Marking Optimization of Weighted Marked Graphs

Cyclic manufacturing systems can be modeled by marked graphs, which are an elementary class of Petri nets. To model systems with bulk services and arrivals and to reduce the size of the model, weighted marked graphs can be used. An important step when designing these systems is the definition of the number of manufacturing resources to be used in order to reach a given productivity. In terms of timed Petri nets, this is known as the marking optimization problem and consists of reaching a given average cycle time while minimizing a linear combination of markings. In this paper, a necessary and sufficient condition to obtain a feasible solution of the marking optimization problem of weighted marked graphs with deterministic times is established. A fast heuristic solution, based on an iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.     

基于贪婪策略的紧密k核子图查询

k核查询是一种社团查询,由于其可以在线性时间内被有效计算,因此在社团检测中具有较广泛的应用。图中边的权值在很多场景下具有较强的语义关系,但现有研究较少考虑图中边的权值。为提升k核查询的效率,在k核的基础上定义加权图中的紧密k核子图查询（CRKSQ）问题,并使用归约方法证明该问题是NP-难的。基于贪婪策略设计启发式算法CRK-G,通过迭代删除节点为CRKSQ问题找到一个近似解。在此基础上,从降低图规模和减少迭代次数两方面研究CRK-G算法的优化策略,分别提出使用图压缩策略的算法CRK-C及使用单次多节点删除策略的算法CRK-F。在Bio-GRID、Email-Enron、DBLP 3个数据集上的实验结果表明,相对于CRK-G算法,CRK-C、CRK-F算法在查询速度上有较大的提升,且平均误差均在8%以内。     

Petri net based decision system modeling in real-time scheduling and control of flexible automotive manufacturing systems

This paper presents the design and the implementation of a Petri net (PN) model for the control of a flexible manufacturing system (FMS). A flexible automotive manufacturing system used in this environment enables quick cell configuration, and the efficient operation of cells. In this paper, we attempt to propose a flexible automotive manufacturing approach for modeling and analysis of shop floor scheduling problem of FMSs using high-level PNs. Since PNs have emerged as the principal performance modeling tools for FMS, this paper provides an object-oriented Petri nets (OOPNs) approach to performance modeling and to implement efficient production control. In this study, we modeled the system as a timed marked graph (TMG), a well-known subclass of PNs, and we showed that the problem of performance evaluation can be reduced to a simple linear programming (LP) problem with m − n + 1 variables and n constraints, where m and n represent the number of places and transitions in the marked graph, respectively. The presented PN based method is illustrated by modeling a real-time scheduling and control for flexible automotive manufacturing system (FAMS) in Valeo Turkey.     

一种面向加权双向图的聚类发掘方法

加权双向图是一种表达具有连接关系的科学和工程问题中的信息的比较准确的方式,加权双向图上聚类发掘的研究具有重要意义.本文提出一种面向加权双向图的聚类发掘方法,它通过定义双向边的调整权和节点的调整度,充分利用加权双向图上边的权值信息和方向信息,比较准确地描述了节点对之间的结构相似性,从而比较好地实现了加权双向图上的聚类发掘.对比实验表明本文方法的聚类发掘结果在聚类质量评价指标上具有更好的表现.     

Multiplicative vertex-colouring weightings of graphs

In this paper we conjecture that the edges of any non-trivial graph can be weighted with integers 1, 2, 3 in such a way that for every edge uv the product of weights of the edges adjacent to u is different than the product of weights of the edges adjacent to v. It is proven here for cycles, paths, complete graphs and 3-colourable graphs. It is also shown that the edges of every non-trivial graph can be weighted with integers 1, 2, 3, 4 in such a way that the adjacent vertices have different products of incident edge weights.In a total weighting of a simple graph G we assign the positive integers to edges and to vertices of G. We consider a colouring of G obtained by assigning to each vertex v the product of its weight and the weights of its adjacent edges. The paper conjectures that we can get the proper colouring in this way using the weights 1, 2 for every simple graph. We show that we can do it using the weights 1, 2, 4 on edges and 1, 2 on vertices.     

Minimizing cycle time and group scheduling, using Petri nets a study of heuristic methods

The objective of this paper is a study of minimizing the maximum completion time min F _max, or cycle time of the last job of a given family of jobs using flow shop heuristic scheduling techniques. Three methods are presented: minimize idle time (MIT); Campbell, Dudek and Smith (CDS); and Palmer. An example problem with ten jobs and five machines is used to compare results of these methods. A deterministic t-timed colored Petri net model has been developed for scheduling problem. An execution of the deterministic timed Petri net allows to compute performance measures by applying graph traversing algorithms starting from initial global state and going into a desirable final state(s) of the production system. The objective of the job scheduling policy is minimizing the cycle time of the last job scheduled in the pipeline of a given family of jobs. Three heuristic scheduling methods have been implemented. First, a sub-optimal sequence of jobs to be scheduled is generated. Second, a Petri net-based simulator with graphical user interface to monitor execution of the sequence of tasks on machines is dynamically designed. A deterministic t-timed colored Petri net model has been developed and implemented for flexible manufacturing systems (FMS). An execution of the deterministic timed Petri net into a reachability graph allows to compute performance measures by applying graph traversing algorithms starting from initial global state to a desirable final state(s) of the production system.     

Complexity of a proposed database storage structure

An alternate method for storing M to N relationships is presented. Implementing this method involves a minimization procedure which is shown to be equivalent to finding the minimal number of bipartite cliques which cover all of the edges of a related bipartite graph. This bipartite edge clique cover problem is known to be NP-complete, suggesting that attention should be focused on finding heuristic, not necessarily optimal, algorithms which produce solutions in polynomial-time. One such heuristic is presented which seems to work well on a variety of bipartite graphs. However, there are bipartite graphs for which its performance is poor, i.e. the heuristic produces solutions significantly worse than optimum. A family of bipartite graphs is presented for which the performance factor is unbounded.     

A Tight Lower Bound for a Special Case of Quadratic 0–1 Programming

We consider a still NP-complete partial case of the unconstrained binary quadratic optimization problem that can be described in terms of an undirected graph with red edges having negative weights and green edges having positive weights. The maximum vertex degree of the graph is three. It can be assumed w.l.o.g. that every vertex is incident to a red and a green edge. We are looking for a vertex cover with respect to the red edges which covers a subset of green edges of total weight as small as possible. We prove that for all connected such graphs except a subclass of special graphs having exactly five green edges it is possible to find a vertex cover with respect to the red edges for which the total weight of uncovered green edges is at least 1/4 fraction of the total weight of all green edges.     

A Kleene–Schützenberger theorem for weighted timed automata

During the last years, weighted timed automata have received much interest in the real-time community. Weighted timed automata form an extension of timed automata and allow us to assign weights (costs) to both locations and edges. This model, introduced by Alur et al. (2001) and Behrmann et al. (2001), permits the treatment of continuous consumption of resources and has led to much research on scheduling problems, optimal reachability and model checking. Also, several authors have derived Kleene-type characterizations of (unweighted) timed automata and their accepted timed languages. The goal of this paper is to provide a characterization of the behaviours of weighted timed automata by rational power series. We define weighted timed automata with weights taken in an arbitrary semiring, resulting in a model that subsumes several weighted timed automata concepts of the literature. For our main result, we combine the methods of Schützenberger, a recent approach for a Kleene-type theorem for unweighted timed automata by Bouyer and Petit as well as new techniques. Our main result also implies Kleene-type theorems for several subclasses of weighted timed automata investigated before, e.g., for timed automata and timed automata with stopwatch observers.     

Discovering Neglected Conditions in Software by Mining Dependence Graphs

Neglected conditions are an important but difficult-to-find class of software defects. This paper presents a novel approach to revealing neglected conditions that integrates static program analysis and advanced data mining techniques to discover implicit conditional rules in a code base and to discover rule violations that indicate neglected conditions. The approach requires the user to indicate minimal constraints on the context of the rules to be sought, rather than specific rule templates. To permit this generality, rules are modeled as graph minors of enhanced procedure dependence graphs (EPDGs), in which control and data dependence edges are augmented by edges representing shared data dependences. A heuristic maximal frequent subgraph mining algorithm is used to extract candidate rules from EPDGs, and a heuristic graph matching algorithm is used to identify rule violations. We also report the results of an empirical study in which the approach was applied to four open source projects (openssl, make, procmail, amaya). These results indicate that the approach is effective and reasonably efficient.     

iCoSim-FMS: An intelligent co-simulator for the adaptive control of complex flexible manufacturing systems

We describe an intelligent co-simulator for real time production control of a complex flexible manufacturing system (CFMS) having machine and tool flexibility. The manufacturing processes associated with the CFMS are complicated with each operation being possibly done by several machining centers. The co-simulator design approach is built upon the theory of dynamic meta-model based supervisory control with the cooperation of its own embedded intelligent blocks. The system is implemented by coupling of the centralized simulation controller (CSC) and real-time simulator for enforcing dynamic strategies of shop floor control. The posteriori adaptive co-simulator is equipped with a concurrent bilateral mechanism for simulation optimization based on appropriate control rules enhancing performance criteria simulation efficiency. A working intelligent adaptive controller prototype (iCoSim-FMS) has been developed to validate the proposed approach and compare its performance with well known FMS heuristic methods.     

基于路径映射的相似子图匹配算法

迄今为止,相关的图相似性匹配方法通常不考虑节点关系以及边权重的实际意义。提出一种基于路径映射 的相似子图匹配方法,用以更精确地查找具有相似拓扑结构的加权图。其创新之处在于充分利用标签信息,综合考虑 拓扑结构特征,克服了忽略节点结构关系和边权重的意义去分析图相似性的弊端。因此,该方法在很大程度上提高了 图相似性匹配的应用范围和匹配精度。实验表明本方法具有较高的查询质量和效率。     

Generalized framework for personalized recommendations in agent networks

An agent network can be modeled as a directed weighted graph whose vertices represent agents and edges represent a trust relationship between the agents. This article proposes a new recommendation approach, dubbed LocPat, which can recommend trustworthy agents to a requester in an agent network. We relate the recommendation problem to the graph similarity problem, and define the similarity measurement as a mutually reinforcing relation. We understand an agent as querying an agent network to which it belongs to generate personalized recommendations. We formulate a query into an agent network as a structure graph applied in a personalized manner that reflects the pattern of relationships centered on the requesting agent. We use this pattern as a basis for recommending an agent or object (a vertex in the graph). By calculating the vertex similarity between the agent network and a structure graph, we can produce a recommendation based on similarity scores that reflect both the link structure and the trust values on the edges. Our resulting approach is generic in that it can capture existing network-based approaches merely through the introduction of appropriate structure graphs. We evaluate different structure graphs with respect to two main kinds of settings, namely, social networks and ratings networks. Our experimental results show that our approach provides personalized and flexible recommendations effectively and efficiently based on local information.     

Petri-net-based dynamic scheduling of flexible manufacturing system via deep reinforcement learning with graph convolutional network

To benefit from the accurate simulation and high-throughput data contributed by advanced digital twin technologies in modern smart plants, the deep reinforcement learning (DRL) method is an appropriate choice to generate a self-optimizing scheduling policy. This study employs the deep Q-network (DQN), which is a successful DRL method, to solve the dynamic scheduling problem of flexible manufacturing systems (FMSs) involving shared resources, route flexibility, and stochastic arrivals of raw products. To model the system in consideration of both manufacturing efficiency and deadlock avoidance, we use a class of Petri nets combining timed-place Petri nets and a system of simple sequential processes with resources (S³PR), which is named as the timed S³PR. The dynamic scheduling problem of the timed S³PR is defined as a Markov decision process (MDP) that can be solved by the DQN. For constructing deep neural networks to approximate the DQN action-value function that maps the timed S³PR states to scheduling rewards, we innovatively employ a graph convolutional network (GCN) as the timed S³PR state approximator by proposing a novel graph convolution layer called a Petri-net convolution (PNC) layer. The PNC layer uses the input and output matrices of the timed S³PR to compute the propagation of features from places to transitions and from transitions to places, thereby reducing the number of parameters to be trained and ensuring robust convergence of the learning process. Experimental results verify that the proposed DQN with a PNC network can provide better solutions for dynamic scheduling problems in terms of manufacturing performance, computational efficiency, and adaptability compared with heuristic methods and a DQN with basic multilayer perceptrons.     

基于KFCMSA的(k，l)加权社交网络匿名算法

图数据隐私保护的研究目前主要集中在简单图,适应范围有限。将权重图数据的隐私保护作为研究对象,可以改善权重图发布之后数据的可用性及有效性。针对在利用聚类匿名化方法处理社交网络数据时,需要增删大量的边和节点,造成严重的数据失真的问题进行了研究。提出了（k,l）加权社交网络匿名算法KFCMSA（联合k成员模糊聚类和模拟退火）,并利用改进的簇划分算法将权重社交网络聚类成不同的簇,对同一簇中节点的边权重进行泛化使节点满足l多样性。在实现k度匿名的同时有效减少了边的改变量,提高了数据的可用性,实现最优聚类的同时防止了同质性攻击。聚类质量实验和数据可用性分析表明该算法具有较高的性能优势和较高边保留率。     

Stochastic graph as a model for social networks

Social networks are usually modeled and represented as deterministic graphs with a set of nodes as users and edges as connection between users of networks. Due to the uncertain and dynamic nature of user behavior and human activities in social networks, their structural and behavioral parameters are time varying parameters and for this reason using deterministic graphs for modeling and analysis of behavior of users may not be appropriate. In this paper, we propose that stochastic graphs, in which weights associated with edges are random variables, may be a better candidate as a graph model for social network analysis. Thus, we first propose generalization of some network measures for stochastic graphs and then propose six learning automata based algorithms for calculating these measures under the situation that the probability distribution functions of the edge weights of the graph are unknown. Simulations on different synthetic stochastic graphs for calculating the network measures using the proposed algorithms show that in order to obtain good estimates for the network measures, the required number of samples taken from edges of the graph is significantly lower than that of standard sampling method aims to analysis of human behavior in online social networks.     

Regular set of representatives for time-constrained MSC graphs

Systems involving both time and concurrency are notoriously difficult to analyze. Existing decidability results apply when clocks on different processes cannot be compared or when the set of timed executions is regular. We prove new decidability results for timed concurrent systems, requiring neither restriction. We consider the formalism of time-constrained MSC graphs (TC-MSC graphs for short) introduced in Akshay et al. (2007) [1], and study if the set of timed executions generated by a TC-MSC graph is empty. This emptiness problem is known to be undecidable in general (Gastin et al., 2009) [11]. Our approach consists of finding a regular set R of representative timed executions, i.e., such that every timed execution of the system has an equivalent, up to commutation, timed execution in R. This allows us to solve the emptiness problem under the assumption that the TC-MSC graph is prohibited from (1) forcing any basic scenario to take an arbitrarily long time to complete and (2) enforcing unboundedly many events to occur within one unit of time.     

State agnostic planning graphs: deterministic,non-deterministic,and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source.We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.     

Heuristic algorithms for scheduling iterative task computations ondistributed memory machines

Many partitioned scientific programs can be modeled as iterative executions of computational tasks and represented by iterative task graphs (ITGs). An ITG may or may not have dependence cycles. In this paper, we consider the symbolic scheduling of ITGs on distributed memory architectures with nonzero communication overhead and propose heuristic algorithms for scheduling both cyclic and acyclic ITGs without searching an entire iteration space. Our approach incorporates techniques of software pipelining, graph unfolding, directed acyclic graph (DAG) scheduling, and load balancing. We analyze the asymptotic optimality of the algorithms to show that the derived schedules are competitive to optimal solutions. We also study the sensitivity of scheduling performance on inaccurate weights. Finally, we present experimental results to demonstrate the effectiveness of the optimization techniques     

A hybrid heuristic for the overlapping cluster editing problem

Clustering problems are applicable to several areas of science. Approaches and algorithms are as varied as the applications. From a graph theory perspective, clustering can be generated by partitioning an input graph into a vertex-disjoint union of cliques (clusters) through addition and deletion of edges. Finding the minimum number of edges additions and deletions required to cluster data that can be represented as graphs is a well-known problem in combinatorial optimization, often referred to as cluster editing problem. However, many real-world clustering applications are characterized by overlapping clusters, that is, clusters that are non-disjoint. In these situations cluster editing cannot be applied to these problems. Literature concerning a relaxation of the cluster editing, where clusters can overlap, is scarce. In this work, we propose the overlapping cluster editing problem, a variation of the cluster editing where the goal is to partition a graph, also by editing edges, into maximal cliques that are not necessarily disjoint. In addition, we also present three slightly different versions of a hybrid heuristic to solve this problem. Each hybrid heuristic is based on coupling two metaheuristicsthat, together, generate a set of clusters; and one of three mixed-integer linear programming models, also introduced in this paper, that uses these clusters as input. The objective with the metaheuristics is to limit the solution exploration space in the models’ resolution, therefore reducing its computational time.Tests results show that the all proposed hybrid heuristic versions are able to generate good-quality overlapping cluster editing solutions. In particular, one version of the hybrid heuristic achieved, at a low computational cost, the best results in 51 of 112 randomly-generated graphs. Although the other two hybrid heuristic versions have harder to solve models, they obtained reasonable results in medium-sized randomly-generated graphs. In addition, the hybrid heuristic achieved good results identifying labeled overlapping clusters in a supervised data set experiment. Furthermore, we also show that, with our new problem definition, clustering a vertex in more than one cluster can reduce the edges editing cost.