Designing a Framework for Solving Multiobjective Simulation Optimization Problems

TL;DR

The paper presents ParMOO, a modular, open-source framework for solving multiobjective simulation optimization (MOSO) problems with expensive, black-box simulations. It introduces an object-oriented architecture with abstract components for global search, surrogates, acquisitions, and optimization, and centers problem modeling on a separable simulation-output space $\mathbf{S}$ and objective space $\mathbf{F}$, enabling problem embeddings to handle mixed-variable and constrained settings. Through two case studies—Fayans EDF calibration and CFR material design—the authors demonstrate structure-exploiting solvers that dramatically reduce surveillance evaluations and accelerate convergence compared with black-box variants, while maintaining flexibility across heterogeneous workflows. The work highlights practical improvements in convergence speed, parallelism, and maintainability, suggesting ParMOO as a scalable pathway for deploying advanced MOSO methods in real-world engineering contexts.

Abstract

Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. While an extensive body of research is dedicated to developing new algorithms and methods for solving these and related problems, it is challenging and time consuming to integrate these techniques into real world production-ready solvers. This is partly due to the diversity and complexity of modern state-of-the-art MOSO algorithms and methods and partly due to the complexity and specificity of many real-world problems and their corresponding computing environments. The complexity of this problem is only compounded when introducing potentially complex and/or domain-specific surrogate modeling techniques, problem formulations, design spaces, and data acquisition functions. This paper carefully surveys the current state-of-the-art in MOSO algorithms, techniques, and solvers; as well as problem types and computational environments where MOSO is commonly applied. We then present several key challenges in the design of a Parallel Multiobjective Simulation Optimization framework (ParMOO) and how they have been addressed. Finally, we provide two case studies demonstrating how customized ParMOO solvers can be quickly built and deployed to solve real-world MOSO problems.

Figures (8)

• Figure 1: The feasible design space ${\mathbf{\mathcal{X}}}$ (left) is mapped into an intermediate simulation output space ${\mathbf{\mathcal{S}}}$ (center) via the black-box simulation $\mathbf{S}$, then to the feasible objective space ${\mathbf{\mathcal{Y}}}$ (right) via the algebraic objective function $\mathbf{F}$.
• Figure 2: A depiction of the data flow in ParMOO. The embedder module takes possibly discrete values from the design space and maps them to a normalized latent space $[0,1]^\ell$. The extractor module accepts candidate designs in the range $[0,1]^\ell$ from the optimization module, and maps them back into $\mathbf{\mathcal{X}}$.
• Figure 3: UML diagram outlining the key dictionaries, components, and methods that make up a MOOP object and its contents.
• Figure 4: Walltimes when performing 1,000 1-3 second simulation evaluations in ParMOO (with batch sizes 8, 16, and 32) with increasing number of threads.
• Figure 5: Iteration vs. $\chi^2$ loss when solving the Fayans EDF calibration with ParMOO, exploiting the sum-of-squares structure (structured) and with a standard (black-box) approach. The total simulations used by the end of iteration $k$ are calculated as $2000 + 10k$.