R-Mgspline: Retrospective Multi-Gradient Search for Multi-Objective Simulation Optimization on Integer Lattices

Abstract

We introduce the R-MGSPLINE (Retrospective Multi-Gradient Search with Piecewise Linear Interpolation and Neighborhood Enumeration) algorithm for finding a local efficient point when solving a multi-objective simulation optimization problem on an integer lattice. In this nonlinear optimization problem, each objective can only be observed with stochastic error and the decision variables are integer-valued. R-MGSPLINE uses a retrospective approximation (RA) framework to repeatedly call the MGSPLINE sample-path solver at a sequence of increasing sample sizes, using the solution from the previous RA iteration as a warm start for the current RA iteration. The MGSPLINE algorithm performs a line search along a common descent direction constructed from pseudo-gradients of each objective, followed by a neighborhood enumeration for certification. Numerical experiments demonstrate R-MGSPLINE’s empirical convergence to a local weakly efficient point.