Research Article Speed Proportional Integrative Derivative Controller: Optimization Functions in Metaheuristic Algorithms Luis Fernando de Mingo L´ opez , 1 Francisco Serradilla Garc´ ıa , 1,2 Jos´ e Eugenio Naranjo Hern´ andez , 1,2 and Nuria G´ omez Blas 1 1 ETSI de Sistemas Inform´ aticos, Universidad Polit´ ecnica de Madrid, Madrid, Spain 2 Instituto Universitario de Investigaci´ on del Autom´ ovil (INSIA), Universidad Polit´ ecnica de Madrid, Madrid, Spain Correspondence should be addressed to Jos´ e Eugenio Naranjo Hern´ andez; joseeugenio.naranjo@upm.es Received 20 January 2021; Revised 7 July 2021; Accepted 2 October 2021; Published 3 November 2021 Academic Editor: Chi-Hua Chen Copyright © 2021 Luis Fernando de Mingo L´ opez et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recent advancements in computer science include some optimization models that have been developed and used in real ap- plications. Some metaheuristic search/optimization algorithms have been tested to obtain optimal solutions to speed controller applications in self-driving cars. Some metaheuristic algorithms are based on social behaviour, resulting in several search models, functions, and parameters, and thus algorithm-specific strengths and weaknesses. e present paper proposes a fitness function on the basis of the mathematical description of proportional integrative derivate controllers showing that mean square error is not always the best measure when looking for a solution to the problem. e fitness developed in this paper contains features and equations from the mathematical background of proportional integrative derivative controllers to calculate the best performance of the system. Such results are applied to quantitatively evaluate the performance of twenty-one optimization algorithms. Furthermore, improved versions of the fitness function are considered, in order to investigate which aspects are enhanced by applying the optimization algorithms. Results show that the right fitness function is a key point to get a good performance, regardless of the chosen algorithm. e aim of this paper is to present a novel objective function to carry out optimizations of the gains of a PID controller, using several computational intelligence techniques to perform the optimizations. e result of these optimizations will demonstrate the improved efficiency of the selected control schema. 1. Introduction Many optimization problems are nondeterministic poly- nomial-time (NP) or NP-hard, and a high computing power is required when trying to solve them [1, 2]. An NP- hard problem “is a problem where a solution for it is at least as hard as finding a solution for the hardest problem whose solution can quickly be checked as being true. Some NP- hard problems are ones in which a working solution can be checked quickly (NP problems) and some are not. NP-hard problems are also NP problems fit into a label called NP- complete” [3]. Many of the problems arising in present-day applications from scientific fields belong in NP-hard problems: they involve search spaces with many dimen- sions, they are multimodal or multiobjective, and the optimization functions are hard to compute or are applied on large volumes of data. Classical optimization methods from operation research make it possible to find optimal solutions for complex problems, but are not useful in practice due to their excessive computational load when applied to real-world systems [4]. For NP-hard problems, the time required to solve a problem grows exponentially with respect to the size of the problem, making the exact methods unpractical. In order to solve the disadvantages of classical trial-and- error methods and mathematical solution search techniques, researchers have proposed various algorithms that mimic natural and artificial phenomena, and black-box optimiza- tion benchmark problems are implemented to evaluate the performance of these algorithms. Hindawi Journal of Advanced Transportation Volume 2021, Article ID 5538296, 12 pages https://doi.org/10.1155/2021/5538296