Comparisons of Hybrid Multi-Objective Programming Algorithms with Grey Target and PCA for Weapon System Portfolio Selection

Abstract

Weapon Systems Portfolio Selection (WSPS) can be considered as a multi-objective decision analysis (MODA) problem. Aiming at its challenging features because of, 1) interactions and independencies among weapon systems, 2) the uncertainty of the sample data set for assessment, and 3) the missing target value of the assessment criteria, the WSPS problem is solved form four perspectives: portfolio without the independencies or target value, portfolio with the independencies but without target value, portfolio with the independencies and target value, portfolio in a incomplete sample data with the independencies and with target value. The synergy concept is introduced to describe the independencies among systems and Grey Target (GT) and principal component analysis (PCA) method are employed in this study to deal with the missing target value and incomplete sample data set. Three hybrid multiobjective programming algorithms are proposed as GT-MOP1, GT-MOP2 and PCA-MOP2 and non-dominated portfolios are generated as by sorting algorithm as a set of Pareto-optimal solutions. Finally, numerical experiments are given under four scenarios to illustrate the feasibilities and advantages of the three hybrid algorithms.

Application of trembling-hand perfect equilibrium to Nash nonlinear Grey Bernoulli model: an example of BRIC’s GDP forecasting

“…Chen et al [7] use fruit fly optimization algorithm-optimized Grey model neural network to perform satisfaction analysis for e-business service. Dou et al [8] compared hybrid multiobjective programming algorithms with Grey target and PCA for weapon system portfolio selection. Froelich and Salmeron [9] studied evolutionary learning of fuzzy Grey cognitive maps for the forecasting of multivariate, intervalvalued time series.…”

Application of game theory on parameter optimization of the novel two-stage Nash nonlinear grey Bernoulli model

“…Thus, inversed accumulated generating operation (IAGO) on the discrete form of solution can generate a prediction value. Grey forecasting has been successfully applied in social and nature science [3][4][5][6][7][8][9][10][11].…”