Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks

In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function $F(x) = \max_{y} f(x,y)$ directly using a covariance matrix adaptation evolution strategy (CMA-ES) in which the rankings of solution candidates are approximated by our proposed worst-case ranking approximation (WRA) mechanism. We develop two variants of WRA combined with CMA-ES and approximate gradient ascent as numerical solvers for the inner maximization problem. Numerical experiments show that our proposed approach outperforms several existing approaches when the objective function is a smooth strongly convex--concave function and the interaction between $x$ and $y$ is strong. We investigate the advantages of the proposed approach for problems where the objective function is not limited to smooth strongly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.ngly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty

Evolutionary Algorithms in Engineering Design Optimization

Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc