Abstract: Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program then solved using exact, heuristic and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding of complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The aim of the present study is to provide a unified framework for IP formulation of graph matching problems. Although there are many surveys on graph matching problems, however, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of difficult problems arising in practice, especially in pattern analysis.

Keywords: Combinatorial optimization, graph matching, integer programming, quadratic assignment problem.

Abstract: Recently, ten knowledge areas (KAs) of project management have been published by the PMBOK® Guide. They comprise specific skills and experiences to ensure accomplishing project goals, and include management of: integration, scope, cost, time, quality, communications, procurement, risk, human resources and stakeholders. This research paper focuses on the ten required KAs for a project manager or a project to be successful. It aims at applying the Softcomputing modeling techniques to describe the relations between the 47 processes and the KAs. Such a model will enable users to predict the overall competencies of the project management. Thus, it provides an assessment tool to envisage, visualize and indicate the overall performance and competency of a project.

The proposed Softcomputing Knowledge Areas Model (SKAM) is a two-stage model. The first stage involves ten models. Each model describes relations between a specific KA and its related processes. The outputs of these ten models will feed into the second stage that will represent the relationship between all the ten KAs and the overall predicted competencies of a project. A combination of Subtractive Clustering and Neurofuzzy modeling techniques are used. Three measures are used to validate the adequacy of the models: the mean average percentage errors, the correlation coefficient and the maximum percentage errors. The highest achieved values for these measures are0.5751, 0.9999 and 4.7283, respectively.

However, although the preliminary findings of the proposed SKAM model are promising, more testing is still required before declaring the adequacy of applying the Softcomputing modeling approach in the project management field.

Keywords: Knowledge Areas, Project Management, PMBOK® Guide, Softcomputing, Modeling.