Set Of Optimizations Research Articles

Reservoir Production Management With Bayesian Optimization: Achieving Robust Results in a Fraction of the Time

Summary In well control (production) optimization, the computational cost of conducting a full-physics flow simulation on a 3D, rich grid-based model poses a significant challenge. This challenge is exacerbated in a robust optimization (RO) setting, where flow simulation must be repeated for numerous geological realizations, rendering RO impractical for many field-scale cases. In this paper, we introduce and discuss a new optimization workflow that addresses this issue by providing computational efficiency, i.e., achieving a near-global optimum of the predefined objective function with minimal forward model (flow-simulation) evaluations. In this workflow, referred to as “Bayesian optimization (BO),” the objective function for samples of decision (control) variables is first computed using a proper design experiment. Then, given the samples, a Gaussian process regression (GPR) is trained to mimic the surface of the objective function as a surrogate model. While balancing the dilemma to select the next control variable between high mean, low uncertainty (exploitation) and low mean, high uncertainty (exploration), a new control variable is selected, and flow simulation is run for this new point. Later, the GPR is updated, given the output of the flow simulation. This process continues sequentially until the termination criteria are satisfied. To validate the workflow and obtain a better insight into the detailed steps, we first optimized a 1D problem. The workflow is then implemented for a 3D synthetic reservoir model to perform RO in a realistic field scenario (8-dimensional and 45-dimensional optimization problems). The workflow is compared with two other commonly used gradient-free algorithms in the literature: particle swarm optimization (PSO) and genetic algorithm (GA). The main contributions are (1) developing a new optimization workflow to address the computational cost of flow simulation in RO, (2) demonstrating the effectiveness of the workflow on a 3D grid-based model, (3) investigating the robustness of the workflow against randomness in initiation samples and discussing the results, and (4) comparing the workflow with other optimization algorithms, showing that it achieves same near-optimal results while requiring only a fraction of the computational time.

Pelvis Treatment Plan Dose Comparison for Proton Therapy Using Single Energy and Dual Energy Computed Tomography Simulation Methods

In proton therapy, plan robustness is ameliorated by expanding the irradiation volume beyond the target, in order to mitigate setup and proton range uncertainties (RU). A byproduct of this expansion is elevated doses to surrounding organs at risk (OARs) which reduce some of the benefits associated with proton therapy. Dual-energy CT (DECT) has been shown in multiple phantom and animal tissue studies to reduce RU without compromising plan robustness. This study quantifies dosimetric differences between single-energy CT (SECT) and DECT for pelvis patients treated with intensity modulated proton therapy (IMPT). Under IRB approval, SECT and DECT scans from 25 IMPT pelvis patients were acquired using a CT scanner. Clinical plans were generated on the SECT images using robust optimization settings of 3.5% RU and 5 mm setup uncertainty in a treatment planning system. Subsequently, the clinical plans were recomputed on the corresponding DECT generated SPR-map images. For each patient, target coverage, mean and maximum OAR doses were compared for both image sets. Comparison of two plans showed systematic differences in target minimum dose (D99%) and V100%. Variations as high as 3.1% with DECT were observed in D99% indicating target under-dosage. On average, use of SECT overestimated V100% by 2.4% when compared to DECT. Since all clinical plans were optimized robustly to meet V95% coverage, higher agreement (<1%) was achieved for V95% (99.9±0.2%), and D95% (99.6±0.3%). DECT relative to SECT indicated slightly higher OAR maximum doses for femoral heads (2.3±2.78%), penile bulb/external genital (1.33±4.00%) and large bowel (0.5±1.25%). Similarly, higher mean dose was observed to rectum (2.08±4.88%), bladder (1.41±0.25%), femoral heads (1.18±6.61%) and penile bulb/external genital (1.78±5.74%) for DECT relative to SECT. Our results show a disparity between evaluated SECT and DECT target and OAR dosimetric parameters. Given the higher accuracies in proton range estimation associated with the use of DECT, its use can imply a potential for more conformal proton plans as well as higher TPS computed target coverage and OAR dose accuracy, both of which enhance overall treatment quality.

Advancing Concrete Mix Proportion through Hybrid Intelligence: A Multi-Objective Optimization Approach.

Concrete mixture design has been a key focus in concrete research. This study presents a new method for concrete mixture design by combining artificial neural networks (ANN), genetic algorithms (GA), and Scipy libraries for hybrid intelligent modeling. This method enables the prediction of concrete mechanical properties and the optimization of mix proportions with single or multi-objective goals. The GA is used to optimize the structure and weight parameters of ANN to improve prediction accuracy and generalization ability (R2 > 0.95, RMSE and MAE < 10). Then, the Scipy library combined with GA-ANN is used for the multi-objective optimization of concrete mix proportions to balance the compressive strength and costs of concrete. Moreover, an AI-based concrete mix proportion design system is developed, utilizing a user-friendly GUI to meet specific strength requirements and adapt to practical needs. This system enhances optimization design capabilities and sets the stage for future advancements. Overall, this study focuses on optimizing concrete mixture design using hybrid intelligent modeling and multi-objective optimization, which contributes to providing a novel and practical solution for improving the efficiency and accuracy of concrete mixture design in the construction industry.

Advanced soft computing techniques for predicting punching shear strength

Accurate prediction of punching shear strength is crucial for ensuring the structural integrity and safety of reinforced concrete (RC) flat slab-column connections. However, estimating punching shear strength in complex configurations, such as RC flat slabs, remains a challenging task due to intricate interactions between various parameters. To address this challenge, this study introduces an innovative approach that combines machine learning techniques with hyperparameter optimization strategies to enhance the precision and efficiency of predicting punching shear strength. Specifically, a comprehensive investigation is conducted to assess the performance of XGBoost optimized by different hyperparameter optimization algorithms such as the forensic-based investigation (FBI), Bayesian optimization (BO), grid search (GS), random search (RS), and default setting (DS). The experimental results of 40 runs on three different datasets confirmed the FBI-XGBoost model as the most appropriate for predicting punching shear strength in terms of efficiency and computation time by achieving the highest RMSE, MAPE, MAE, and R2 values. In addition, the statistical results exposed the infeasibility of using RS for the XGBoost model. While the GS method was able to configure the XGBoost model well, doing so required extensive computational time, while the BO-FBI model achieved acceptable prediction accuracy in a reasonable training time. The FBI-XGBoost model was further compared with empirical methods, including ACI-318-08, BS8110-97, and CEB-FIP-90, based on the predictive-to-actual ratio. FBI-XGBoost was identified as the best model by attaining the ratio value closest to 1 and the lowest standard deviation (1.011 ± 0.108). Overall, the statistical experimental results and hypothesis test values firmly support the FBI-XGBoost model as the most reliable free-formulae method for predicting punching shear strength in RC flat slab-column systems.

Learning and optimization under epistemic uncertainty with Bayesian hybrid models

Hybrid (i.e., grey-box) models are a powerful and flexible paradigm for predictive science and engineering. Grey-box models use data-driven constructs to incorporate unknown or computationally intractable phenomena into glass-box mechanistic models. The pioneering work of statisticians Kennedy and O’Hagan introduced a new paradigm to quantify epistemic (i.e., model-form) uncertainty. While popular in several engineering disciplines, prior work using Kennedy–O’Hagan hybrid models focuses on prediction with accurate uncertainty estimates. This work demonstrates computational strategies to deploy Bayesian hybrid models for optimization under uncertainty. Specifically, the posterior distributions of Bayesian hybrid models provide a principled uncertainty set for stochastic programming, chance-constrained optimization, or robust optimization. Through two illustrative case studies, we demonstrate the efficacy of hybrid models, composed of a structurally inadequate glass-box model and Gaussian process bias correction term, for decision-making using limited training data. From these case studies, we develop recommended best practices and explore the trade-offs between different hybrid model architectures.

Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem

The capital allocation framework presents capital allocation principles as solutions to particular optimisation problems and provides a general solution of the quadratic allocation problem via a geometric proof. However, the widely used haircut allocation principle is not reconcilable with that optimisation setting. Our study complements and generalises the unified capital allocation framework. The goal of the study is to contribute in the following two ways. First, we provide an alternative proof of the quadratic allocation problem based on the Lagrange multipliers method to reach the general solution, which complements the geometric proof. This alternative approach to solve the quadratic optimisation problem is, in our opinion, easier to follow and understand by researchers and practitioners. Second, we show that the haircut allocation principle can be accommodated by the optimisation setting with the quadratic optimisation criterion if one of the original conditions is relaxed. Two examples are provided to illustrate the accommodation of this allocation principle.

Multi-objective optimization decision-making of an underwater vehicle rotary docking skirt structure

This study determines the design parameters, analysis methods, and mesh size of a finite-element analysis model in the structural design of a rotary docking skirt (RDS) structure for an underwater vehicle. The impact of the structural design variables on the response is then studied. The sample points determined using the optimal Latin hypercube method are analyzed and fitted with the Kriging model, response surface model, and radial basis function. After comparing the fitting accuracies of the three approximation models, an approximation model of the RDS structure is determined. Next, several typical multi-objective optimization algorithms are tested and the improved nondominated sorting genetic algorithm II (INSGA-II) is selected for establishing an optimization model of the RDS structure. INSGA-II obtains the Pareto solution set of multi-objective optimization. The weights are obtained by combining the subjective and objective weights determined through the subjective-weighting analytic hierarchy process and the objective-weighting entropy weight method, respectively. Based on the combination weight, the technique for order preference by similarity to the ideal solution method is selected for multi-objective optimization decision-making. The final decision-making scheme of the rotary docking skirt structure improved the optimization effect compared to the initial scheme.

Optimizing Data Pipelines for Machine Learning in Feature Stores

Data pipelines (i.e., converting raw data to features) are critical for machine learning (ML) models, yet their development and management is time-consuming. Feature stores have recently emerged as a new "DBMS-for-ML" with the premise of enabling data scientists and engineers to define and manage their data pipelines. While current feature stores fulfill their promise from a functionality perspective, they are resource-hungry---with ample opportunities for implementing database-style optimizations to enhance their performance. In this paper, we propose a novel set of optimizations specifically targeted for point-in-time join, which is a critical operation in data pipelines. We implement these optimizations on top of Feathr: a widely-used feature store, and evaluate them on use cases from both the TPCx-AI benchmark and real-world online retail scenarios. Our thorough experimental analysis shows that our optimizations can accelerate data pipelines by up to 3× over state-of-the-art baselines.

HYBRID PARTICLE SWARM OPTIMIZATION AND GREY WOLF OPTIMIZER FOR SETTING PID PARAMETERS OF BLDC MOTORS

BLDC (Brushless DC) motors have advantages over asynchronous motors and dc motors in various aspects. Particularly in electric bicycles and flying cars, BLDC motors are utilized widely. Electric bicycles and flying cars are becoming increasingly popular, and as a result, the significance of BLDC motors and their cost-effective and efficient utilization has been growing rapidly. PID (Proportional Integral Derivative) controllers are generally used in motor control because they are cheap and perform well. Many methods have been used to adjust PID parameters. Although methods such as Ziegler-Nichols, Cohen-Coon etc. are widely used, there are also new methods such as optimization algorithms PSO (Particle Swarm Optimization), Whale Optimization Technique, Gray Wolf Optimization technique etc. The hybrid method: HPSOGWO (Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer) is a combination of PSO and GWO (Grey Wolf Optimizer) techniques, and it can be used for tuning PID parameters. As associated with this, the aim of this study is to show the superiority of HPSOGWO algorithm in optimizing the PID parameters. In the content of this study, the essentials regarding the optimization background, and details of the BLDC motor modeling was explained first. After that, the methodology of the hybrid solution was expressed and then the application phase was explained in detail, by including the results generally. In the context of the intelligent optimization approach of this study, the results were obtained in the MATLAB Simulink environment. The application of the used solution method revealed its superiority over the study conducted solely with GWO in various parameters.

Low Trace-Count Template Attacks on 32-bit Implementations of ASCON AEAD

The recently adopted Ascon standard by NIST offers a lightweight authenticated encryption algorithm for use in resource-constrained cryptographic devices. To help assess side-channel attack risks of Ascon implementations, we present the first template attack based on analyzing power traces, recorded from an STM32F303 microcontroller board running Weatherley’s 32-bit implementations of Ascon-128. Our analysis combines a fragment template attack with belief-propagation and key-enumeration techniques. The main results are three-fold: (1) we reached 100% success rate from a single trace if the C compiler optimized the unmasked implementation for space, (2) the success rate was about 95% after three traces if the compiler optimized instead for time, and (3) we also attacked a masked version, where the success rate was over 90% with 20 traces of executions with the same key, all after enumerating up to 224 key candidates. These results show that suitably-designed template attacks can pose a real threat to Ascon implementations, even if protected by first-order masking, but we also learnt how some differences in programming style, and even compiler optimization settings, can significantly affect the result.

Two-stage process production of microbial lipid by co-fermentation of glucose and N-acetylglucosamine from food wastes with Cryptococcus curvatus

Microbial lipids were produced through a two-stage process with Cryptococcus curvatus by co-fermenting rice and shrimp shells hydrolysates. In the first stage, biomass production of glucose and N-acetylglucosamine was optimized by response surface methodology with the maximum biomass yield (17.60 g/L) under optimum conditions (43.2 g/L mixed sugar concentration, pH 5.8, 200 rpm, and 28 °C). In the second stage, according to a single-factor optimization setting (43.2 g/L sugar mixture solutions, pH 5.5, and shift time of 36 h), lipid titer of 10.08 g/L with content of 55.30 % was achieved. Scaling up to a 5-L bioreactor increased lipid content to 60.07 % with 0.233 g/g yield. When Cryptococcus curvatus was cultured in the blends of rice hydrolysates and shrimp shells hydrolysate, lipid content and yield were 52.25 % and 0.204 g/g. The fatty acid compositions of lipid were similar to those of typical vegetable oils.

Study of a hull form optimization system based on a Gaussian process regression algorithm and an adaptive sampling strategy, Part II: Multi-objective optimization

Ships have a wide variety of performance specifications and experience complex navigation conditions. Thus, an efficient numerical optimization system for general hull forms must be able to deal with multi-objective optimization problems. Based on a Gaussian process regression (GPR) algorithm and an adaptive sampling strategy, the authors have developed a single-objective optimization system, SBO-MSE + LCB, which is more efficient than the conventional simulation-based design (SBD) optimization system. However, the application of this system to hull form multi-objective optimization problems presents problems such as excessive new samplings, insufficient exploration of new sample points, and unsuitable convergence criteria. To solve the above problems, we first propose an adaptive sampling strategy based on the idea of spatial clustering. The strategy not only effectively controls the number of sampling numbers at each iteration in the SBO-MSE + LCB optimization system but also enables new sample points to achieve the multi-objective efficient exploration of optimal solution sets for optimization. Then, from the perspective of the convergence and diversity of Pareto optimal solution sets, we design adaptive sampling convergence criteria suitable for multi-objective optimization problems. Based on this, we enable the SBO-MSE + LCB optimization system to solve multi-objective optimization problems and verify its applicability with several cases for which the multi-objective mathematical optimization is performed. Finally, we use the SBO-MSE + LCB multi-objective optimization system and the SBD optimization system to optimize the total resistance coefficient of a deep-sea aquaculture vessel at the scantling and ballast drafts. The results show that the optimization efficiency of the SBO-MSE + LCB multi-objective optimization system is improved by 33.33% from the SBD optimization system for similar optimization performance, proving its advantage in efficiency in practical applications.

Fault Diagnosis of Support Vector Machine Analog Circuits Based on Improved Particle Swarm Optimization

The development of electronic circuits requires that the reliability and security of circuit equipment and system operation are also increasing. In addition, due to the complexity of the operating environment, it is very important to strengthen the fault diagnosis and real-time testing technology of analog circuits in circuit systems. Based on this, this paper studied the fault diagnosis of analog circuits with Support Vector Machine (SVM), and introduced Improved Particle Swarm Optimization (IPSO) algorithm to optimize the parameters of SVM. In other words, the dynamic weight setting and factor improvement of Particle Swarm Optimization (PSO) algorithm aim to accelerate algorithm performance improvement, and information extraction and diagnosis model construction are carried out on the basis of considering circuit fault characteristics. Through the performance test and application analysis of the improved algorithm proposed in the study, the error value of the improved algorithm was basically stable at 0.0103 in the late stage of classification training, and its prediction accuracy rate was more than 80%, and the classification consumption time was less. At the same time, the accuracy of fault feature extraction results in training and test scenarios was above 94%, and the search performance was obviously better than other comparison algorithms, which effectively improved the fault diagnosis accuracy and efficiency. The IPSO algorithm model can effectively identify analog circuit fault information, and shows good information optimization performance. It has certain validity and rationality in circuit fault diagnosis and security assurance.

Best Effort Workload Disparity Minimization in Multi-Agent Systems With Capacity Constraints

In this paper we propose a load balancing problem formulation where agents cooperate with the aim of simultaneously minimizing both the workload disparity among the agents and the overall workload transfer, under network capacity constraints. Notably, in our computational setting, the network is not just a device for the distributed solution of an optimization problem; on the contrary, the problem shares the same sparsity pattern as the network, and this aspect allows to solve it without the need for the agents to store large amount of data. In particular, while the load balancing process occurs over directed links, agents' communication is assumed to be bidirectional. For this optimization setting, first, an optimality condition is derived; then, a provably convergent distributed algorithm to compute the optimal solution is developed, and an upper bound on the convergence rate is characterized. Simulation results are provided to corroborate the validity and performance of our theoretical findings.

Differential Evolution with Group-Based Competitive Control Parameter Setting for Numerical Optimization

Differential evolution (DE) is one of the most popular and widely used optimizers among the community of evolutionary computation. Despite numerous works having been conducted on the improvement of DE performance, there are still some defects, such as premature convergence and stagnation. In order to alleviate them, this paper presents a novel DE variant by designing a new mutation operator (named “DE/current-to-pbest_id/1”) and a new control parameter setting. In the new operator, the fitness value of the individual is adopted to determine the chosen scope of its guider among the population. Meanwhile, a group-based competitive control parameter setting is presented to ensure the various search potentials of the population and the adaptivity of the algorithm. In this setting, the whole population is randomly divided into multiple equivalent groups, the control parameters for each group are independently generated based on its location information, and the worst location information among all groups is competitively updated with the current successful parameters. Moreover, a piecewise population size reduction mechanism is further devised to enhance the exploration and exploitation of the algorithm at the early and later evolution stages, respectively. Differing from the previous DE versions, the proposed method adaptively adjusts the search capability of each individual, simultaneously utilizes multiple pieces of successful parameter information to generate the control parameters, and has different speeds to reduce the population size at different search stages. Then it could achieve the well trade-off of exploration and exploitation. Finally, the performance of the proposed algorithm is measured by comparing with five well-known DE variants and five typical non-DE algorithms on the IEEE CEC 2017 test suite. Numerical results show that the proposed method is a more promising optimizer.

Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

A Bilevel Model for Robust Network Design and Biomass Pricing Under Farmers’ Risk Attitudes and Supply Uncertainty

This paper addresses an integrated biomass pricing and logistics network design problem. A bilevel design and pricing model is proposed to capture the dynamic decision process between a biofuel producer as a Stackelberg leader and farmers as Stackelberg followers. The bilevel optimization model is transformed into a tractable single-level formulation by using optimality constraints. Other unique characteristics of our problem at hand include the incorporation of the harvesting time and frequency decisions in the biomass supply chain network design problem for the first time and consideration of the uncertainty in switchgrass yield in a robust optimization setting to take into account the risk-averse behavior of the farmers (suppliers). To efficiently solve the model, we propose a Benders decomposition algorithm enhanced by surrogate constraints, strengthened Benders cuts, and in-out cut loop stabilization. The numerical experiments show that the proposed algorithm is significantly superior to the branch-and-cut approach of CPLEX in terms of run times and gaps. We conduct a case study with data from Texas to validate the capabilities of our mathematical model and solution approach. Based on extensive experiments, the benefits of modeling are analyzed, and significant insights are explored. Funding: This research was partially supported by the National Natural Science Foundation of China [Grants 71771135, 72171129]; and the scholarship from China Scholarship Council (CSC) [Grant CSC 201906210092]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0357 .

A near-optimum multi-objective optimization approach for structural design

Multi-objective design optimization problems offer a set of solution alternatives within a Pareto-front. In structural design, the design variables are typically the section properties. The outcomes of these design variables are usually used in selecting standard sections. However, the properties of the selected standard sections normally have different values from the determined design variables. Accordingly, the values of the objective functions for these solutions will change after selecting standard sections. This change may be different among these solutions. Thus far, only Pareto-optimal solutions have been standardized in the literature. The effects of the inclusion of non-Pareto solutions in the standardization process have never been examined. In this paper, the differences between including the near-optimal solutions and not including them in the final structural design optimization set are explored. The paper investigates the impact of selecting standard sections on both Pareto-front solutions and near-optimal solutions, and it studies the importance of keeping track of the near-optimal solutions. A modified version of a multiple-objective particle swarm optimization method, enhanced with a proposed computationally efficient section standardization algorithm, is used to solve multi-objective system-reliability design optimization problems. The concepts of the paper are applied to examples of bridge structures. The results demonstrate the efficiency of the proposed technique in capturing final design solutions that would have been otherwise missed due to standardization.

Application of a wavelength angle mapper for variable selection in iterative optimization technology predictions of drug content in pharmaceutical powder mixtures

Process analytical technology (PAT) is an essential tool within pharmaceutical manufacturing to ensure consistent quality and maintain process control. Near-infrared (NIR) spectroscopy is one of the most popular PAT techniques, particularly for monitoring active pharmaceutical ingredient (API) concentrations. To interpret the spectral outputs of NIR spectroscopy, advanced multivariate models are required. Calibration-free models such as iterative optimization technology (IOT) algorithms are increasingly of interest, due primarily to their reduced material and time burdens. Variable/wavelength selection is a common method to improve prediction performance and robustness for IOT by focusing on spectral regions with the most relevant information. However, currently proposed wavelength selection approaches rely on training sets for optimization, therefore reducing or removing the advantages of IOT over empirical calibration-dependent models. In this work, a true calibration-free wavelength selection method is proposed based on measuring the difference between individual wavelengths of a mixture spectra and the net analyte signals via a wavelength angle mapper (WAM). An extension of the WAM utilizing a spectral window of wavelength instead of individual wavelengths, called SWAM, was also developed. However, the SWAM method does require a small training set to optimize wavelength selection parameters. The WAM and SWAM methods showed similar prediction performance for API in pharmaceutical powder blends when compared against other calibration-dependent models and the base IOT algorithm.

A memory footprint optimization framework for Python applications targeting edge devices

The advantages of processing data at the source motivate developers to offload computations at the edges of IoT networks. However, the computational resource constraints of edge computing devices limit the opportunities for deploying applications developed in high-level languages at the edge. In contrast to C/C++, applications developed in Python and other dynamic high-level languages, often require an increased amount of memory size, due to their inherent static memory management approach. Therefore, developers targeting the deployment of applications in dynamic high-level languages at the edge need support by methodologies and tools, which will allow these applications to exploit the limited memory resources efficiently. This work presents a memory optimization framework for applications developed in the Python programming language targeting edge devices. Aiming to avoid the inherent pitfalls of static memory management that Python’s integrated memory manager imposes, the framework targets the reduction of the required memory footprint, by integrating a set of static and dynamic optimizations. The evaluation results, based on a set of representative real-life benchmark suites and applications, show 64% average memory footprint reduction, over the CPython’s minimum baseline of 24 MB. Additionally, we investigate the impact of memory size reduction on execution time and energy consumption. The results show 51% lower execution time and 47.3% reduction in the energy consumed.