An Upper Bound on the Hausdorff Distance Between a Pareto Set and its Discretization in Bi-Objective Convex Quadratic Optimization

We provide upper bounds on the Hausdorff distances between the efficient set and its discretization in the decision space, and between the Pareto set (also called the Pareto front) and its discretization in the objective space, in the context of bi-objective convex quadratic optimization on a compact feasible set. Our results imply that if t … Read more

PyMOSO: Software for Multi-Objective Simulation Optimization with R-PERLE and R-MinRLE

We present the PyMOSO software package for (1) solving multi-objective simulation optimization (MOSO) problems on integer lattices, and (2) implementing and testing new simulation optimization (SO) algorithms. First, for solving MOSO problems on integer lattices, PyMOSO implements R-PERLE, a state-of-the-art algorithm for two objectives, and R-MinRLE, a competitive benchmark algorithm for three or more objectives. … Read more

Multi-objective Ranking and Selection: Optimal Sampling Laws and Tractable Approximations via SCORE

Consider the multi-objective ranking and selection (MORS) problem in which we select the Pareto-optimal set from a finite set of systems evaluated on three or more stochastic objectives. Solving this problem is difficult because we must determine how to allocate a simulation budget among the systems to minimize the probability that any systems are misclassified. … Read more

Bi-objective Simulation Optimization on Integer Lattices using the Epsilon-Constraint Method in a Retrospective Approximation Framework

We consider multi-objective simulation optimization (MOSO) problems on integer lattices, that is, nonlinear optimization problems in which multiple simultaneous objective functions can only be observed with stochastic error, e.g., as output from a Monte Carlo simulation model. The solution to a MOSO problem is the efficient set, which is the set of all feasible decision … Read more

An Introduction to Multi-Objective Simulation Optimization

The multi-objective simulation optimization (MOSO) problem is a nonlinear multi-objective optimization problem in which multiple simultaneous and conflicting objective functions can only be observed with stochastic error. We provide an introduction to MOSO at the advanced tutorial level, aimed at researchers and practitioners who wish to begin working in this emerging area. Our focus is … Read more

SCORE Allocations for Bi-objective Ranking and Selection

The bi-objective R&S problem is a special case of the multi-objective simulation optimization problem in which two conflicting objectives are known only through dependent Monte Carlo estimators, the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the bi-objective R&S problem is a set … Read more