problems such as the General Factor Problem and the Regular Subgraph Problem. We classify the parameterized complexity of the considered problems taking upper bounds on the number of editing steps and the maximum degree of the resulting graph as parameters.     

Exhaustive and Efficient Constraint Propagation: A Graph-Based Learning Approach and Its Applications

This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised classification subproblems which can be solved in quadratic time using label propagation based on $k$ -nearest neighbor graphs. Considering that this time cost is proportional to the number of all possible pairwise constraints, our approach actually provides an efficient solution for exhaustively propagating pairwise constraints throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are further used to adjust the similarity matrix for constrained spectral clustering. Other than the traditional constraint propagation on single-source data, our approach is also extended to more challenging constraint propagation on multi-source data where each pairwise constraint is defined over a pair of data points from different sources. This multi-source constraint propagation has an important application to cross-modal multimedia retrieval. Extensive results have shown the superior performance of our approach.     

Computing diameter constrained reliability of a network with junction points

We consider a network with unreliable communication channels and perfectly reliable nodes. The diameter constrained reliability for such a network is defined as the probability that between each pair of nodes, there exists a path consisting of operational edges whose number is upper bounded by a given integer. The problem of computing this characteristic is NP-hard, just like the problem of computing the probability of a network’s connectivity. We propose a formula that lets one use junction points to compute the reliability of a two-pole system with diameter constraints, which makes the computations faster.     

一种基于新约束处理方法的遗传算法

针对目前的约束处理方法中存在的问题,提出一种新的约束处理方法。该方法通过可行解和不可行解混合交叉的方法对问题的解空间进行搜索,对可行种群和不可行种群分别进行选择操作。避免了惩罚策略中选取惩罚因子的困难,使得约束处理问题简单化。实例测试结果表明,该约束处理方法的有效性。     

基于可满足性模理论的多处理机通信延迟优化任务调度方法

在一组相同处理器上调度带有通信延迟的任务图以实现其最短的执行时间,这在并行计算的调度理论和实践中具有重要的意义。针对具有通信延迟的任务图调度问题,提出一种基于可满足性模理论（SMT）的改进SMT方法。首先,将处理器映射约束和任务执行顺序等约束条件进行编码,将任务图调度问题转化为SMT问题;然后,调用SMT求解器对可行解空间进行搜索,以确定问题最优解。在约束编码阶段,使用整型变量表示任务和处理器的映射关系,从而降低处理器约束编码的复杂程度;在求解器调用阶段,通过添加独立任务的约束条件减小求解器的搜索空间,进一步提升最优解的查找效率。实验结果表明,与原始SMT方法相比,改进SMT方法在20 s和1 min超时实验中的平均求解时间分别减少了65.9%与53.8%,并且在处理器数量较多时取得了更大的效率优势。改进的SMT方法可以有效求解带通信延迟的任务图调度问题,尤其适用于处理器数量较多的调度场景。     

Variable ordering and constraint propagation for constrained CP-nets

A Conditional Preferences network (CP-net) is a known graphical model for representing qualitative preferences. In many real world applications we are often required to manage both constraints and preferences in an efficient way. The goal here is to select one or more scenarios that are feasible according to the constraints while maximizing a given utility function. This problem has been modelled as a CP-net where some variables share a set of constraints. This latter framework is called a Constrained CP-net. Solving the constrained CP-net has been proposed in the past using a variant of the branch and bound algorithm called Search CP. In this paper, we experimentally study the effect of variable ordering heuristics and constraint propagation when solving a constrained CP-net using a backtrack search algorithm. More precisely, we investigate several look ahead strategies as well as the most constrained heuristic for variable ordering during search. The results of the experiments conducted on random Constrained CP-net instances generated through the RB model, clearly show a significant improvement when adopting these techniques for specific graph structures as well as the case where a large number of variables are sharing constraints.