Susan R. Hunter We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum … Read more
A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more
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
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
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
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
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
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