Multi-objective Optimization Method Research Articles

Machine learning classification approaches to optimize ROP and TOB using drilling and geomechanical parameters in a carbonate reservoir

Drilling optimization has been broadly developed in terms of influential parameters. The assessment time and the effects of both geomechanical and drilling parameters were vital challenges of investigations. Drilling factors are applied force or rotation of drilling agents such as weight on bit (WOB), and geomechanical features represent mechanical indexes of rocks including unconfined compressive strength (UCS). Optimization efforts have been demonstrated on complex prediction methods whereas the simplicity of classification can offer some optimal ranges utilizing machine learning classifications in an accelerated process. In this study, a novel procedure using the supervised and semi-supervised learning approaches was conducted to classify and optimize the rate of penetration (ROP) and torque on bit (TOB). Firstly, in the case well, user-defined classes were assigned based on geomechanical units (GMU) and the ranges of high ROP and low TOB, thus classes divided drilling factors as GMUs of the case. Secondly, the feature selection was carried out by neural pattern recognition with three multi-objective optimization methods for classification. The inputs of classifications were WOB, hook load, pump pressure, flow rate, UCS, and internal friction angle. Classification approaches were decision trees, support vector machine (SVM), and ensemble learning. Finally, the bagged trees permutation and Laplacian SVM (LapSVM) algorithm separately revealed the significance of parameters and predicted the optimal ROP and TOB regions. Findings showed (1) in supervised classification of the case well, the cubic SVM and bagged trees had the highest area under the curve (AUC) and accuracy, on average 0.97 and 0.96, respectively. (2) The average accuracy of the supervised classifications in a test well was 91% except for the fine SVM, which makes them reliable for the fields with the least information. (3) The permutation outcomes for significant features, flow rate and UCS, exposed influential parameters for ROP and TOB optimization. (4) The semi-supervised method, LapSVM, not only acquired both ROP and TOB labels with an accuracy of 88% but also presented their optimal ranges in 95% of the assessed zones. (5) LapSVM deals with a limited training section perfectly opposed to the supervised version, which is vital for drilling investigation. (6) Implementing machine learning classification approaches with rock properties is a key factor in achieving effective drilling parameters in less time. More importantly, the recommended drilling factors concerning geomechanical properties can ameliorate both drilling performance and perception of upcoming collapse.

A stacking-based ensemble prediction method for multiobjective aerodynamic optimization of high-speed train nose shape

A stacking-based ensemble prediction method is proposed in order to improve the efficiency and accuracy of aerodynamic shape optimization. This can be divided into a two-level model. The first-level model uses various base learners to predict the training dataset and obtain various combinations of predictions. In the second-level model, the meta-learner is trained using various combinations of predictions as inputs and the true response values as outputs. The RMSE and R-Square metrics results show that the performance metrics of the stacked models are significantly better than those of the original surrogate models, except for the stacked RBFNN model. The stacked Kriging model and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0039 and 0.8418 for aerodynamic drag coefficient, respectively. The stacked Kriging model, RBFNN model, and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0024 and 0.76 for aerodynamic lift coefficient, respectively. Four state-of-the-art multiobjective optimization algorithms are used to perform the optimization process. The results of hypervolume and Pareto fronts demonstrate the effectiveness of the selected FDV-NSGAII algorithm. After optimization, the drag and lift coefficients before and after optimization are reduced by 1.9% and 12.7%, respectively.

A multi-objective optimal collaborative gas flow regulation method for non-stationary ventilation network based on improved NSGA-Ⅲ algorithm

After the shockwave of a coal and gas outburst disappears, the influx of a high concentration of gas causes ventilation network disorder. This will further lead to the occurrence of secondary disasters, resulting in serious human and economic losses. This study focuses on solving the cooperative regulation problem of non-stationary ventilation networks (NSVNs) after a disaster. The NSVN solution model is dynamically combined with the ventilation network regulation method to simulate the results of post-disaster cooperative regulation. The Pareto optimal solution for decision variables is obtained with the goals of reducing the affected area, preventing the reversal of branch airflow, and rapidly discharging the high concentration of gas. In this regard, an NSGA-III algorithm based on segmented hybrid coding with conditional distribution sampling is designed to solve the problem of the population crossover operation under the dynamic change of the decision variables. In addition, according to the applicability of the decision variables in the regulation of NSVNs, the sampling distribution function that meets the practical application requirements is selected. Moreover, conditional distribution sampling is carried out for chromosome generation via real number coding, the aim of which is to improve the search efficiency and optimization effect. Via the hierarchical logical relationship between the decision variables, conversion is carried out to generate population individuals of different dimensions to realize the dynamic inputs of the NSVN solution model and calculate the corresponding target values. Finally, the feasibility of the proposed model and solution method is verified by studying and analyzing the case of an airflow disaster in a coal mine in Jiulishan, China. This study provides theoretical support for the cooperative regulation of NSVNs, as well as guidance for the post-disaster emergency rescue work in possible coal and gas herniation accidents.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

A prediction method for dynamic multiobjective optimization based on joint subspace and correlation alignment

Dynamic multiobjective optimization is a significant challenge in accurately capturing changes in Pareto optimal sets (PS), encompassing both location and manifold changes. Existing approaches primarily focus on tracking changes in the location of the PS, often overlooking the potential impact of changes in the PS manifold, which can be decomposed into rotation and distortion changes. Such oversights can lead to a reduction in the overall performance of an algorithm. To address this issue, a prediction method based on joint subspace and correlation alignment (PSCA) is proposed. PSCA leverages a subspace alignment strategy to effectively capture rotation change in the PS manifold while employing a correlation alignment strategy to capture distortion change. By integrating these two strategies, a quasi-initial population is generated that embodies the captured rotation and distortion change patterns in a new environment. Then, the promising individuals are selected from this quasi-initial population based on their nondominated relations and crowding degree to form the initial population in the new environment. To evaluate the effectiveness of PSCA, we conduct experiments on fourteen benchmark problems. The experimental results demonstrate that PSCA achieves significant improvements over several state-of-the-art algorithms.

Optimization and experimental study of stationary endwall of stator labyrinth cavity in a low-speed research compressor

Controlling the leakage flow of the labyrinth seal cavity is very important for the efficiency and aerodynamic matching design of aero-engine high-pressure compressor. However, due to the complexity of the geometry and internal flow of the labyrinth seal cavity, the design optimization of the labyrinth seal cavity is rarely studied. In this paper, a multi-objective design optimization method was used to optimize the stationary endwall of the shrouded stator labyrinth cavity, and the optimal endwall shape was obtained. Based on the optimal geometry, the 3D printing and aerodynamic testing of experimental parts were carried out, and the aerodynamic performance and flow field details of the optimal geometry were analyzed by unsteady numerical simulation. The experimental results show that for the optimal geometry, it has a little effect on the total pressure ratio, but the efficiency at the design point is increased by 1.4 %. The numerical results show that the optimal cavity shape reduces low-energy fluid, thus reduces the total pressure loss of S3. At the near stall point, the optimal S3 still has a better performance, which means that the optimal shape is not limited to the design point. From the result, an engineering design criterion can be concluded. It is suggested that the labyrinth seal cavity should be designed to match the velocity components of the leakage flow with the mainstream of the stator properly to make the leakage flow go evenly in the blade passage instead of gathering to the suction side.

Multi-objective structural optimization and degradation model of magnesium alloy ureteral stent

BackgroundMg alloys have attractive properties, including biocompatibility, biodegradability, and ideal mechanical properties. Moreover, Mg alloys are regarded as one of the promising candidates for manufacturing ureteral stents. This study proposed a multi-objective optimization method based on the Kriging surrogate model, NSGA-Ⅲ, and finite element analysis to improve the degradation performance of Mg alloy ureteral stents. MethodsThe finite element model for the degradation of Mg alloy ureteral stents has been established to compare the degradation performance of the stents under different parameters. Latin hypercube sampling was adopted to generate train sample points in the design space. Meanwhile, the Kriging surrogate model was constructed between strut parameters and stent degradation behavior. The NSGA-Ⅲ was utilized to determine the optimal solution in the global design space. ResultsThe optimized stent achieved 5.52 ​× ​degradation uniformity (M), 10 ​× ​degradation time (DT), and 4 ​× ​work time (FT). The errors between the Kriging surrogate model and the finite element calculation results were less than 6%. ConclusionThe optimized stent achieved better degradation performance. The degradation behavior of stents was dependent on the design parameters. The multi-objective optimization method based on the Kriging surrogate model and finite element analysis was effective in stent design optimization problems.

A self-adaptive joint optimization framework for marine hybrid energy storage system design considering load fluctuation characteristics

Recently, with the development of new energy technologies, all-electric ships (AESs) with hybrid energy storage system (HESS) are becoming a promising solution to reduce fuel consumption and emissions. However, the high maneuverability of ships during the actual navigation places higher performance requirements on the HESS, which presents a nonlinear and multi-objective challenge for the HESS design. Therefore, it is necessary to consider the coupling between HESS sizing and energy management strategy (EMS). In this paper, a self-adaptive joint optimization framework (SJOF) for marine HESS design considering load fluctuation characteristics is proposed, which can find the optimal decision solution with excellent system economic and battery life performance for AES HESS design. Based on the rain flow counting (RFC) method, a multi-objective joint optimization method considering life cycle cost (LCC) and battery degradation index (BDI) is introduced into SJOF. Besides, a novel EMS including the self-adaptive segmentation mechanism (SSM) and power allocation is proposed, which can achieve the most efficient energy scheduling.

Compressive response and optimization design of a novel hierarchical re-entrant origami honeycomb metastructure

Metastructures have drawn extensive attention from researchers due to their excellent mechanical properties. In this paper, to further enhance the mechanical properties of the re-entrant origami honeycomb metastructure, the bio-inspired hierarchical design is introduced on the re-entrant origami honeycomb metastructure, a novel hierarchical re-entrant origami honeycomb (HROH) metastructure is proposed. The crashworthiness of the novel HROH is researched under low-velocity and high-velocity impact. The results indicate a significant improvement in the energy absorption capacity of the novel HROH compared to both the conventional hierarchical re-entrant honeycomb and the re-entrant origami honeycomb. The plateau stress of the novel HROH under different compression velocities are derived by the two-scale method. And the theoretical results are in good agreement with the numerical results. Moreover, the influences of the dihedral angles and wall thickness on impact resistance also are studied. To increase the wall thickness will improve the plateau stress and SEA–strain curve of the HROH, while increasing the dihedral angles will diminish the plateau stress and SEA–strain curve. In addition, to obtain the optimal structure of the HROH, a multi-objective optimization method based on surrogate models and the non-dominated sorting genetic algorithm II (NSGA-II) is employed. The results exhibit high accuracy in the crashworthiness optimization. This study provides a crucial reference for the design and application of buffer protection structure in fields such as automotive, aerospace and defense.

Multi-objective optimization and integrated indicator-driven two-stage project recommendation in time-dependent software ecosystem

Context:Time-dependent software ecosystem is a complex system, where there are many projects and developers. Recommending projects to developers in a time-dependent software ecosystem can improve their quality and development speeds. However, the time-dependence of projects and developers results in an increased difficulty of project recommendation. Objective:To better recommend projects to developers in a time-dependent software ecosystem, we propose a method of multi-objective optimization and integrated indicator-driven two-stage project recommendation, which is fulfilled according to the change of developer communities and their projects. Method:According to the change of developer communities and their projects, a method of multi-objective optimization and integrated indicator-driven two-stage project recommendation is fulfilled. In the first stage, a constrained multi-objective optimization model for project recommendation to developer communities is established, and an improved NSGA-II algorithm is adopted to solve this model, with the purpose of obtaining the recommended projects to a developer community. For the second stage, an integrated indicator for project recommendation to developers is built to determine the developers of a project. Results:The proposed method is applied to project recommendation for nine time-dependent software ecosystems in GitHub, and compared with six state-of-the-art ones. The experimental results show that our method has significant advantages in recommendation accuracy and efficiency. Conclusion:According to the experimental results, we conclude that the proposed method can timely and accurately recommend projects to developers in a time-dependent software ecosystem, which reduces the difficulty of solving the problem of project recommendation.

Data-Driven Multi-Objective Optimization Approach to Loaded Meshing Transmission Performances for Aerospace Spiral Bevel Gears.

Loaded meshing transmission performance optimization has been an increasingly significant target for the design and manufacturing of aerospace spiral bevel gears with low noise and high strength. An innovative data-driven multi-objective optimization (MOO) method is proposed for the loaded meshing transmission performances of aerospace spiral bevel gears. Data-driven tooth surface modeling is first used to obtain a curvature analysis of loaded contact points. An innovative numerical loaded tooth contact analysis (NLTCA) is applied to develop the data-driven relationships of machine tool settings with respect to loaded meshing transmission performance evaluations. Moreover, the MOO function is solved by using an achievement function approach to accurate machine tool settings output, satisfying the prescribed requirements. Finally, numerical examples are given to verify the proposed methodology. The presented approach can serve as a powerful tool to optimize the loaded meshing transmission performances with higher computational accuracy and efficiency than the conventional methods.

An efficient framework for controllable micromixer design through the fusion of data-driven modeling and machine learning insights: Numerical and experimental analysis

Micromixers are inevitable components in microfluidics, micro-electro-mechanical devices, and numerous bio-chemical assays. By assays, we mean diverse analytical procedures encompassing gene engineering, the manipulation of genetic material; nanoparticle synthesis, focusing on the controlled creation of nanoparticles; and cell lysis, involving cell membranes disruption for the release of intracellular substances for diagnostic purposes. In these assays, the homogeneous mixture of two or more fluids is crucial. However, designing an efficient micromixer providing high homogeneity and low pressure drop, while maintaining controllability, is challenging. Controllability refers to the design of a micro-system tailored to meet the specific requirements of a given assay. This study proposes a controllable framework, combining machine learning and statistical modeling. The framework begins with the generation of a reference parametric micro-structure, herein a microchannel with L-shaped baffles and featuring seven variables. A response surface method, a data-driven modeling scheme, is used to establish functional relationships between design variables and objective functions. The study reveals that the baffle height significantly impacts the system functionality, increasing the mixing index by over 40% and the pressure drop by more than 220% when reaching its upper limit. Dean-like secondary vortexes are generated in the microchannel at Re = 10, demonstrating the efficiency of the implemented baffles. Subsequently, multi-objective optimization methods, non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE), are employed, with adaptable variable constraints. Comparative analysis of the methods shows that DE finds superior optimum solutions in fewer iterations. Finally, an optimum structure is fabricated using soft lithography, and experimental tests are conducted for validation.

Multi-Objective Topology Optimization Method for Hybrid-Type Motors Combining Combinatorial Optimization and Local Search

Multi-Objective Topology Optimization Method for Hybrid-Type Motors Combining Combinatorial Optimization and Local Search

Geometrical projection improved multi-objective particle swarm optimization for unsupervised nonlinear hyperspectral unmixing

ABSTRACT In recent years, a series of bilinear mixture models (BMMs) have been well studied, based on which nonlinear unmixing algorithms for hyperspectral images have been proposed. However, the performance of unsupervised nonlinear spectral unmixing can be largely affected by the collinearity and the nonconvex unmixing problem’s inherent complexity. To solve the problems, this paper proposes a geometrical projection improved multi-objective particle swarm optimization (GPMOPSO) method for nonlinear unmixing, which consists of two dynamically updating procedures. First, under the assumption of the BMMs, observed pixels are geometrically projected to their approximate linear mixture components to alleviate the collinearity. Second, the linear mixture components are efficiently decomposed to refined endmembers and abundances in an improved linear unmixing framework using multi-objective particle swarm optimization. Two advanced multi-objective optimization strategies are adopted to balance the influence of an endmember distance constraint and an abundance sparsity constraint on the achieved unsupervised linear unmixing process, respectively. Then, accurate unmixing variables can be fed back to the geometrical projection procedure to produce more reliable linear mixture components which facilitate the execution of the former in turn. Experimental results of both simulated data and real hyperspectral remote sensing data verify the superior nonlinear unmixing performance of the proposed method.

Multi-objective optimization integrating weighted average surrogate model and NSGA-II intelligent algorithm applied to a self-excited oscillation mixer used in mixed flow descaling

This study proposes a multi-objective optimization method based on a hybrid of computational fluid dynamics (CFD) and experimental techniques, which integrates a weighted average surrogate model and the NSGA-II intelligent algorithm. To validate the feasibility of this method, structural optimization for the self-excited oscillation mixer (SEOM) was conducted. The optimization objectives aimed to reduce potential abrasives accumulation in the mixed-flow cavity and minimize erosion on the elbow of the slurry outlet caused by mixed slurry, thereby enhancing the service life and rust removal efficiency of the mixed flow rotary jet descaling (MFD). A comparison between the optimized model and original model revealed a 2.51% increase in negative pressure within the cavity of the optimized model, as well as a 10.36% decrease in velocity at the outlet of mixed slurry based on simulation results. Experimental methods measured both mass flow rate of inhaled abrasive particles and impact force of mixed slurry outlet. The experimental results demonstrated that compared to its original counterpart, the optimized model exhibited superior performance with a 22.81% increase in abrasive particle flow rate and an 11.34% reduction in mixed slurry impact force indirectly, verifying better simulation effectiveness for SEOM with optimized structure. This approach also enhanced efficiency and surface quality of MFD processing strip steel, providing guidance for structural optimization of similar SEOMs used in mixed flow descaling.

Exploring the Explainable Aspects and Performance of a Learnable Evolutionary Multiobjective Optimization Method

Multiobjective optimization problems have multiple conflicting objective functions to be optimized simultaneously. The solutions to these problems are known as Pareto optimal solutions, which are mathematically incomparable. Thus, a decision maker must be employed to provide preferences to find the most preferred solution. However, decision makers often lack support in providing preferences and insights in exploring the solutions available. We explore the combination of learnable evolutionary models with interactive indicator-based evolutionary multiobjective optimization to create a learnable evolutionary multiobjective optimization method. Furthermore, we leverage interpretable machine learning to provide decision makers with potential insights about the problem being solved in the form of rule-based explanations. In fact, we show that a learnable evolutionary multiobjective optimization method can offer advantages in the search for solutions to a multiobjective optimization problem. We also provide an open source software framework for other researchers to implement and explore our ideas in their own works. Our work is a step toward establishing a new paradigm in the field on multiobjective optimization: explainable and learnable multiobjective optimization . We take the first steps toward this new research direction and provide other researchers and practitioners with necessary tools and ideas to further contribute to this field.

A machine learning proxy based multi-objective optimization method for low-carbon hydrogen production

With industrial informatization, rich data frameworks provide the possibility of efficient design and global optimization of methane to hydrogen processes. However, the high coupling between mixed variables leads to the difficulty of first-principles modeling (FPM) to capture the optimal Pareto front in infeasible domains. In this paper, a machine learning proxy (MLP) method is proposed to minimize economic, exergy destruction, CO2 emissions, and maximize hydrogen production. First, process simulation as FPM is built using physical properties, energy balance, and reaction kinetics to analyze single variable effects and objective trade-offs. Then, datasets consisting of feed, heat transfer, and design variables are built by sampling the FPM in design and extended spaces. The eXtreme Gradient Boosting (XGBoost) with hyperparameter optimization is built as a proxy FPM, capturing the complex mapping between variables and objectives. Finally, the Pareto front is searched in design and extended spaces by combining the proxy model and genetic algorithm. The proposed method benefits 20.2%, 37.2%, 46.7%, and 2.3% in economic, exergy destruction, CO2 emissions and hydrogen production respectively compared to the heuristic design. XGBoost not only can effectively proxy FPM to capture the complex behavior of reforming techniques, but also can perform better in infeasible domains that are difficult to explore with FPM.

Bilevel optimization with a multi-objective lower-level problem: risk-neutral and risk-averse formulations

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective optimization. To solve bilevel problems with a multi-objective lower level, different approaches can be considered depending on the interpretation of the lower-level optimality. An optimistic formulation that was previously introduced for the deterministic case consists of minimizing the upper-level function over all non-dominated lower-level solutions. In this paper, we develop new risk-neutral and risk-averse formulations, address their main computational challenges, and develop the corresponding deterministic and stochastic gradient-based algorithms.

Intelligent multi-objective optimization of 3D printing low-carbon concrete for multi-scenario requirements

This study presents, for the first time, a universal theoretical framework based on machine learning (ML) algorithms for the multi-objective optimization (MOO) design of 3D printing low-carbon concrete to meet the sustainability requirements of the construction industry. The study focuses on the simultaneous reduction of carbon emissions and costs during the design process. Specifically, the applicable scenarios are primarily classified into two categories: meet aesthetics requirements (printing layer height error-HE and printing layer width error-WE approaching 0) and strengths requirements (compressive strength-CS approaching 60 MPa and interlayer bonding strength-IBS as high as possible). Through a comparison with the traditional design method, 3D printing concrete based on the intelligent design method achieves a 44% reduction in costs and a 19% reduction in carbon emissions while meeting aesthetics requirements. Under strengths requirements, there is a 57% reduction in costs and a 22% reduction in carbon emissions. This demonstrates the indispensable and crucial role of the MOO method employed in this study in achieving the lowest costs and carbon emissions. Additionally, the results of experimental verification demonstrate that the models developed in this study have successfully achieved a close alignment between design values and experimental values within the allowable error range (The errors are 3.46%–9.83%). This not only holds the potential to drive the widespread application of 3D printing technology in the construction industry but also presents new possibilities for cleaner production, contributing to the achievement of sustainable development goals.

Surrogate model-based optimization of methanol synthesis process for multiple objectives: A pathway towards achieving sustainable development goals

This work combines a generalized regression neural network (GRNN) with a non-dominated sorting genetic algorithm (NSGA-II) to optimize a methanol synthesis plant for multiple objectives. The proposed method begins by developing and validating the model for the methanol synthesis involving the recycling of unreacted gas stream into the methanol reactor feed. The data generated using this model is used to develop a GRNN-based surrogate model to expedite the evaluation of fitness values for the optimization algorithm. The objective functions considered for simultaneous optimization are minimizing the total energy cost per unit of energy input (TEC), maximizing overall resource utilization (R), and minimizing CO2-gram equivalent emissions per unit of energy input (EPEI). Pareto optimal solutions are obtained for three bi-and one tri-objective optimization case studies using the GRNN-assisted multi-objective optimization (GRNNAMOO) method. The developed GRNNAMOO approach reduces the computational time from multiple days to a few seconds for all case study scenarios. For the tri-objective optimization case, the operating point selected using multi-criteria decision-making achieves 84.37% of R, 10.45 $/GJ of TEC, and an EPEI value of 81.34 gCO2eq/MJ. These results represent 7.05% higher R, 0.34 $/GJ lower TEC, and 0.82 gCO2eq/MJ lower EPEI than the Aspen plus simulation results. Further, the carbon footprint values obtained are significantly lower than 110 gCO2eq/MJ reported for modern methanol plants for nearly the same R and TEC values. The proposed approach aligns with the United Nations' sustainability development goals by lowering energy costs and promoting sustainable energy through improved environmental sustainability in methanol production plants.