Bi-Objective Simulation Optimization on Integer Lattices Using the Epsilon-Constraint Method In a Retrospective Approximation Framework
Abstract: We propose the retrospective partitioned epsilon-constraint with relaxed local enumeration (R-PERLE) algorithm to solve the bi-objective simulation optimization problem on integer lattices. In this nonlinear optimization problem, both objectives can only be observed with stochastic error, the decision variables are integer-valued, and a local solution is called a local efficient set. R-PERLE employs a version of sample average approximation called retrospective approximation (RA) to repeatedly call the PERLE 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. As the number of RA iterations increases, R-PERLE provably converges to a local efficient set with probability one under appropriate regularity conditions. We discuss the design principles that make our algorithm efficient and demonstrate that R-PERLE performs favorably relative to the current state of the art, MO-COMPASS, in our numerical experiments.