Mathematical Modeling And Optimization Algorithm For Project Portfolio Selections Based On Interaction Effect

The project portfolio selection is well known as one of the most essential parts in project management,it can provide the support of judgement for the project managers reasonably.In constrained conditions,it also can seek one or several projects from candidates and guarantee to accompolish the strategic objectives and run the projects successfully at the same time.It involves multi-objective optimization problems,operational research and decision technologies,when it comes to the research area.It has the characteristics of multi-field,transdisciplinary and wide range application.As for the projects of investment,research and development,engineering and technology,researchers are eager to employ the methods of project portfolio selection.The larger the project scale is,the harder the constrained conditions and the more complex the judgement will be.So,there must be some solutions to deal with it,the research of project portfolio selections emerge because of this,it is also extremely useful for the research and applications.As the development of economy,the project management converts from project scheduling to project portfolio selections.It draws the attention of more and more researchesrs because of the increasing project numbers,composite constraints and interactions.The problems of project portfolio selections turn the researches to be more strategic,complex and comprehensive.Recently,as the number of complex projects improved,using of optimization algorithm,?Big Data?,?Internet+? and also some novel concepts,the research of project portfolio selection comes into our horizon again.Under the constraints of theoretical and practical situation,the research should gain one more step,and keep pace with the reality.Through the literature of project portfolio selections,we can draw the conclusions that the research recently expands to the field of project portfolio selections with interactions,the harder we design the model,the more challenge we come up with the optimization method.Buiding the model considering the preferences of decision makers,multi-stage and dynamic change during the project selections,giving an early estimation to the success rate of projects executing,achieving the best pareto frontiers by means of the improved heuristic optimization algorithms.The project portfolio selection also has the method of critical success factors.All the things refered above can provide the project manager some exact and efficient support to decide.This paper proposes an intensive research about the modeling and optimization algorithms in the domain of project portfolio selections considering interactions and other essential factors.The main researches are illustrated below:Firstly,the paper proposes the project portfolio selection based on interaction effect.We identify the interaction effect though the analysis of core factors in project portfolio selection.We also conclude the the influence of interaction effect as well.As follows,the paper illustrates the framework of research,and gives the definition of the core problems.In order to meet the demand of integrity,the researches of ours include resource constraints,multi-stage,preference incorporation.Secondly,the paper proposes the model construction of the project portfolio selection considering interaction effect.Aiming at solving the project portfolio selection in the constraint situation of limited resources,we propose the model based on the baseline,with the help of the principle of inclusion-exclusion and the improved PSO algorithm we could easily solve the pareto frontiers of the problem.From the comparative experiments,we can achieve that the solution of our model is more competitive than the model without considering interation effect.Furthermore,the proposed PSO algorithm achieves the better performance in the section of generational distance,diversity,maximum spread,and error rate.Thirdly,the paper proposes the multi-stage project portfolio selection by considering the resource gain and risk accumulation.The core target of the model confirms the max revenue in each period and max revenue in whole proceeding time.The differential evolutionary algorithm with different strategy of mutation and parameter settings are used to solve the solutions.The optimal strategic adjustment period and the relatively best method can be achieved by the analysis of results which makes the research meaningful.The comparative experiments prove that the solution of multi-stage project portfolio selection problem based on interaction effect have the better results than that without considering such effect.The proposed differential evolutionary algorithm also has the character of ?high speed? and ?global best? that the compared methods.Fourthly,the project portfolio selection with interaction effect considering the preference of decision makers represents the level of preference using the non-outranking model extracted by fuzzy theory.By the method of constructing the model of the specific problem,it transforms the existing problem to the problem which contains multi-objective best candidates and also can be solved by the method of improved ant algorithm.The case study proves the model and algorithm effective because the comprehensive model,controlling premature convergence and accurate results.Fifthly,the paragraph proposes the project portfolio selection model considering the critical success factors.The mehod achieve the goals though evaluating the relationships between critical success factors by regression model and it also train the artifical neural networks to achieve the effect which the critical success factors contributes to the success rate of project portfolio.By means of the comparison with the score system by experts,it turns out to be high accuracy,and it also can provide the decision supports which are valuable in both academic research and engineering applications for project managers.