Multi-objective Evolutionary Algorithm Based On Decomposition Research Articles

Correction: Bu et al. A Decomposition-Based Multi-Objective Evolutionary Algorithm for Solving Low-Carbon Scheduling of Ship Segment Painting. Coatings 2024, 14, 368

In the original publication [...]

Research on the Short-Term Economic Dispatch Method of Power System Involving a Hydropower-Photovoltaic-Pumped Storage Plant

The auxiliary regulation capacity of pumped-storage power stations can be utilized as an effective method to regulate the output of a hydro-photovoltaic complementary system, further mitigating the power fluctuations of the system and enhancing the photovoltaic absorption. This study aims to minimize power fluctuations and maximize the economic benefits of electricity generation in a hydropower-photovoltaic-pumped-storage complementary system (HPPCS), which are treated as the objective functions. It explores the participation of the HPPCS in grid active power balance auxiliary services. By modulating the participation ratio of the HPPCS in the grid’s active balance service, the system output is aligned to fluctuate proportionally with the daily load curve trend. Consequently, a short-term economic dispatch model for the integrated HPPCS is developed. The case study focuses on the considerable impact of weather conditions on photovoltaic (PV) power generation. In this model, the outputs of cascading hydro-power stations and pumped-storage power stations are considered as the decision variables. A decomposition-based multi-objective evolutionary algorithm is applied to derive an optimized intra-day dispatch Pareto solution set for the cascading HPPCS in each of these scenarios. Additionally, this study compares the Pareto solution sets for the HPPCS in various extents of its participation in grid auxiliary services. The results of the case study suggest that the system is capable of timely adjustments during the peak and trough periods of load demand. Considering the economic benefits, it enables the pumped-storage station to generate electricity for the grid during periods of high electricity prices and to store energy by pumping water when prices are low.

A Decomposition-Based Multi-Objective Evolutionary Algorithm for Solving Low-Carbon Scheduling of Ship Segment Painting

Ship painting, as one of the three pillars of the shipping industry, runs through the whole process of ship construction. However, there are low scheduling efficiency and excessive carbon emissions in the segmental painting process, and optimizing the scheduling method is an important means to achieve the sustainable development of the ship manufacturing industry. To this end, firstly, a low-carbon scheduling mathematical model for the segmented painting workshop is proposed, aiming to reduce carbon emissions and improve the painting efficiency of the segmented painting workshop. Second, an artificial bee colony algorithm designed based on a decomposition strategy (MD/ABC) is proposed to solve the model. In the first stage, five neighborhood switching methods are designed to achieve the global search employed for each solution. In the second stage, the Technique of Ordering the Ideal Solutions (TOPSIS) improves the competition mechanism through the co-evolution between neighboring subproblems and designs the angle to define the relationship between neighboring subproblems to enhance the localized search and improve population quality. The solution exchange strategy is used in the third stage to improve the efficiency of the algorithm. In addition, a two-stage coding method is designed according to the characteristics of the scheduling problem. Finally, the algorithm before and after the improvement and with other algorithms is analyzed using comparative numerical experiments. The experimental results show the effectiveness of the algorithm in solving the low-carbon scheduling problem of ship segmental painting and can provide reliable guidance for the scheduling program of segmented painting workshops in shipyards.

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Decomposition with adaptive composite norm for evolutionary multi-objective combinatorial optimization

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective problem into a series of single-objective subproblems for collaborative optimization. The weighted sum (WS) method and the Tchebycheff (TCH) method are the two most popular scalarization methods. They have pros and cons in solving multi-objective combinatorial optimization problems (MOCOPs) the WS method allows MOEA/D to converge faster than the TCH method; the WS-based MOEA/D cannot obtain unsupported non-dominated vectors, while the TCH-based one can overcome this shortcoming. This inspired us to use the WS method to drive the population towards the Pareto front and then switch to the TCH method to maintain a more diverse population. To better balance convergence and diversity, we propose a new scalarization strategy called adaptive composite norm (ACN). The ACN strategy can combine the WS and the TCH with dynamic weighting. The experiments consider 16 instances including 4 MOCOPs and run on the PlatEMO. Results reveal that MOEA/D-ACN can rank first and significantly outperform the other evolutionary multi-objective combinatorial optimization algorithms on almost all instances.

Multi-objective cooperative optimization of reservoir scheduling and water resources allocation for inter-basin water transfer project based on multi-stage coupling model

The efficient coupling of a water allocation model with a reservoir operation model is key to maximizing the benefits of inter-basin water transfer (IBWT) projects. Most existing studies of IBWT operations and management do not account for matching water transfer and demand, and instead seek to optimize either the water allocation model or the reservoir scheduling model. In this paper, we propose a multi-stage joint optimization framework for reservoir scheduling and water allocation models that considers the key operation indicators of the project in the water source area and the multi-dimensional objectives in the receiving area. We derived a functional relationship that balances considerations regarding water, the economy, and ecology (WEE) in the receiving area and applied it to the water allocation model. The reservoir operation model was developed by considering the multiple benefits of water transfer and power generation in the water resource area. To reduce the complexity of the model and the tightness of its coupling, the model was divided into multiple stages of optimization and solved using the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) algorithm. The results showed the allocation schemes of water resources influenced the competition between the economic and ecological benefits. Using the WEE model, a more reasonable water transfer and allocation method can be selected according to different development needs. As such, the water shortage rate of each user in the receiving area is kept below 8%, and there is significant improvement in all indicators compared with the conventional scheme. In addition, this model enables the reservoir group to achieve a power generation capacity of more than 5.64 kWh with the goal of meeting the water transfer demand, maintaining the reservoir empty rate at about 10%, and reducing the risk of water shortages. Our study can serve as a reference for effectively addressing the challenges associated with IBWT projects, and it can inform socioeconomic development in receiving areas while optimizing water transmission and allocation.

Design and analysis of solar hybrid combined cooling, heating and power system: A bi-level optimization model

The planning and operation optimization of hybrid combined cooling, heating and power (CCHP) systems is the prerequisite and foundation for its advantages such as economy, energy saving, and high efficiency. This study constructed a bi-level optimization model of a hybrid CCHP system. Firstly, an upper-level capacity planning model of the hybrid CCHP system is constructed considering system economy, energy, and environmental performance. Secondly, a lower-level operation optimization model is proposed, considering the operation and maintenance cost of the system. Thirdly, a multi-objective honey badger algorithm (MOHBA) is developed based on the characteristics of the studied problem and the features of the bi-level optimization model. Finally, the optimization results indicate that the hybrid CCHP can save 32.79 % of the total cost, 49.74 % of primary energy, and 60.18 % of carbon emissions compared to the separation production (SP) system. In addition, compared with improving the strength Pareto evolutionary algorithm (SPEA2), non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective evolutionary algorithm based on decomposition (MOEAD), and multi-objective particle swarm optimization (MOPSO), the proposed MOHBA can provide superior optimization results. The proposed bi-level planning model achieves improved economic, energy, and environmental performance of the hybrid CCHP system compared to the single-level planning model for the given operation modes.

Optimal power flow research of AC–DC hybrid grid with multiple energy routers

AC/DC hybrid grids are the future development trends of grids, and energy routers (ERs) can play key roles in controlling power flow, realizing the regulation of electric energy and improving power quality in the grids. At present, there have been many studies on the structure and control strategy of ERs, but only a few studies are on the power flow distribution and optimization of AC/DC hybrid grids with ERs. To enhance the efficacy of ERs in system-wide regulation and operational optimization, a multi-objective optimal power flow model is formulated for AC–DC hybrid systems with multiple ERs. In order to make ERs play a better role in overall regulation and operation optimization, the multi-objective optimal power flow model of AC–DC hybrid system with multi-ERS is established based on Newton–Raphson method (NR) and alternating iteration method with power consumption and voltage deviation as optimization objectives. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to optimize the model, and a smoother Pareto solution set is obtained compared with multi-objective particle swarm optimization (MOPSO). Then, fuzzy membership method is used to make compromise decision on the Pareto solution set to obtain the optimal compromise solution. Simulation and analysis on an enhanced IEEE 69 bus system verifies the validity of the model. In addition, the results obtained from the compromise solution are compared with the optimization results of MOPF obtained by MOPSO and that of single-objective power flow (SOPF) obtained by Particle Swarm Algorithm (PSO) in the same system. It is proved that the optimization model established can achieve the optimization objectives of reducing voltage deviation and power loss simultaneously to improve the overall performance of the system and optimize the operation state of the system.

Hybrid Flow Shop Scheduling Problem with Energy Utilization using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III) Optimization

Hybrid flow shop scheduling (HFS) is an on sought problem modelling for production manufacturing. Due to its impact on productivity, researchers from different backgrounds have been attracted to solve its optimum solution. The HFS is a complex dilemma and provides ample solutions, thus inviting researchers to propose niche optimization methods for the problem. Recently, researchers have moved on to multi-objective solutions. In real-world situations, HFS is known for multi-objective problems, and consequently, the need for optimum solutions in multi-objective HFS is a necessity. Regarding sustainability topic, energy utilization is mainly considered as one of the objectives, including the common makespan criteria. This paper presents the existing multi-objective approach for solving energy utilization and makespan problems in HFS scheduling using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), and a comparison to other optimization models was subjected for analysis. The model was compared with the most sought algorithm and latest multi-objective algorithms, Strength Pareto Evolutionary Algorithm 2 (SPEA -II), Multi-Objective Algorithm Particle Swarm Optimization (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The research interest starts with problem modelling, followed by a computational experiment with an existing multi-objective approach conducted using twelve HFS benchmark problems. Then, a case study problem is presented to assess all models. The numerical results showed that the NSGA-III obtained 50% best overall for distribution performance metrics and 42% best in convergence performance metrics for HFS benchmark problems. In addition, the case study results show that NSGA-III obtained the best overall convergence and distribution performance metrics. The results show that NSGA-III can search for the best fitness solution without compromising makespan and total energy utilization. In the future, these multi-objective algorithms’ potential can be further investigated for hybrid flow shop scheduling problems.

A solution potential-based adaptation reference vector evolutionary algorithm for many-objective optimization

Decomposition-based multiobjective evolutionary algorithms are widely utilized for solving multiobjective optimization problems (MOPs). These algorithms have a higher degree of diversity due to a uniform distribution of the reference vectors in the objective space. However, these algorithms may struggle to select a suitable candidate set for solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). To solve this problem, a solution potential-based adaptation reference vector evolutionary algorithm (SPARVEA) is proposed in this paper. In the algorithm, a concept called solution potential is presented to assess whether the direction of convergence of the solution to the ideal solution has potential. The solution potential is obtained with an evaluation function to calculate the potentials of the corresponding solutions. A solution potential-based adaptation strategy is then designed for adapting the reference vector to better guide the direction of convergence of the solution when solving MaOPs with irregular PFs. A modified angle penalty distance (mAPD) is adjusted to improve the convergence rate of the solution set in many-objective optimization problems. The proposed algorithm SPARVEA is compared with state-of-the-art many-objective evolutionary algorithms on four test sets with irregular PFs and four practical problems. Experimental results demonstrate the superior performance of SPARVEA on many-objective optimization problems. This contribution helps to advance the development of efficient algorithms for solving many-objective optimization problems.

Traffic-Aware Optimization of Task Offloading and Content Caching in the Internet of Vehicles

Emerging in-vehicle applications seek to improve travel experiences, but the rising number of vehicles results in more computational tasks and redundant content requests, leading to resource waste. Efficient compute offloading and content caching strategies are crucial for the Internet of Vehicles (IoV) to optimize performance in time latency and energy consumption. This paper proposes a joint task offloading and content caching optimization method based on forecasting traffic streams, called TOCC. First, temporal and spatial correlations are extracted from the preprocessed dataset using the Forecasting Open Source Tool (FOST) and integrated to predict the traffic stream to obtain the number of tasks in the region at the next moment. To obtain a suitable joint optimization strategy for task offloading and content caching, the multi-objective problem of minimizing delay and energy consumption is decomposed into multiple single-objective problems using an improved Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) via the Tchebycheff weight aggregation method, and a set of Pareto-optimal solutions is obtained. Finally, the experimental results verify the effectiveness of the TOCC strategy. Compared with other methods, its latency is up to 29% higher and its energy consumption is up to 83% higher.

Interaction-Based Prediction for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization poses great challenges to evolutionary algorithms due to the change of optimal solutions or Pareto front with time. Learning-based methods are popular to extract the changing pattern of optimal solutions for predicting new solutions. They tend to use all variables as features (i.e., inputs) to build prediction models. However, there are usually some irrelevant and redundant variables, which increase training difficulty and decrease prediction accuracy. This paper proposes a new interaction-based prediction method, which captures the correlation of variables with prediction targets and selects the most relevant variables to build prediction models using neural networks. In particular, the interaction between variables is detected to remove redundant variables. In addition, a correction procedure is developed to further improve predicted solutions according to the prediction error in past environments. The predicted solutions are used to update the population according to a specifically designed update strategy. Integrating the interaction-based prediction (IP) method into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D), a new algorithm named IP-DMOEA is put forward. Experimental results on a typical dynamic multiobjective test suite demonstrate the better performance of the proposed IPDMOEA than state-of-the-art algorithms in terms of convergence speed and solution quality. The proposed IP-DMOEA is also successfully applied to the multirobot task scheduling problem.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

A localized decomposition evolutionary algorithm for imbalanced multi-objective optimization

Multi-objective evolutionary algorithms based on decomposition (MOEA/Ds) convert a multi-objective optimization problem (MOP) into a set of scalar subproblems, which are then optimized in a collaborative manner. However, when tackling imbalanced MOPs, the performance of most MOEA/Ds will evidently deteriorate, as a few solutions will replace most of the others in the evolutionary process, resulting in a significant loss of diversity. To address this issue, this paper suggests a localized decomposition evolutionary algorithm (LDEA) for imbalanced MOPs. A localized decomposition method is proposed to assign a local region for each subproblem, where the inside solutions are associated and the solution update is restricted inside (i.e., solutions are only replaced by offspring within the same local region). Once off-spring are generated within an originally empty region, the best one is reserved for this subproblem to extend diversity. Meanwhile, the subproblem with the largest number of associated solutions will be found and one of its associated solutions with the worst aggregated value will be removed. Moreover, to speed up convergence for each subproblem while balancing the population's diversity, LDEA only evolves the best-associated solution in each subproblem and correspondingly tailors two decomposition methods in the environmental selection. When compared to nine competitive MOEAs, LDEA has shown the advantages in tackling two benchmark sets of imbalanced MOPs, one benchmark set of balanced yet complicated MOPs, and one real-world MOP.

Pareto and decomposition based approaches for the multi-objective home health care routing and scheduling problem with lunch breaks

Home health care (HHC) is a fast-growing area of research that has received increasing attention in recent years due to the rise in life expectancy and the fall in birth rates. It is expected to reduce length of stay in hospital as well as to allow patients to receive care and assistance in their home. Several models and algorithms have been proposed to manage the various constraints and criteria. However, multi-objectives HHC routing and scheduling problems (HHCRSP) with practical and complicated constraints as well as Pareto dominance based approaches are still scarce in the literature. In this paper, we focus on modeling and solving the multi-objectives HHCRSP with lunch breaks, multiple time windows, duty length, skill requirement and a mix of soft and hard services. A mixed integer linear programming (MILP) model with three objectives is proposed, which aims to minimize tardiness of soft services and caregivers’ waiting times and also to balance their workload. Two approaches, Pareto and decomposition based, with multi-objective evolutionary algorithms are proposed to solve the multi-objective HHCRSP. We developed a memetic algorithm (NSGA-LS), resulting from the hybridization of non-dominated sorting genetic algorithm II (NSGA-II) with multidirectional local search (MDLS), to trade-off between exploration and exploitation. Computational results and performance measures inferred that NSGA-LS has a better performance compared to other algorithms. According to the hyper-volume indicator, NSGA-LS obtained 93.75% better solutions for the tested instances in a pairwise comparison between algorithms while multiobjective evolutionary algorithm based on decomposition (MOEA/D) has a better complexity. Sensitivity analysis of the percentage of soft/flexible services and the maximum allowed tardiness showed that increasing them significantly improved the quality and trade-off of solutions.

An efficient multi-objective optimization framework for thin-walled tubular deployable composite boom

As a crucial structural component in space applications such as solar sails and solar arrays, the thin-walled tubular deployable composite booms (DCBs) demonstrate extensive utilization by employing stored elastic strain energy to achieve folding and deploying functions. This paper introduces a multi-objective optimization framework that integrates an analytical model with a genetic algorithm. By utilizing a multi-objective evolutionary algorithm based on de-composition (MOEA/D), the optimization objectives of minimizing folding moment and maximizing bending stiffness are pursued. Multiple constraints associated with failure avoidance, laminate stacking sequence design principles, and the folding moment range of actuator in the folding mechanism are considered in the optimization. The multi-objective optimization design of the tubular DCBs is performed to obtain the optimal combinations of cross-sectional radius, central angle, and ply scheme. Experimental validation confirms the efficacy of the optimization results. Additionally, an in-depth analysis on the influence of genetic algorithm types, hyperparameters, and different design variables on the optimization outcomes is thoroughly discussed. The findings of this study offer significantly insights for the practical engineering applications of tubular DCBs.

A multi-stage ensemble model for power load forecasting based on decomposition, error factors, and multi-objective optimization algorithm

Short-term power load forecasting plays an important role in ensuring the stable operation of power systems and improving economic benefits. However, most of the previous studies ignored the limitations of a single prediction model and the useful information in the error factors, resulting in low prediction accuracy. Therefore, this paper proposes a multi-stage integrated model based on decomposition, error factors, and a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The proposed model consists of three stages: in the first stage, the gated recurrent unit (GRU) is used to predict the components of complete ensemble empirical modal decomposition with adaptive noise, and new data sets are obtained by combining them with the original data sets to fully mine the data characteristics. In the second stage, the MOEA/D based on angle and distance selection strategy and adaptive population generation strategy is used to optimize GRU network parameters with accuracy and diversity as the objective functions, obtaining several load forecasting models and error forecasting models that consider accuracy and diversity. In the third stage, a new nonlinear integration method based on GRU optimized by MOEA/D is used to integrate load forecasting values and error forecasting values, considering error factors to further improve forecasting accuracy. Experimental results on the Australian wholesale electricity market and energy market datasets show that the proposed model outperforms the comparative model in terms of accuracy and generalization and can be widely applied in load forecasting.

Decomposition-based multiobjective evolutionary algorithm with density estimation-based dynamical neighborhood strategy

Decomposition-based multiobjective evolutionary algorithm with density estimation-based dynamical neighborhood strategy

A stable-state multi-objective evolutionary algorithm based on decomposition

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) has been shown to effectively solve real-world multi-objective optimization problems (MOPs). The uniformly distributed weight vectors guide the population to continuously evolve towards the Pareto front (PF). However, the random matching mode between individuals and weight vectors leads to some excellent individuals being replaced in the evolution process. Meanwhile, the number of replaced individuals in the neighborhood is not controlled. This causes a waste of computing resources and fails to balance the diversity and convergence of the population effectively. Referring to the influence on body adjustment of homeostasis in the medical field, the stable-state mechanism is proposed to keep the dynamic balance between exploration and exploitation. Therefore, this paper presents the stable-state multi-objective evolutionary algorithm based on decomposition (MOEA/D-SS) that adopts a new stable-state replacement strategy to adjust the number of replaced individuals within each neighborhood. Furthermore, a stable-state neighborhoods adjustment strategy was proposed to adjust the size of each neighborhood. This mechanism can adjust the convergence and diversity of newly generated individuals at different stages. Finally, several benchmark test suites (i.e., ZDT, DTLZ, and UF) and a practical optimization problem are used to test the performance of MOEA/D-SS. The experimental results demonstrate that the proposed algorithm outperforms other comparative algorithms.

A New Hyper-Heuristic Multi-Objective Optimisation Approach Based on MOEA/D Framework.

A multi-objective evolutionary algorithm based on decomposition (MOEA/D) serves as a robust framework for addressing multi-objective optimization problems (MOPs). However, it is widely recognized that the applicability of a fixed offspring-generating strategy in MOEA/D can be limited, despite its foundation in the MOEA/D methodology. Consequently, hybrid algorithms have gained popularity in recent years. This study proposes a novel hyper-heuristic approach that integrates the estimation of distribution (ED) and crossover (CX) strategies into the MOEA/D framework based on the view of successful replacement rate (SSR) and attempts to explain the potential reasons for the advantages of hybrid algorithms. The proposed approach dynamically switches from the differential evolution (DE) operator to the covariance matrix adaptation evolution strategy (CMA-ES) operator. Simultaneously, certain subproblems in the neighbourhood denoted as B(i) employ the Improved Differential Evolution (IDE) operator to generate new individuals for balancing the high evaluation costs associated with CMA-ES. Numerical experiments unequivocally demonstrate that the suggested approach offers distinct advantages when applied to a three-objective test suite. These experiments also validate a significant enhancement in the efficiency (SRR) of the DE operator within this context. The perspectives and experimental findings, with a focus on the Success Rate Ratio (SRR), have the potential to provide valuable insights and inspire further research in related domains.