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

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 multi-objective 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.