[PDF] Top 20 Solving Hard Graph Problems with Combinatorial Computing and Optimization

... Note that (1.1) can be rewritten in matrix form as max{c T x | Ax ≤ b and x ≥ 0}, and that the minimization of f (x) can be determined by the maximization of −f (x). Linear programming has many applications in a wide ... See full document

... 17 This is the directed path. It contains a vertex index in the form , the coordinates (in relation to the program drawing board – not a real-life coordinate system) and a value for the demand of the vertex, . The last ... See full document

... 9 When applying genetic algorithms (GA) to a problem with a single objective function, we randomly select a set of individuals (chromosomes) to form the initial population. We then evaluate their fitness functions. Using ... See full document

... address hard coreference problems, along with a constrained optimization framework that uses this knowledge in coreference de- cision ...on hard, Winograd-style, pronoun reso- lution cases, ... See full document

... to optimization, companies tend to opt for small improvements or an existing working design, often abandoning the search for the ultimate optimum ...that optimization work can be carried out using computers ... See full document

... Incremental Problems Algorithm Quickest-To-Ultimate (Q2U in short, see Algorithm 1) was introduced by Kalin- owski et ...a hard problem, and they resort to a mixed integer program for finding ... See full document

... For these instances, the lower bound computed during the first phase can be improved by the LP relaxation of the Set Covering formulation only in two cases, whereas the Branch-and-Price does not lead to further ... See full document

... Although subgraph isomorphism is NP-complete, the algorithms we introduced and compared in the previous chapter were working comfortably with instances with many hundreds of vertices in the pattern graph, and over ... See full document

... We are also developing a grid portal system for some optimization problem softwares including the SDPARA. The system will enable users to easily perform parallel computa- tion through the Internet. GridLib in ... See full document

... case. Combinatorial optimization problems can be solved using different methods, usually integer programming ...a combinatorial optimization problem in which all the variables must be ... See full document

... a Combinatorial Optimization Problem ...of graph coloring ...the graph is random, the number of nodes is 100, the number of edges is 300, the weight is 1∼5, and the number of colors is ... See full document

... for optimization problems, whose concept was introduced in ...a combinatorial optimization problem is explored in a more guided and efficient way than in the more basic ...colony ... See full document

... with hard computational problems, a common strategy is to con- sider approximations which focus on “abstract” solutions which characterize properties of the actual “concrete” ...a graph coloring ... See full document

... 1 INTRODUCTION Since their introduction in the early eighties electronic spreadsheet programs such as Excel, Lotus 1-2-3 and Quattro Pro have grown to be the most common tool managers use to model and analyze ... See full document

... for solving these problems, including the development of novel heuristic improvements and the thorough elaboration of important ...plex optimization algorithms is usually quite different from what is ... See full document

... The optimization of discrete problems is largely encountered in engineering and information do- ...mains. Solving these problems with continuous-variables approach then convert the continuous ... See full document

... In the first experiment, we investigate the influence of the aggregation scheme on so- lution quality and computation time. We start by solving the robust problem exactly using an IP formulation which contains one ... See full document

... a graph instance representing this distribution is generated in a random ...evolving graph it has the advantage of being robust and general, that is, structural properties that are true in this model will ... See full document

... of problems is a challenging ...known combinatorial optimization problems; exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden ... See full document

... ‘*’ indicates that the obtained result is the same as the best known result. HH: hyper-heuristic method. Best results are highlighted in bold. VII. D ISCUSSION As shown throughout this work, in both problem domains (exam ... See full document