Multi-objective optimization with Kriging surrogates using “moko”, an open source package

Abstract

Many modern real-world designs rely on the optimization of multiple competing goals. For example, most components designed for the aerospace industry must meet some conflicting expectations. In such applications, low weight, low cost, high reliability, and easy manufacturability are desirable. In some cases, bounds for these requirements are not clear, and performing mono-objective optimizations might not provide a good landscape of the required optimal design choices. For these cases, finding a set of Pareto optimal designs might give the designer a comprehensive set of options from which to choose the best design. This article shows the main features and functionalities of an open source package, developed by the present authors, to solve constrained multi-objective problems. The package, named moko (acronym for Multi-Objective Kriging Optimization), was built under the open source programming language R. Popular Kriging based multiobjective optimization strategies, as the expected volume improvement and the weighted expected improvement, are available in the package. In addition, an approach proposed by the authors, based on the exploration using a predicted Pareto front is implemented. The latter approach showed to be more efficient than the two other techniques in some case studies performed by the authors with moko.

Effectiveness of Surrogate-Based Optimization Algorithms for System Architecture Optimization

“…Dealing with multi-objective optimization problems has also been an important topic of research for SBO algorithms [42]. Many strategies have been studied, including multi-objective variations of the Expected Improvement [43] and Probability of Improvement (PoI) [33] criteria, the Expected Hypervolume Improvement (EHVI) [44], or simply optimizing for the estimated objective values themselves [24]. Infill criteria for multi-objective optimization are discussed in more details in a later section.…”

Preface to the special issue of the International Symposium on Solid Mechanics (MecSol 2017)

“…• X-FEM, G-FEM, and BEM: crack propagation and X-FEM modelling (Angelo et al, 2018); G-FEM modelling (Sato et al, 2018) and dynamic analysis (Weinhardt et al, 2018); BEM analysis of buckling of anisotropic plates (Monteiro and Daros, 2018), and 3D frictional contact (Ubessi and Marczak, 2018). • Structural Reliability Methods and Reliability-Based Design Optimization: Multi-objective optimization (Passos and Luersen, 2018) and experimental crack identification (Oliveira Filho et al, 2018). • Multiaxial and Fretting Fatigue: identification of fatigue limits and continuum damage mechanics (Castro and Bemfica, 2018), stress-life curves for alloy steels (Duran et al, 2018) and assessment of fatigue limits (Bandeira et al, 2018).…”