We investigate one stage stochastic multiobjective optimization problems where the objectives are the expected values of random functions. Assuming that the closed form of the expected values is difficult to obtain, we apply the well known Sample Average Approximation (SAA) method to solve it. We propose a smoothing infinity norm scalarization approach to solve the SAA problem and analyse the c...

Abstract Most real-world optimization problems are subject to uncertainties in parameters. In many situations where the uncertainties can be estimated to a certain degree, various stochastic programming (SP) methodologies are used to identify robust plans. Despite substantial advances in SP, it is still a challenge to solve practical SP problems, partially due to the exponentially increasing nu...

Uncertainty in activity durations is a key characteristic of many real world scheduling problems in manufacturing, logistics and project management. RCPSP/max with durational uncertainty is a general model that can be used to represent durational uncertainty in a wide variety of scheduling problems where there exist resource constraints. However, computing schedules or execution strategies for ...

In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, name...

This paper presents an asymptotic analysis of a Monte Carlo method, variously known as sample average approximation (SAA) or sample path optimization (SPO), for a general two-stage stochastic minimization problem. We study the case when the second-stage problem may have multiple local optima or stationary points that are not global solutions and SAA is implemented using a general nonlinear prog...

While solutions of Distributionally Robust Optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the Sample Average Approximation (SAA), there is no guarantee. In this paper, we introduce class Optimistic (DOO) models, and show that it always possible to beat SAA if consider not just worst-case models but also best-case ones. We show, however, comes at cost:...

In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, name...

Linear averaging is a popular method for combining forecasts of chance, but it is of limited use in the context of incoherent or abstaining judges. Recently proposed, the coherent approximation principle (CAP) generalizes linear averaging to have wider applicability yet suffers from computational intractability in cases of interest. This paper proposes a unified framework that views CAP and lin...

Large scale stochastic linear programs are typically solved using a combination of mathematical programming techniques and sample-based approximations. Some methods are designed to permit sample sizes to adapt to information obtained during the solution process, while others are not. In this paper, we experimentally examine the relative merits of approximations based on adaptive samples and tho...

The quadratic optimal control problem for linear time-delay singularly perturbed systems is investigated via successive approximation approach (SAA) in this paper. Based on singular perturbation theory, the system is decomposed into two subsystems of a slow-time scale and a fast-time scale. The slow-time scale time-delay optimal control problem is transformed first into a sequence of nonhomogen...