Global sensing search for nonlinear global optimization

Hedar, Abdel-Rahman; Deabes, Wael; Amin, Hesham H.; Almaraashi, Majid; Fukushima, Masao

doi:10.1007/s10898-021-01075-2

Cited by 4 publications

(3 citation statements)

References 69 publications

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“…The simulated annealing algorithm is a classical stochastic scheme for searching global optima by minimizing the system of energy through an annealing schedule ( 8 ). Evolutionary methods that imitate biological creatures’ behaviors are presented continuously ( 9 , 10 ). Among them, a genetic algorithm is a bio-inspired heuristic search through heredity and mutation ( 11 , 12 ).…”

Section: Introductionmentioning

confidence: 99%

Deep Q-learning to globally optimize a k-D parameter search for medical imaging

Zhang¹,

Liang²,

Luke³

et al. 2023

Quant Imaging Med Surg

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Background Estimation of the global optima of multiple model parameters is valuable for precisely extracting parameters that characterize a physical environment. This is especially useful for imaging purposes, to form reliable, meaningful physical images with good reproducibility. However, it is challenging to avoid different local minima when the objective function is nonconvex. The problem of global searching of multiple parameters was formulated to be a k -D move in the parameter space and the parameter updating scheme was converted to be a state-action decision-making problem. Methods We proposed a novel Deep Q-learning of Model Parameters (DQMP) method for global optimization which updated the parameter configurations through actions that maximized the Q-value and employed a Deep Reward Network (DRN) designed to learn global reward values from both visible fitting errors and hidden parameter errors. The DRN was constructed with Long Short-Term Memory (LSTM) layers followed by fully connected layers and a rectified linear unit (ReLU) nonlinearity. The depth of the DRN depended on the number of parameters. Through DQMP, the k -D parameter search in each step resembled the decision-making of action selections from 3 k configurations in a k -D board game. Results The DQMP method was evaluated by widely used general functions that can express a variety of experimental data and further validated on imaging applications. The convergence of the proposed DRN was evaluated, which showed that the loss values of six general functions all converged after 12 epochs. The parameters estimated by the DQMP method had relative errors of less than 4% for all cases, whereas the relative errors achieved by Q-learning (QL) and the Least Squares Method (LSM) were 17% and 21%, respectively. Furthermore, the imaging experiments demonstrated that the imaging of the parameters estimated by the proposed DQMP method were the closest to the ground truth simulation images when compared to other methods. Conclusions The proposed DQMP method was able to achieve global optima, thus yielding accurate model parameter estimates. DQMP is promising for estimating multiple high-dimensional parameters and can be generalized to global optimization for many other complex nonconvex functions and imaging of physical parameters.

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Section: Introductionmentioning

confidence: 99%

Deep Q-learning to globally optimize a k-D parameter search for medical imaging

Zhang¹,

Liang²,

Luke³

et al. 2023

Quant Imaging Med Surg

View full text Add to dashboard Cite

show abstract

“…The internet connection and other unrelated applications are turned off throughout the analysis, ensuring that unnecessary background activities are not accessing computational resources throughout the solvers' performance. The unconstrained and constrained NLP problems are selected amongst the standard benchmark problems [27][28][29], and they are reported in [72]. Specifically, the benchmark problems include combinations of logarithmic, trigonometric, and exponential terms, non-convex and convex functions, a minimum of two to a maximum of thirty variables, and a maximum of nine constraint functions for the constrained optimization problems.…”

Section: Benchmark Test Functions Analysismentioning

confidence: 99%

“…For this reason, we will focus on all the solvers that are either written on or can be implemented in MATLAB. The NLP problems used in this comparison have been selected amongst the standard benchmark problems [27][28][29] with up to thirty variables and up to nine scalar constraints.…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Nonlinear Programming Solvers: Performance Evaluation, Benchmarking, and Multi-UAV Optimal Path Planning

Lavezzi

Guye

Cichella

et al. 2023

Drones

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In this paper, we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. We conduct a comparative analysis of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems. The comparison metrics involve accuracy, convergence rate, and computational time. MATLAB is chosen as the implementation platform due to its widespread adoption in academia and industry. Our study includes solvers which are either freely available or require a license, or are extensively documented in the literature. Moreover, we differentiate solvers if they allow the selection of different optimal search methods. We assess the performance of 24 algorithms on a set of 60 benchmark problems. We also evaluate the capability of each solver to tackle two large-scale UAV optimal path planning scenarios, specifically the 3D minimum time problem for UAV landing and the 3D minimum time problem for UAV formation flying. To enrich our analysis, we discuss the effects of each solver’s inner settings on accuracy, convergence rate, and computational time.

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