Zelda B. Zabinsky

Danielle F. Morey, Giulia Pedrielli, Cherry Y. Wakayama et al.

In complex real-world settings, optimization is challenged by the presence of diverse models of differing fidelity. In many optimization problems, a single model is treated as the most accurate representation of the underlying system, while other models are evaluated primarily by their agreement with this presumed most accurate model. Yet in real-world applications, model accuracy is rarely known a priori and assuming a single most accurate model can be misleading. This paper addresses this gap by proposing a flexible set-based optimization methodology called Set-Based Optimization with Multiple Models (S-BOMM) that works with multiple models without the assumption of a most accurate high-fidelity model. Unlike traditional optimization approaches that focus on finding an optimal solution according to the high-fidelity model, our methodology utilizes consistency between models to identify good solutions across multiple models. A probabilistic analysis of the consistency method is provided that bounds the likelihood of the methodology producing correct or incorrect results. Empirical results demonstrate the effectiveness of S-BOMM on test problems. By focusing on the consistency across models rather than relying on a single best solution, this set-based approach offers a practical alternative to optimization problems where multiple models must be considered without assuming a single most accurate high-fidelity model.

Hao Huang, Zelda B. Zabinsky

A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier for stochastic multi-objective optimization problems. MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution to estimate the objective functions. A finite-time performance analysis for deterministic multi-objective problems provides a bound on the probability that MOPBnB(so) captures the Pareto optimal set. Asymptotic convergence of MOPBnB(so) on stochastic problems is derived, in that the algorithm captures the Pareto optimal set and the estimations converge to the true objective function values. Numerical results reveal that the variant with multiple replications is extremely intensive in terms of computational resources compared to MOPBnB(so). In addition, numerical results show that MOPBnB(so) outperforms a genetic algorithm NSGA-II on test problems.

Peeyush Kumar, Wolf Kohn, Zelda B. Zabinsky

Many applications require solving non-linear control problems that are classically not well behaved. This paper develops a simple and efficient chattering algorithm that learns near optimal decision policies through an open-loop feedback strategy. The optimal control problem reduces to a series of linear optimization programs that can be easily solved to recover a relaxed optimal trajectory. This algorithm is implemented on a real-time enterprise scheduling and control process.