Multi-objective Optimization Issue Research Articles

Hypervolume-Based Cooperative Coevolution With Two Reference Points for Multiobjective Optimization

An important issue in hypervolume-based evolutionary multi-objective optimization (EMO) algorithms is the specification of a reference point for hypervolume calculation. However, its appropriate specification has not been carefully studied in the literature. Some recent studies have pointed out the importance and difficulty of the reference point specification. Its appropriate specification depends on problem characteristics such as the Pareto front shape and the number of objectives. In this paper, the difficulty of the reference point specification in hypervolume-based EMO algorithms is circumvented by using two reference points. Instead of using only a single reference point, we propose a new hypervolume-based EMO algorithm that can effectively utilize two reference points cooperatively. Experimental results show that the proposed algorithm has good and robust performance on a wide range of test problems. In comparison to hypervolume-based EMO algorithms with only a single reference point, the proposed algorithm can find a wider and more uniformly distributed solution set. On a recently proposed real-world problem suite, the proposed algorithm shows competitive performance in comparison to state-of-the-art algorithms.

Metaheuristic algorithms and their applications in wireless sensor networks: review, open issues, and challenges

AbstractMetaheuristic algorithms have wide applicability, particularly in wireless sensor networks (WSNs), due to their superior skill in solving and optimizing many issues in different domains. However, WSNs suffer from several issues, such as deployment, localization, sink node placement, energy efficiency, and clustering. Unfortunately, these issues negatively affect the already limited energy of the WSNs; therefore, the need to employ metaheuristic algorithms is inevitable to alleviate the harm imposed by these issues on the lifespan and performance of the network. Some associated issues regarding WSNs are modelled as single and multi-objective optimization issues. Single-objective issues have one optimal solution, and the other has multiple desirable solutions that compete, the so-called non-dominated solutions. Several optimization strategies based on metaheuristic algorithms are available to address various types of optimization concerns relating to WSN deployment, localization, sink node placement, energy efficiency, and clustering. This review reports and discusses the literature research on single and multi-objective metaheuristics and their evaluation criteria, WSN architectures and definitions, and applications of metaheuristics in WSN deployment, localization, sink node placement, energy efficiency, and clustering. It also proposes definitions for these terms and reports on some ongoing difficulties linked to these topics. Furthermore, this review outlines the open issues, challenge paths, and future trends that can be applied to metaheuristic algorithms (single and multi-objective) and WSN difficulties, as well as the significant efforts that are necessary to improve WSN efficiency.

Multi-Objective Optimization of a Two-Stage Helical Gearbox with Second Stage Double Gear-Sets Using TOPSIS Method

The multi-criteria decision-making (MCDM) method was applied in a novel way in this study to the multi-objective optimization problem (MOOP) of designing a two-stage helical gearbox with double gear-sets in the second stage. Finding the best fundamental components to increase gearbox efficiency and decrease gearbox cross-section area was the aim of this study. Three main design factors were chosen for investigation in this work: the first stage gear ratio and the first and second stage coefficients of wheel face width (CWFW). Phase 1 solves the single-objective optimization problem to reduce the gap between variable levels, and phase 2 solves the MOOP to determine the optimal critical design factors. This additionally splits the MOOP into two phases. Additionally, the TOPSIS method was used as an MCDM approach to address the multi-objective optimization issue, and the entropy approach was used to compute the weight criteria. In this study, gearbox efficiency is calculated by considering power losses during idle motion. The multi-objective optimization of a helical gearbox with second stage double gear-sets is addressed using the TOPSIS technique for the first time.

Multi-Objective Optimization of a Two-Stage Helical Gearbox Using MARCOS Method

In order to address the Multi-Objective Optimization Problem (MOOP) in building a two-stage helical gearbox, this work presents a novel application of the Multi-Criterion Decision-Making (MCDM) method. The aim of the study is to determine the optimal primary design factors that will increase gearbox efficiency while decreasing gearbox volume. Three main design parameters were chosen for assessment in this work: the first stage’s gear ratio, and the first and second stages’ Coefficients of Wheel Face Width (CWFW). In addition, the MOOP is divided into two phases: phase 1 solves the single-objective optimization problem to reduce the gap between variable levels, and phase 2 solves the MOOP to determine the optimal primary design factors. Furthermore, the Entropy approach was picked to compute the weight criteria, and the MARCOS method was chosen as an MCDM method to handle the multi-objective optimization issue. The following are important characteristics of the study: Firstly, the MCDM method (MARCOS technique) was successfully applied to solve a MOOP for the first time. Secondly, this work has looked into power losses during idle motion to calculate the efficiency of a two-stage helical gearbox. The results of the study were used in the design of a two-stage helical gearbox in order to identify the optimal values for three important design parameters.

Application of a Multi-Criterion Decision-Making Method for Solving the Multi-Objective Optimization of a Two-Stage Helical Gearbox

This paper provides a novel application of a multi-criterion decision-making (MCDM) method to the multi-objective optimization problem of designing a two-stage helical gearbox. This study’s goal is to identify the ideal primary design elements that increase gearbox efficiency while reducing the gearbox cross-section area. In this work, three primary design parameters were selected for investigation: the gear ratio of the first stage and the coefficients of wheel face width (CWFW) of the first and second stages. The multi-objective optimization problem was further split into two phases: phase 1 solved the single-objective optimization problem of minimizing the gap between the variable levels, and phase 2 solved the multi-objective optimization issue of identifying the ideal key design factors. Moreover, the multi-objective optimization problem was handled by the SAW method as an MCDM approach, and the weight criteria were computed using the entropy approach. This study’s significant characteristics are as follows: First, a multi-objective optimization problem was successfully solved using the MCDM approach (SAW technique) for the first time. Second, the power losses in idle motion were investigated in this work in order to determine the efficiency of a two-stage helical gearbox. From this study’s findings, the ideal values for three major design parameters can be determined for the design of a two-stage helical gearbox.

Multi-Objective Optimization in 3D Floorplanning

Three-dimensional integrated circuits can significantly mitigate the challenges posed by shrinking feature sizes and enable heterogeneous integration. This paper focuses on the 3D floorplanning problem. We formulate it as a multi-objective optimization issue and employ multi-objective simulated annealing to simultaneously optimize area, wirelength and number of vias. During the optimization process, neighboring solutions are explored in the design space through inter-layer or intra-layer perturbations, and decision criteria for the exploration process are formulated based on the dominance relationship of solutions. Test results on the GSRC benchmark demonstrate that our approach delivers superior performance in optimizing area and wirelength. Compared to 2D floorplanning, our method reduces the area by approximately 49% and the wirelength by 21%. Compared to other similar 3D floorplanning methods, we raise the success rate in satisfying the fixed-outline constraint to 100% and improve the wirelength by 3%. The multi-objective simulated annealing method proposed in this paper can effectively address the 3D floorplanning problem.

Multi-Objective Inspection Optimization of Periodically Inspected Multi-Failure Mode System

This paper examines the multi-objective availability and cost optimization of a periodically inspected system. A system with [Formula: see text] independent failure modes is specifically considered. The principal characteristic of the proposed model is that the inspection and maintenance time is nonnegligible and corrective maintenance results in as good as a new unit. This paper focuses on evaluating the general expressions for limiting availability and long-run average cost of the system undergoing periodic inspections. The multi-objective optimization issue is solved by first generating the Pareto-optimal solutions using particle swarm optimization and then selecting the best compromise solution using a fuzzy method. A numerical illustration is also presented to highlight the applicability of the proposed work.

Multi-objective optimization of a sequentially inspected system prone to revealing and non-revealing failures via particle swarm optimization and a fuzzy method

ABSTRACT Maintenance models rely heavily on the failure characteristics and inspection or maintenance actions. This paper introduced a sequentially inspected system whose failure alternated between revealing and non-revealing failures. The distinctive characteristic of the proposed model is that inspections are imperfect, inspection and maintenance time are non-negligible, and corrective maintenance is perfect. The proposed study contributed on the multi-objective availability and cost optimization issue of the aforementioned system, which was lacking in the prior studies. This paper focused on evaluating the general expressions for limiting availability and long-run average cost of the sequentially inspected system and addressed the multi-objective optimization issue using particle swarm optimization to generate the Pareto optimal solutions followed by a fuzzy method to select the best compromise solution. Moreover, reasonable results were achieved using a numerical case study and the findings of the existing studies were found to be the special case of this model.

Task Offloading Strategy for Unmanned Aerial Vehicle Power Inspection Based on Deep Reinforcement Learning.

With the ongoing advancement of electric power Internet of Things (IoT), traditional power inspection methods face challenges such as low efficiency and high risk. Unmanned aerial vehicles (UAVs) have emerged as a more efficient solution for inspecting power facilities due to their high maneuverability, excellent line-of-sight communication capabilities, and strong adaptability. However, UAVs typically grapple with limited computational power and energy resources, which constrain their effectiveness in handling computationally intensive and latency-sensitive inspection tasks. In response to this issue, we propose a UAV task offloading strategy based on deep reinforcement learning (DRL), which is designed for power inspection scenarios consisting of mobile edge computing (MEC) servers and multiple UAVs. Firstly, we propose an innovative UAV-Edge server collaborative computing architecture to fully exploit the mobility of UAVs and the high-performance computing capabilities of MEC servers. Secondly, we established a computational model concerning energy consumption and task processing latency in the UAV power inspection system, enhancing our understanding of the trade-offs involved in UAV offloading strategies. Finally, we formalize the task offloading problem as a multi-objective optimization issue and simultaneously model it as a Markov Decision Process (MDP). Subsequently, we proposed a task offloading algorithm based on a Deep Deterministic Policy Gradient (OTDDPG) to obtain the optimal task offloading strategy for UAVs. The simulation results demonstrated that this approach outperforms baseline methods with significant improvements in task processing latency and energy consumption.

Multi-objective optimization operation of multiple water sources under inflow-water demand forecast dual uncertainties

Uncertainties in inflow and water demand forecasts bring risks to water resources management. Therefore, the research on multi-objective optimization operation of multiple water sources under uncertainties holds critical research significance and application value. This paper proposes a model for the multi-objective optimization operation of multiple water sources that can consider the inflow and water demand forecast dual uncertainties. In handling uncertainties, this paper adopts a scenario generation method based on joint distribution-Monte Carlo (JDMC), which allows for a quantitative consideration of the correlation between uncertainties. Moreover, the variable weight method and LINGO 20.0 are employed for solving multi-objective optimization issues to obtain stable Pareto frontiers. The proposed model is applied to the water receiving area inside Jiangsu Province of the South-to-North Water Transfer East Route Project (SNWTERP) in China. The main findings are as follows: 1) The impact of the inflow and water demand forecast uncertainties on the operation results is synergistic rather than antagonistic. Considering only a single uncertainty may result in water receiving area facing more severe water shortages or purchasing spot water at high prices. 2) There is a strong spatial correlation between uncertainties. If we ignore or only qualitatively consider the correlation between uncertainties, the impact of uncertainties on operation results will be underestimated or overestimated. 3) The Pareto frontiers are convex functions, indicating that decision-makers should choose a solution in the middle part.

Multi-objective shuffled frog leaping algorithm for deployment of sensors in target based wireless sensor networks

In this research, –coverage –connected problem is viewed as multi-objective problem and shuffling frog leaps algorithm is proposed to address multi-objective optimization issues. The shuffled frog leaping set of rules is a metaheuristic algorithm that mimics the behavior of frogs. Shuffled frog leaping algorithms are widely used to seek global optimal solutions by executing the guided heuristic on the given solution space. The basis for the success of this SFL algorithm is the ability to exchange information among a group of individuals which phenomenally explores the search space. SFL improves the overall lifespan of the network, the cost of connection among the sensors, to enhance the equality of coverage among the sensors and targets, reduced sensor count for increased coverage, etc. When it comes to coverage connectivity issues, each target has to be covered using k sensors to avoid the loss of data and m sensors connected enhance the lifespan of the network. When the targets are covered by k sensors then the loss of data will be reduced to an extended manner. When the sensors are connected with m other sensors then the connectivity among the sensors will not go missing and hence the lifespan of the network will be improved significantly. Therefore, the sensor node number in coverage indicates the total number of sensor nodes utilised to cover a target, and the number of sensor nodes in connected reflects the total number of sensor nodes that provide redundancy for a single failed sensor node. Connectivity between sensor nodes is crucial to the network’s longevity. The entire network backbone acts strategically when all the sensors are connected with one or the other to pertain to the connectivity of the network. Coverage is yet another key issue regarding the loss of data. The proposed algorithm solves the connectivity of sensors and coverage of targets problems without weighted sum approach. The proposed algorithm is evaluated and tested under different scenarios to show the significance of the proposed algorithm.

Modeling techno-economic multi-objectives of smart homes considering energy optimization and demand management

The research suggests an approach that prioritizes customer needs and aims to reduce energy expenses while safeguarding customer privacy. Furthermore, it is recommended that smart homes incorporate a home energy management system to optimize appliance energy consumption. Conversely, the introduction of demand-side management addresses the energy management challenges faced by smart households. The main goal of this approach is to decrease energy usage and electricity costs for customers. Moreover, it enhances user satisfaction while waiting at common intervals. The primary emphasis of this study is on a smart residence furnished with energy management technology and smart home gadgets capable of supplying electricity to the grid. These objectives are considered distinct aspects in the multi-objective optimization issue stemming from this approach. The study utilizes the grasshopper optimization algorithm (GOA) to optimize battery and home appliance scheduling in smart homes with flexible devices. The goal is to reduce the overall cost of microgrid systems through demand-side management implementation. This comparison highlights the superiority of the proposed method in optimizing energy consumption and reducing carbon emissions in a variety of scenarios. By achieving lower energy costs and carbon emissions while maintaining a comfortable indoor environment, the proposed method proves to be a highly effective and sustainable solution for energy management in buildings. These simulation results provide strong evidence of the method’s potential to significantly impact energy efficiency and environmental sustainability in real-world applications. Furthermore, the consistent minimization of the discomfort index showcases the method’s ability to prioritize occupant comfort while still achieving significant energy savings and emissions reductions. Overall, the comparison with other algorithms solidifies the effectiveness and practicality of the proposed method in addressing the complex challenges of energy management and sustainability in smart homes.

An Efficient Optimization Approach for Designing Machine Models Based on Combined Algorithm

Many intrusion detection algorithms that use optimization have been developed and are commonly used to detect intrusions. The process of selecting features and the parameters of the classifier are essential parts of how well an intrusion detection system works. This paper provides a detailed explanation and discussion of an improved intrusion detection method for multiclass classification. The proposed solution uses a combination of the modified teaching–learning-based optimization (MTLBO) algorithm, the modified JAYA (MJAYA) algorithm, and a support vector machine (SVM). MTLBO is used with supervised machine learning (ML) to select subsets of features. Selection of the fewest features possible without impairing the accuracy of the results in feature subset selection (FSS) is a multiobjective optimization issue. This paper presents MTLBO as a mechanism and investigates its algorithm-specific, parameter-free idea. This study used the modified JAYA (MJAYA) algorithm to optimize the C and gamma parameters of the support vector machine (SVM) classifier. When the proposed MTLBO-MJAYA-SVM algorithm was compared with the original TLBO and JAYA algorithms on a well-known intrusion detection dataset, it was found to outperform them significantly.

Adaptive hierarchical optimization control for electrohydraulic suspension with resistor-capacitor operator

The controller design for integrated electrohydraulic suspension with leaf spring is a complicated and challenging task, aiming to achieve optimal dynamic performance for heavy vehicles. Considering the hysteresis property of leaf spring, parameter uncertainties and nonlinearity, a novel hierarchical optimization control strategy including upper and bottom controllers is proposed to effectively suppress the vertical vibration of vehicle body. To describe the hysteresis property of leaf spring, a novel resistor-capacitor operator hysteresis model is identified by experiment and optimized by genetic algorithm. Based on hysteresis model, the filter adaptive backstepping control with sprung mass uncertainty is designed as upper controller to generate the desired active force for electrohydraulic actuator. Then, the projection adaptive fuzzy sliding mode control is designed as bottom controller for nonlinear actuator with time-varying fluid parameter to accurately track the required target force. Additionally, a stratified sampling algorithm is investigated to optimize the parameters of hierarchical control strategy for addressing multi-objective optimization issue of electrohydraulic suspension with leaf spring. Finally, the results show that the proposed method has better robustness and effectiveness, and it can ensure ride comfort, safety and optimal performance.

Analysis of Manufacturing Companies by Weight Sum Method

In this from analysis EDAS method is the most ideal solution Short-distance and negative-best The solution with the longest distance from the solution Determines, but the comparison of these distances Does not consider importance. From the result it is seen that Market turmoil ranks first, with management support having the lowest ranking. This article addresses the issue of customer complexity, Customer center, innovation, service diversity and Explores the relationship between business performance and. The study of 332 manufacturing companies provides the basis for empirical inquiry. There are two broad types of financing research dealing with the use of rates Read Corporate Structure. Increased market complexity and impending Competitiveness is their position in the freight-service continuum by expanding the business power to expand Is a traditional service to manufacturing-manufacturing companies. World-class quality of life, production plays a key role in improving companies. However, linearity in the system they are combined with standard Production and consumption patterns. This is a measure of performance and Store site status report is not financial. This research science includes macroeconomics; Financial risk management, audit scenarios, equity returns, investment decisions, financial results and Good Corporate Management There are 147 models of manufacturing companies listed on the Indonesian Stock Exchange. Sustained performance in organizational research is one of the primary ideas. Its importance and effectiveness of the many advances that have appeared over the years are, despite criticisms, a difficult concept to apply in a scientifically rigorous manner. Multi-Objective Optimization Issues Mostly big dominance Lead to unpaid packages, Because of the size of the problem or the number of goals to create a complete non-dominant set Requires significant calculation time Related at the same time Most of the solutions are unsuitable for the decision maker (DM) Shows that Manufacturing Companies Alternative: Perceived benefits, technical resources, management support, computer perspective, market turmoil, peer pressure. Evaluation Preference: Technology, Organization, Environment. From the result it is seen that Market turbulence and is got the first rank whereas is the Management support got is having the lowest rank

Analysis of Manufacturing Companies by Weight Sum Method

In this from analysis EDAS method is the most ideal solution Short-distance and negative-best The solution with the longest distance from the solution Determines, but the comparison of these distances Does not consider importance. From the result it is seen that Market turmoil ranks first, with management support having the lowest ranking. This article addresses the issue of customer complexity, Customer center, innovation, service diversity and Explores the relationship between business performance and. The study of 332 manufacturing companies provides the basis for empirical inquiry. There are two broad types of financing research dealing with the use of rates Read Corporate Structure. Increased market complexity and impending Competitiveness is their position in the freight-service continuum by expanding the business power to expand Is a traditional service to manufacturing-manufacturing companies. World-class quality of life, production plays a key role in improving companies. However, linearity in the system they are combined with standard Production and consumption patterns. This is a measure of performance and Store site status report is not financial. This research science includes macroeconomics; Financial risk management, audit scenarios, equity returns, investment decisions, financial results and Good Corporate Management There are 147 models of manufacturing companies listed on the Indonesian Stock Exchange. Sustained performance in organizational research is one of the primary ideas. Its importance and effectiveness of the many advances that have appeared over the years are, despite criticisms, a difficult concept to apply in a scientifically rigorous manner. Multi-Objective Optimization Issues Mostly big dominance Lead to unpaid packages, Because of the size of the problem or the number of goals to create a complete non-dominant set Requires significant calculation time Related at the same time Most of the solutions are unsuitable for the decision maker (DM) Shows that Manufacturing Companies Alternative: Perceived benefits, technical resources, management support, computer perspective, market turmoil, peer pressure. Evaluation Preference: Technology, Organization, Environment. From the result it is seen that Market turbulence and is got the first rank whereas is the Management support got is having the lowest rank.

Cost Optimal Production-Scheduling Model Based on VNS-NSGA-II Hybrid Algorithm—Study on Tissue Paper Mill

With the development of the customization concept, small-batch and multi-variety production will become one of the major production modes, especially for fast-moving consumer goods. However, this production mode has two issues: high production cost and the long manufacturing period. To address these issues, this study proposes a multi-objective optimization model for the flexible flow-shop to optimize the production scheduling, which would maximize the production efficiency by minimizing the production cost and makespan. The model is designed based on hybrid algorithms, which combine a fast non-dominated genetic algorithm (NSGA-II) and a variable neighborhood search algorithm (VNS). In this model, NSGA-II is the major algorithm to calculate the optimal solutions. VNS is to improve the quality of the solution obtained by NSGA-II. The model is verified by an example of a real-world typical FFS, a tissue papermaking mill. The results show that the scheduling model can reduce production costs by 4.2% and makespan by 6.8% compared with manual scheduling. The hybrid VNS-NSGA-II model also shows better performance than NSGA-II, both in production cost and makespan. Hybrid algorithms are a good solution for multi-objective optimization issues in flexible flow-shop production scheduling.

An efficient multi-objective gorilla troops optimizer for minimizing energy consumption of large-scale wireless sensor networks

The multi-objective gorilla troops optimizer (MOGTO) is a new version of the gorilla troops optimizer (GTO) proposed in this paper to address multi-objective optimization issues. The Pareto optimum solutions acquired by the GTO are saved in an external archive. In the multi-objective search region, the archive was used to mimic the gorilla groups’ collective behavior. The suggested approach is evaluated statistically and qualitatively in solving various multi-objective issues using the congress on evolutionary computation (CEC) 2020 test bed. In large-scale wireless sensor networks, the proposed algorithm is also utilized to discover the minimal number of sink nodes with the lowest localization error, which will cap the whole network and increase the network lifespan. Meanwhile, the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm version 2 (NSGA-II), multi-objective grey wolf optimizer (MOGWO), multi-objective whale optimization algorithm (MOWOA), multi-objective sine–cosine algorithm (MOSCA), multi-objective slime mould algorithm (MOSMA), multi-objective particle swarm optimization with ring topology and special crowding distance (MO_Ring_PSO_SCD), hybrid NSGAII-MOPSO, multi-objective evolutionary algorithm based on decomposition (MOEA/D), and improved multi-objective manta ray foraging optimization (IMOMRFO) are the ten familiar and strong optimization models, which are compared with the proposed algorithm. Simulation results in CEC’2020 test functions indicated that the proposed MOGTO can provide remarkable results than other optimization models in terms of Pareto set proximity (PSP), inverted generational distance in decision space (IGDX), and hyper volume (HV) indicators. Additionally, simulation results in large-scale wireless sensor networks show that the proposed algorithm can discover the smallest number of sink nodes and diminish the network’s energy usage.

Multi-Objective chimp Optimizer: An innovative algorithm for Multi-Objective problems

The Multi-Objective Chimp Optimization Algorithm (MOChOA), a multi-objective variation of the recently proposed ChOA, is developed in this research to address multi-objective optimization issues in various engineering problems. The optimization community has recently been offered numerous evolutionary and meta-heuristic optimization strategies for tackling optimization challenges. When analyzing multi-objective optimization (MOO) problems, these approaches frequently produce poor solutions because they do not accurately estimate the Pareto optimal solutions or increase the distribution across all objectives. The significant and impressive performance of the ChOA has been a great inspiration for this paper to study on its multi-objective version called MOChOA. In this approach, a memory structure has been exploited as an archive to store the non-dominated solutions alongside a leader selection strategy and grid mechanism. The leader selection procedure consists of analyzing the archive contents to choose the best candidates for the leader of independent groups, which are drivers, barriers, chasers, and attackers. The strategy also guarantees the exploration of search space. Twelve test problems with various shapes and different dimensions have opted to evaluate MOChOA. The results of coverage, generational distance, averaged Hausdorff distance, spacing, diversity, and other metrics are considered in the performance evaluation of the algorithm. According to results, MOChOA can provide competitive results and outperform well-known intelligent algorithms such as ANSGAIII, ARMOEA, dMOPSO, EFRRR, IBEA, SPEA2SDE, SPEAR, and tDEA. Alongside the remarkable performance of the proposed algorithm, its light-weight structure causes a fast execution. The proposed MOChOA can be applied in various multi-objective optimization application, including engineering, science, chemical processes, economics and logistics when appropriate decisions must be made in the face of competing objectives.

Optimization of sustainable milling of SKD11 steel under minimum quantity lubrication

In this study, the sustainably face milling of SKD11 steel under a minimum quantity lubrication condition was investigated. The goal of this work is twofold: (i) observing the impact of main milling parameters, including cutting speed ( Vc), depth of cut ( ap), and feed per tooth ( fz) on surface roughness ( Ra) and specific cutting energy (SCE), and (ii) finding out an optimal combination of cutting parameters for ameliorating the surface quality, productivity, and diminishing energy consumption. For this purpose, the experiment was designed by using the Box–Behnken matrix. A series of 15 experimental runs have been conducted to acquire experimental data. The regression models of Ra and SCE were subsequently developed and evaluated by using the analysis of variance. Finally, the multi-objective optimization issue was resolved by using the technique for order of preference by similarity to ideal solution (TOPSIS) algorithm and the desirability approach (DA). The results show that the parameter fz reveals the highest impact on surface roughness and SCE, followed by ap and Vc. The TOPSIS method allows finding the optimal solution with a reduction of 46% in terms of SCE when compared with that achieved by DA. This is significant in the context of sustainable manufacturing. This research is expected to enrich the knowledge of milling SKD11, and the achieved results can be used for research community and manufacturing industries.