A Framework for Meta-heuristic Parameter Performance Prediction Using Fitness Landscape Analysis and Machine Learning

The behaviour of an optimization algorithm when attempting to solve a problem depends on the values assigned to its control parameters. For an algorithm to obtain desirable performance, its control parameter values must be chosen based on the current problem. Despite being necessary for optimal performance, selecting appropriate control parameter values is time-consuming, computationally expensive, and challenging. As the quantity of control parameters increases, so does the time complexity associated with searching for practical values, which often overshadows addressing the problem at hand, limiting the efficiency of an algorithm. As primarily recognized by the no free lunch theorem, there is no one-size-fits-all to problem-solving; hence from understanding a problem, a tailored approach can substantially help solve it. To predict the performance of control parameter configurations in unseen environments, this thesis crafts an intelligent generalizable framework leveraging machine learning classification and quantitative characteristics about the problem in question. The proposed parameter performance classifier (PPC) framework is extensively explored by training 84 high-accuracy classifiers comprised of multiple sampling methods, fitness types, and binning strategies. Furthermore, the novel framework is utilized in constructing a new parameter-free particle swarm optimization (PSO) variant called PPC-PSO that effectively eliminates the computational cost of parameter tuning, yields competitive performance amongst other leading methodologies across 99 benchmark functions, and is highly accessible to researchers and practitioners. The success of PPC-PSO shows excellent promise for the applicability of the PPC framework in making many more robust parameter-free meta-heuristic algorithms in the future with incredible generalization capabilities

Model-Assisted Online Optimization of Gain-Scheduled PID Control Using NSGA-II Iterative Genetic Algorithm

In the practical control of nonlinear valve systems, PID control, as a model-free method, continues to play a crucial role thanks to its simple structure and performance-oriented tuning process. To improve the control performance, advanced gain-scheduling methods are used to schedule the PID control gains based on the operating conditions and/or tracking error. However, determining the scheduled gain is a major challenge, as PID control gains need to be determined at each operating condition. In this paper, a model-assisted online optimization method is proposed based on the modified Non-Dominated Sorting Genetic Algorithms-II (NSGA-II) to obtain the optimal gain-scheduled PID controller. Model-assisted offline optimization through computer-in-the-loop simulation provides the initial scheduled gains for an online algorithm, which then uses the iterative NSGA-II algorithm to automatically schedule and tune PID gains by online searching of the parameter space. As a summary, the proposed approach presents a PID controller optimized through both model-assisted learning based on prior model knowledge and model-free online learning. The proposed approach is demonstrated in the case of a nonlinear valve system able to obtain optimal PID control gains with a given scheduled gain structure. The performance improvement of the optimized gain-scheduled PID control is demonstrated by comparing it with fixed-gain controllers under multiple operating conditions

Using Spiral Dynamic Algorithm for Maximizing Power Production of Wind Farm

This paper presents a preliminary study of a model-free approach based on spiral dynamic algorithm (SDA) for maximizing wind farms power production. The SDA based approach is utilized to find the optimal control parameter of each turbine to maximize the total power production of a wind farm. For simplicity, a single row wind farm model with turbulence interaction between turbines is used to validate the proposed approach. Simulation results demonstrate that the SDA based method produces higher total power production compared to the particle swarm optimization (PSO) and game theoretic (GT) based approaches

Parameter Estimation of Linear Dynamical Systems with Gaussian Noise

We present a novel optimization-based method for parameter estimation of a time-varying dynamic linear system. This method optimizes the likelihood of the parameters given measured data using an optimization algorithm tailored to the structure of this maximum likelihood estimation problem. Some parameters of the covariance of process and measurement noise can also be estimated. This is particularly useful when offset-free Model Predictive Control with a linear disturbance model is performed. To reduce the complexity of the maximum likelihood estimation problem we also propose an approximate formulation and show how it is related to the actual problem. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. We also present how to use Sequential Quadratic Programming efficiently for the optimization of our formulations. Finally, we show the performance of the proposed methods through numerical simulations. First, on a minimal example with only one parameter to be estimated, and second, on a system with heat and mass transfer. Both methods can successfully estimate the model parameters in these examples.Comment: Submitted to IEEE European Control Conference 2023 (ECC23). Contains 8 pages including 6 figure

Which is the best PID variant for pneumatic soft robots an experimental study

This paper presents an experimental study to compare the performance of model-free control strategies for pneumatic soft robots. Fabricated using soft materials, soft robots have gained much attention in academia and industry during recent years because of their inherent safety in human interaction. However, due to structural flexibility and compliance, mathematical models for these soft robots are nonlinear with an infinite degree of freedom (DOF). Therefore, accurate position (or orientation) control and optimization of their dynamic response remains a challenging task. Most existing soft robots currently employed in industrial and rehabilitation applications use model-free control algorithms such as PID. However, to the best of our knowledge, there has been no systematic study on the comparative performance of model-free control algorithms and their ability to optimize dynamic response, i.e., reduce overshoot and settling time. In this paper, we present comparative performance of several variants of model-free PID-controllers based on extensive experimental results. Additionally, most of the existing work on model-free control in pneumatic soft-robotic literature use manually tuned parameters, which is a time-consuming, labor-intensive task. We present a heuristic-based coordinate descent algorithm to tune the controller parameter automatically. We presented results for both manual tuning and automatic tuning using the Ziegler–Nichols method and proposed algorithm, respectively. We then used experimental results to statistically demonstrate that the presented automatic tuning algorithm results in high accuracy. The experiment results show that for soft robots, the PID-controller essentially reduces to the PI controller. This behavior was observed in both manual and automatic tuning experiments; we also discussed a rationale for removing the derivative term

Annealing Optimization for Progressive Learning with Stochastic Approximation

In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained stochastic optimization problems, with the constraints originating mainly from model assumptions that define a trade-off between complexity and performance. This trade-off is closely related to over-fitting, generalization capacity, and robustness to noise and adversarial attacks, and depends on both the structure and complexity of the model, as well as the properties of the optimization methods used. We develop an online prototype-based learning algorithm based on annealing optimization that is formulated as an online gradient-free stochastic approximation algorithm. The learning model can be viewed as an interpretable and progressively growing competitive-learning neural network model to be used for supervised, unsupervised, and reinforcement learning. The annealing nature of the algorithm contributes to minimal hyper-parameter tuning requirements, poor local minima prevention, and robustness with respect to the initial conditions. At the same time, it provides online control over the performance-complexity trade-off by progressively increasing the complexity of the learning model as needed, through an intuitive bifurcation phenomenon. Finally, the use of stochastic approximation enables the study of the convergence of the learning algorithm through mathematical tools from dynamical systems and control, and allows for its integration with reinforcement learning algorithms, constructing an adaptive state-action aggregation scheme.Comment: arXiv admin note: text overlap with arXiv:2102.0583