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Abstract:In traditional information technology project portfolio management (ITPPM), managers often pay more attention to the optimization of portfolio selection in the initial stage. In fact, during the portfolio implementation process, there are still issues to be optimized. Organizing cooperation will enhance the efficiency, although it brings more immediate risk due to the complex variety of links between projects. In order to balance the efficiency and risk, an optimization method is presented based on the complex network theory and entropy, which will assist portfolio managers in recognizing the structure of the portfolio and determine the cooperation range. Firstly, a complex network model for an IT project portfolio is constructed, in which the project is simulated as an artificial life agent. At the same time, the portfolio is viewed as a small scale of society. Following this, social network analysis is used to detect and divide communities in order to estimate the roles of projects between different portfolios. Based on these, the efficiency and the risk are measured using entropy and are balanced through searching for adequate hierarchy community divisions. Thus, the activities of cooperation in organizations, risk management, and so on-which are usually viewed as an important art-can be discussed and conducted based on quantity calculations.

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There are some adjustable parameters which directly influence the performance and stabihty of Particle Swarm Optimization algorithm. In this paper, stabilities of PSO with constant parameters and time-varying parameters are analyzed without Lipschitz constraint. Necessary and sufficient stability conditions for acceleration factor q) and inertia weight w are presented. Experiments on benchmark functions show the good performance of PSO satisfying the stability condition, even without Lipschitz constraint. And the inertia weight w value is enhanced to ( -1,1 ).The PSO (Particle Swarm Optimization) algorithm is a population based parallel optimization technique introduced by Kennedy and Eberhart [ 1 ]. There are some adjustable parameters, such as inertia weight, acceleration factor, scaled factor, and so on, which are always selected empirically [ 2 -4 ] and influence the convergence performance and stability of the algorithm greatly. In ILef.[ 5 ], the state equations of particles are simplified as a constant coefficient dynamic system and stability is analyzed by Clerc [ 5 ].In this paper, standard PSO algorithm is modified as a second-order discrete dynamic system. In Section 2, the eigenvalues distribution and stability area of particles are analyzed as a constant coefficient dynamic system at a certain time. On the basis of the analysis, in Section 3, necessary and sufficient conditions for stability of time-varying PSO without Lipschitz constraint are given. Furthermore, simulation results demonstrate the conditions are critical to system stability.1 Standard PSO algorithm State equation of each particle in one dimension of searching space of a Standard PSO algorithm is defined in the following way: rid : W 9 rid 4" C 1 " rand/d 9 (Pia -X'id) + c2 " randpd (pgd -xid),satisfying I v~ I ~< Vm~-As an up bound of velocity vector in each iteration, Vmax can be presented as the Lipschitz condition of particles dynamic systems. I xi(k + 1) -xi(k) ]~< Vmax, (1.3) where w is the inertia weight, xia is the current position of the particle, Pid is the 'personal' best position of the particle, Pgd is the swarm best position amongst all particles, c l and c2 are acceleration factors, randia and randpd are two random numbers in the range [ 0, 1 ]. In the searching space, particles "flow" to the target by swarm information Pgd and its own information Pid. Convergence analysis of PSOIn this part, stabilities of both constant coefficient dynamic system in a certain time and time-varying dynamic system are analyzed based on standard PSO equation (1.1) and (1.2). Constant coefficient PSO dynamic systemEquations ( 1.1 ) and (1.2) can be simplified as :vi(t + 1) = w 9 -9" x(t) + p, (2.1)Xi(t + 1) xi(t ) + 7] 9 + 1), (2.2) where acceleration factor is 9i = ci • rand/, 9 = 9, + 92; P = (91 " Pid + 92 " Pgd)/(91 + 92); 7] is the scaled factor; p is the input of the system. So the above equations are equivalent to:xi(t + 1) =(1 + 7]. w-77. 9) " x(t)-~]" w 9 x(t -1) +p.(2.3) At a ce~ain time k, parameters are constant, and the second...