@ARTICLE{26583204_120009894_2014, 
	author = {Sergey Avdoshin and Aleksey Lifshits}, 
	keywords = {, project portofolio, multi-objective model, fuzzy numbers, genetic algorithmant colony optimization},
	title = {Project portfolio formation based on fuzzy multi-objective model},
	journal = {},
	year = {2014},
	number = {1 (27)},
	pages = {14-22},
	url = {https://bijournal.hse.ru/en/2014--1 (27)/120009894.html},
	publisher = {},
	abstract = {Sergey Avdoshin - Professor, Head of School of Software Engineering, Faculty of Business Informatics,National Research University Higher School of EconomicsAddress: 20, Myasnitskaya str., Moscow, 101000, Russian FederationE-mail: savdoshin@hse.ru Alexey Lifshits - MSc Program Student, School of Software Engineering, Faculty of Business Informatics,National Research University Higher School of EconomicsAddress: 20, Myasnitskaya str., Moscow, 101000, Russian FederationE-mail: alexeus1992@yandex.ru     Leading IT companies run simultaneously several dozens or even several hundreds of projects. One of the major objectives is to decide whether a project meets the current strategic goalsand resource limits of a company or not. This leads firms to the issue of a project portfolio formation, where the challenge is to choose a subset of projects which meet the strategic objectivesof a company in the best way. In this present article we propose a multi-objective mathematical model of the project portfolio formation problem, defined on the fuzzy trapezoidal numbers.     We provide an overview of methods for solving this problem, which are a Branch and bound approach, an adaptive parameter variation scheme based on the epsilon-constraint method, ant colony optimization method and genetic algorithm. After our analysis, we choose the ant colony optimization method and SPEA II method, which is a modification ofgenetic algorithm. We describe the implementation of these methods applied to the project portfolio formation problem.The ant colony optimization is based on the max min antsystem with one pheromone structure and one ant colony. Three modifications of our SPEA II implementation have been considered. The first adaptation uses the binary tournament selection, while the second requires the rank selection method. The last one is based on another variant of generating initial population. Part of the population is generated by a non-random manner on the basis of solving a one-criterion optimization problem. This fact makes the population stronger than the initial one which is generated completely at random.     We compare the ant colony optimization algorithm and the three modifications of a genetic algorithm on the basis of the following parameters: speed of execution and the C-metric between each pair of algorithms. Genetic algorithm with non-random initial population show better results than other methods. Thus, we propose using this algorithm for solving project portfolio formation problem.},
	annote = {Sergey Avdoshin - Professor, Head of School of Software Engineering, Faculty of Business Informatics,National Research University Higher School of EconomicsAddress: 20, Myasnitskaya str., Moscow, 101000, Russian FederationE-mail: savdoshin@hse.ru Alexey Lifshits - MSc Program Student, School of Software Engineering, Faculty of Business Informatics,National Research University Higher School of EconomicsAddress: 20, Myasnitskaya str., Moscow, 101000, Russian FederationE-mail: alexeus1992@yandex.ru     Leading IT companies run simultaneously several dozens or even several hundreds of projects. One of the major objectives is to decide whether a project meets the current strategic goalsand resource limits of a company or not. This leads firms to the issue of a project portfolio formation, where the challenge is to choose a subset of projects which meet the strategic objectivesof a company in the best way. In this present article we propose a multi-objective mathematical model of the project portfolio formation problem, defined on the fuzzy trapezoidal numbers.     We provide an overview of methods for solving this problem, which are a Branch and bound approach, an adaptive parameter variation scheme based on the epsilon-constraint method, ant colony optimization method and genetic algorithm. After our analysis, we choose the ant colony optimization method and SPEA II method, which is a modification ofgenetic algorithm. We describe the implementation of these methods applied to the project portfolio formation problem.The ant colony optimization is based on the max min antsystem with one pheromone structure and one ant colony. Three modifications of our SPEA II implementation have been considered. The first adaptation uses the binary tournament selection, while the second requires the rank selection method. The last one is based on another variant of generating initial population. Part of the population is generated by a non-random manner on the basis of solving a one-criterion optimization problem. This fact makes the population stronger than the initial one which is generated completely at random.     We compare the ant colony optimization algorithm and the three modifications of a genetic algorithm on the basis of the following parameters: speed of execution and the C-metric between each pair of algorithms. Genetic algorithm with non-random initial population show better results than other methods. Thus, we propose using this algorithm for solving project portfolio formation problem.}
}