A VNS Algorithm for Noisy Problems and Its Application to Project Portfolio Analysis

Motivated by an application in project portfolio analysis under uncertainty, we develop an algorithm S-VNS for solving stochastic combinatorial optimization (SCO) problems based on the Variable Neighborhood Search (VNS) metaheuristic, and show its theoretical soundness by a mathematical convergence result. S-VNS is the first generalpurpose algorithm for SCO problems using VNS. It combines a classical VNS search strategy with a sampling approach with suitably increasing sample size. After the presentation of the algorithm, the considered application problem in project management, which combines a project portfolio decision on an upper level and project scheduling as well as staff assignment decisions on a lower level, is described. Uncertain work times require a treatment as an SCO problem. First experimental results on the application of S-VNS to this problem are outlined.