Many-objective Evolutionary Algorithms Research Articles

A decomposition-based many-objective evolutionary algorithm with Q-learning guide weight vectors update

When dealing with regular, simple Pareto fronts (PFs), the decomposition-based multi-objective optimization algorithm (MOEA/D) performs well by presetting a set of uniformly distributed weight vectors. However, its performance declines when faced with complex and irregular PFs. Many algorithms address this problem by periodically adjusting the distribution of the weight vectors, but these methods do not take into account the performance of the population and are likely to update the weight vectors at the wrong time. In addition, for the SBX crossover operator, the setting of its distribution index will largely affect the exploration and convergence ability of the algorithm, so a single parameter setting will have negative impacts. To tackle these challenges, this paper proposes a method to simultaneously adaptively update weight vectors and optimize SBX parameter via Q-learning(RL-MaOEA/D). In order to make the strategies made by Q-learning more accurate, Two different metrics (CD and NCD) are proposed that capture diversity and convergence of individual and population respectively. RL-MaOEA/D is compared with seven state-of-the-art algorithms on different problems, and the simulation results reflect that the proposed algorithm has better performance.

An adaptive interval many-objective evolutionary algorithm with information entropy dominance

Interval many-objective optimization problems (IMaOPs) involve more than three conflicting objectives with interval parameters. Various real-world applications under uncertainty can be modeled as IMaOPs to solve, so effectively handling IMaOPs is crucial for solving practical problems. This paper proposes an adaptive interval many-objective evolutionary algorithm with information entropy dominance (IMEA-IED) to tackle IMaOPs. Firstly, an interval dominance method based on information entropy is proposed to adaptively compare intervals. This method constructs convergence entropy and uncertainty entropy related to interval features and innovatively introduces the idea of using global information to regulate the direction of local interval comparison. Corresponding interval confidence levels are designed for different directions. Additionally, a novel niche strategy is designed through interval population partitioning. This strategy introduces a crowding distance increment for improved subpopulation comparison and employs an updated reference vector method to adjust the search regions for empty subpopulations. The IMEA-IED is compared with seven interval optimization algorithms on 60 interval test problems and a practical application. Empirical results affirm the superior performance of our proposed algorithm in tackling IMaOPs.

A joint vehicular device scheduling and uncertain resource management scheme for Federated Learning in Internet of Vehicles

Federated learning (FL) offers an effective framework for the efficient process in vehicular edge computing. However, FL encompasses the process of distributing and uploading model parameters, which are inevitably transmitted in a wireless network environment. Some challenges in FL-assisted Internet of Vehicles (IoV) sceneries gradually emerging, such as data heterogeneity, concerned device resources, and unstable communication environment, which necessitate intelligent vehicle selection schemes that accelerate training efficiency. Based on these, we consider a new scenario, specifically an FL-assisted IoV system under uncertain communication conditions, and develop an interval many-objective vehicle selection and bandwidth allocation (IMoVSBA) joint optimization scheme. This scheme takes into account computation latency, energy consumption, server utilization, and data quality, while meeting multi-criteria resource optimization requirements. Among these, server utilization is a new objective designed specifically for this joint optimization problem. For the proposed problem, a novel interval many-objective evolutionary algorithm with individual comprehensive indicator to control the evolution direction (IMaOEACI) is designed. Simulation results demonstrate that this method outperforms other schemes in terms of accuracy, training cost, and server utilization, effectively improving training efficiency in wireless channel environments and reasonably utilizing bandwidth resources. It provides significant scientific value and application potential in the field of the IoVs.

An enhanced diversity indicator-based many-objective evolutionary algorithm with shape-conforming convergence metric

As the number of objectives increases, many-objective optimization problems (MaOPs) become increasingly complex. Traditional indicator-based many-objective evolutionary algorithms can often ensure the convergence of the population but tend to struggle with maintaining its diversity. In this paper, an enhanced diversity indicator-based many-objective evolutionary algorithm with shape-conforming convergence metric, namely, MaOEA-DISC, is presented to relieve this weakness. In MaOEA-DISC, firstly, we focus on the inter-individual spacing relationships within the population based on Iϵ+ Indicator, proposing a novel enhanced diversity Iϵ+ Indicator to ensure the enhancement of population diversity while converging. Secondly, we propose a new metric of individual convergence, which calculates the convergence of individuals based on the shape of Pareto front, reducing the errors caused by the shape of the Pareto front when measuring individual convergence, thereby assessing individual convergence more accurately. Finally, to further improve the convergence speed of the population, different mating strategies are employed for mating in the parental generation. MaOEA-DISC is compared with other algorithms on various benchmark MaOPs ranging from 3 to 10 objectives, as well as a real-world MaOPs. Experimental results demonstrate that when dealing with MaOPs, MaOEA-DISC not only achieves excellent population convergence and diversity but also effectively maintains a balance between them, showing promising practical value.

Diagnostic benchmarking of many-objective evolutionary algorithms for real-world problems

Despite progress in multiobjective evolutionary algorithms (MOEAs) research, their efficacy in real-world scenarios remains unclear. This article introduces a diagnostic benchmarking framework to evaluate MOEAs, comprising (1) flexible MOEA construction software, (2) performance evaluation metrics and (3) real-world applications for benchmarking, reflecting diverse mathematical challenges. Utilizing this framework, NSGA-II, NSGA-III, RVEA, MOEA/D and Borg MOEA were evaluated across four applications with three to ten objectives. Collectively, the four applications capture challenges such as stochastic objectives, severe constraints, nonlinearity and complex Pareto frontiers. The study demonstrates how MOEAs that have shown strong performance on standard test problems can struggle on real-world applications. The benchmarking framework and results have value for enhancing the design and use of MOEAs in real-world applications. Further, the results highlight the need to improve the adaptability and ease-of-use of MOEAs given the often ill-defined nature of real-world problem-solving.

A many-objective evolutionary algorithm based on three states for solving many-objective optimization problem

In recent years, researchers have taken the many-objective optimization algorithm, which can optimize 5, 8, 10, 15, 20 objective functions simultaneously, as a new research topic. However, the current research on many-objective optimization technology also encounters some challenges. For example: Pareto resistance phenomenon, difficult diversity maintenance. Based on the above problems, this paper proposes a many-objective evolutionary algorithm based on three states (MOEA/TS). Firstly, a feature extraction operator is proposed. It can extract the features of the high-quality solution set, and then assist the evolution of the current individual. Secondly, based on Pareto front layer, the concept of “individual importance degree” is proposed. The importance degree of an individual can reflect the importance of the individual in the same Pareto front layer, so as to further distinguish the advantages and disadvantages of different individuals in the same front layer. Then, a repulsion field method is proposed. The diversity of the population in the objective space is maintained by the repulsion field, so that the population can be evenly distributed on the real Pareto front. Finally, a new concurrent algorithm framework is designed. In the algorithm framework, the algorithm is divided into three states, and each state focuses on a specific task. The population can switch freely among these three states according to its own evolution. The MOEA/TS algorithm is compared with 7 advanced many-objective optimization algorithms. The experimental results show that the MOEA/TS algorithm is more competitive in many-objective optimization problems.

Many-objective evolutionary algorithm with multi-strategy selection mechanism and adaptive reproduction operation

Many-objective evolutionary algorithm with multi-strategy selection mechanism and adaptive reproduction operation

A many-objective evolutionary algorithm based on interaction force and hybrid optimization mechanism

In many-objective optimization, both convergence and diversity are equally important. However, in high-dimensional spaces, traditional decomposition-based many-objective evolutionary algorithms struggle to ensure population diversity. Conversely, traditional Pareto dominance-based many-objective evolutionary algorithms face challenges in ensuring population convergence. In this paper, we propose a novel many-objective evolutionary algorithm based on interaction force and hybrid optimization mechanism (MaOEAIH) for effectively addressing the difficulty in balancing convergence and diversity. First, we use the concept of interaction force to simulate the convergence (akin to gravity) and diversity (repulsion) of the population. Subsequently, we design an optimization mechanism that combines decomposition and Pareto dominance to enhance the convergence and diversity of the population separately. Simultaneously, to eliminate dominance resistance solutions, we propose a quartile method based on boundary solutions. Additionally, Random perturbations are also introduced to certain individuals within the population to facilitate their escape from local optima. MaOEAIH is compared with some state-of-the-art algorithms on 31 well-known test problems with 3-15 objectives. The experimental results show that, compared to other algorithms, MaOEAIH not only obtains solution sets of higher quality when dealing with different types of many-objective optimization problems, but also effectively addresses key challenges including insufficient selection pressure, difficulty balancing convergence and diversity, and susceptibility to population entrapment in local optima within many-objective optimization scenarios.

A dual-population Constrained Many-Objective Evolutionary Algorithm based on reference point and angle easing strategy.

Constrained many-objective optimization problems (CMaOPs) have gradually emerged in various areas and are significant for this field. These problems often involve intricate Pareto frontiers (PFs) that are both refined and uneven, thereby making their resolution difficult and challenging. Traditional algorithms tend to over prioritize convergence, leading to premature convergence of the decision variables, which greatly reduces the possibility of finding the constrained Pareto frontiers (CPFs). This results in poor overall performance. To tackle this challenge, our solution involves a novel dual-population constrained many-objective evolutionary algorithm based on reference point and angle easing strategy (dCMaOEA-RAE). It relies on a relaxed selection strategy utilizing reference points and angles to facilitate cooperation between dual populations by retaining solutions that may currently perform poorly but contribute positively to the overall optimization process. We are able to guide the population to move to the optimal feasible solution region in a timely manner in order to obtain a series of superior solutions can be obtained. Our proposed algorithm's competitiveness across all three evaluation indicators was demonstrated through experimental results conducted on 77 test problems. Comparisons with ten other cutting-edge algorithms further validated its efficacy.

Cooperative interference to achieve interval many-objective evolutionary algorithm for association privacy secure computing migration

In this paper, we study secure computing migration scenarios in uncertain environments with the presence of multiple malicious eavesdroppers (MEs). Specifically, when edge servers (ESs) execute tasks delivered by smart devices (SDs), SDs may move beyond the coverage of ESs, and computing migration (CM) of unfinished tasks is required to ensure service continuity. There is a risk of privacy leakage during task migration, and MEs use colluding eavesdropping to eavesdrop on the migrated tasks, and we consider eavesdropping on the associated tasks through data sharing among MEs to improve the eavesdropping efficiency. For eavesdropping in MEs, we achieve eavesdropping strikes using cooperative interference by jammers, which benefit by providing jamming services. In addition, uncertain computational scenarios directly affect the efficiency of task execution, and we consider the uncertainty factor in the malicious eavesdropping environment. To this end, this paper proposes the secure computational migration of associative privacy in uncertain environments (SCMAPUE) model, which transforms uncertainties into interval parameters, and optimizes the five objectives of migration delay, maximum completion time, energy consumption, load balancing and migration reliability to achieve efficient task execution and reliable migration. Aiming at the model characteristics, this paper designs an interval many-objective evolutionary algorithm for reliable migration (IMaOEA-RM), which employs a condition-based interval confidence strategy and a multi-access secure migration selection strategy to improve the convergence of the algorithm, and utilizes a dual-migration crossover strategy in order to adjust the jammer partners and improve the population diversity. Simulation results show that our proposed IMaOEA-RM algorithm can provide a more reliable and efficient migration scheme than existing algorithms.

Surrogate-Assisted and Filter-Based Multiobjective Evolutionary Feature Selection for Deep Learning.

Feature selection (FS) for deep learning prediction models is a difficult topic for researchers to tackle. Most of the approaches proposed in the literature consist of embedded methods through the use of hidden layers added to the neural network architecture that modify the weights of the units associated with each input attribute so that the worst attributes have less weight in the learning process. Other approaches used for deep learning are filter methods, which are independent of the learning algorithm, which can limit the precision of the prediction model. Wrapper methods are impractical with deep learning due to their high computational cost. In this article, we propose new attribute subset evaluation FS methods for deep learning of the wrapper, filter and wrapper-filter hybrid types, where multiobjective and many-objective evolutionary algorithms are used as search strategies. A novel surrogate-assisted approach is used to reduce the high computational cost of the wrapper-type objective function, while the filter-type objective functions are based on correlation and an adaptation of the reliefF algorithm. The proposed techniques have been applied in a time series forecasting problem of air quality in the Spanish south-east and an indoor temperature forecasting problem in a domotic house, with promising results compared to other FS techniques used in the literature.

A many-objective evolutionary algorithm combining simplified hypervolume and a method for reference point sampling based on angular relationship

Determining the path for an evolutionary algorithm is crucial for its performance. Current methods for sampling reference points guiding evolutionary algorithms are inadequate for dealing with convex and concave Pareto fronts,and the uniformity of sampling results decreases significantly in high-dimensional spaces. In this paper,we propose a reference point sampling method based on angular relationships to tackle these issue. And we propose the concept of optimally distributed individuals based on the IGD indicator to ensure the distribution of the evolutionary process and prevent the algorithm from converging to local optima. Additionally,we introduce a novel method for calculating individuals’ fitness within the population,ensuring convergence,uniformity,and distribution of the evolutionary algorithm,thereby enhancing selection pressure among non-dominated individuals. Experimental results on diverse benchmark test problems demonstrate that the proposed algorithm competes favorably with six advanced evolutionary algorithms for many-objective optimization.

An adaptive boundary-based selection many-objective evolutionary algorithm with density estimation

An adaptive boundary-based selection many-objective evolutionary algorithm with density estimation

A space sampling based large-scale many-objective evolutionary algorithm

Large-scale multiobjective optimization problems have attracted increasing attention in both engineering applications and scientific research. Academically, large-scale multiobjective problems involve hundreds or thousands of decision variables. Due to the large decision space, the performance of traditional multiobjective evolutionary algorithms decreases dramatically when dealing with large-scale multiobjective problems, especially many-objective problems. With this in mind, a space sampling based large-scale many-objective evolutionary algorithm (LSMaOEA) is proposed in this article. Specifically, a space sampling method is developed that alternately performs upper/lower-linkage sampling and individual-linkage sampling to sample a set of individuals in the decision space. An environmental selection strategy based on nondominated sorting and reference vector association is proposed. Thus, the proposed LSMaOEA can alleviate excessively dense sampling at boundaries and improve the diversity of existing space sampling based algorithms for large-scale many-objective problems. In the experiments, the proposed algorithm is assessed by comparing it with eight state-of-the-art multi/many-objective evolutionary algorithms. The evaluation is conducted using two popular indicators across nine challenging multiobjective optimization benchmark problems with up to 2000 decision variables. The extensive experimental results consistently reveal that the proposed algorithm outperforms all the compared algorithms.

Two-stage many-objective evolutionary algorithm: enhanced dominance relations and control mechanisms for separated balance

Although the multiobjective evolutionary algorithms (MOEAs) have been proved to bring promising prospects for solving multiobjective optimization problems (MOPs), the performance of the algorithm deteriorates sharply in high-dimensional objective space due to the weak selection pressure and the unregulated balance, which is caused by the increase of objective space dimension. Some current MOEAs with two-stage strategy (TS) strive to address above issues by dividing the evolutionary process into two independent stages, in which convergence and diversity are handled separately within successive generations of different stages. However, TS-MOEAs have some weaknesses, such as sensitivity to stage division, and incomplete separation of convergence and diversity. In this paper, TS/KW-MaOEA is proposed for solving many-objective optimization problems (MaOPs), which keeps TS as the central and equips a perfect control mechanism for separated balance. More specifically, TS/KW-MaOEA can automatically adjust the balance trend and provide appropriate selection pressure for MaOPs according to the Kondratiev wave (KW) search model and the objective space dimension. To verify the effectiveness of the proposed algorithm, a series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms on 15 benchmark problems with up to 30 objectives. Experimental results indicate that the proposed algorithm is highly competitive against peer competitors.

SEA: Many-objective evolutionary algorithm with selection evolution strategy

Balancing the convergence and diversity of the population is crucial for solving multi-objective problems. As the number of objectives increases, the inherent conflict between maintaining diversity and ensuring convergence becomes more significant. To address this challenge, we propose a novel evolutionary algorithm that selectively emphasizes either convergence or diversity, guided by the convergence and diversity indicators of the current population and a predefined priority criterion. During the iterative process, the algorithm strategically aims to either approach the true Pareto front to improve convergence or foster a more uniform distribution within the current Pareto layer to enhance diversity. Continuous monitoring of these indicators enables the algorithm to effectively manage and fine-tune the convergence and diversity of the population. We meticulously evaluated the performance of the proposed algorithm by comparing it with eight state-of-the-art evolution algorithms on 31 benchmark problems. The experimental results unequivocally demonstrated the outstanding performance of the proposed algorithm in solving multi-objective problems. Furthermore, the algorithm can be seamlessly incorporated into other evolution algorithms to strike a delicate balance between diversity and convergence, thereby empowering them to tackle challenging many-objective optimization tasks with enhanced efficiency and accuracy.

Deep and wide search assisted evolutionary algorithm with reference vector guidance for many-objective optimization

Many-objective optimization problems appear in a large many practical cases, but maintaining the convergence and diversity of solutions becomes a big challenge. In response to this, a deep and wide search assisted evolutionary algorithm with reference vector guidance (RVEA-DWC) is proposed. In the algorithm, a novel environmental selection criterion based on substituting Iɛ+ indicator for distance is introduced to enhance the convergence, and once the selected individuals exceed the population size after multiple traversals, those with poor convergence or diversity are randomly eliminated. In addition, to tackle the irregular Pareto front shapes, the invalid reference vectors are deleted regularly, and a certain number of reference vectors with local diversity and global diversity are added, so as to conduct a overall search that combines deep search and wide search to balance exploitation and exploration. An experimental study of 5, 10, 15, 20 objectives is conducted on 60 test instances. The results demonstrate that the proposed algorithm is superior to the other twelve many-objective evolutionary algorithms.

Data-guided for discovering high-strength, cost-effective, and low-carbon rice husk ash concrete

This study aims to present a data-guided intelligent design framework for discovering high-strength, cost-effective, and low-carbon rice husk ash concrete (RHC). First, gradient boosting (GB) models were developed to predict compressive strength of RHC based on a dataset with 1150 samples. The CatBoost model outperforms XGBoost and LightGBM models on the test set, and its determination of coefficient (R2), root mean squared error (RMSE), and mean absolute error (MAE) are 0.984, 3.270 MPa, and 2.290 MPa respectively. With the best prediction model, SHapley Additive exPlanations (SHAP) was utilized to shed light on the model outputs. The curing age is the most dominant features effecting the compressive strength of RHC, and the next two are the contents of cement and water. Then, a computational design framework was proposed by integrating the machine learning-based model and the evolutionary algorithm. Considering compressive strength, materials cost, embodied carbon, and embodied energy, the multi-objective optimization was conducted leveraging the improved adaptive geometry estimation based many-objective evolutionary algorithm (AGE-MOEA II). The optimal solutions of the different design scenarios were achieved using the multi-criteria decision-making method. The research can provide a theoretical reference for the capability of developing RHC mixture using data-guided approachesto promote the sustainable development of concrete industry.

A many-objective evolutionary algorithm under diversity-first selection based framework

Many-objective optimization problems (MaOPs) have attracted wide attention. However, most solving methods prioritize the convergence or take the convergence and diversity into account. This causes the difficulty in balancing convergence and diversity of the population still remains, especially for these problems with irregular Pareto fronts. To this end, we propose a many-objective evolutionary algorithm under diversity-first selection based framework (DSFMO), which first emphasizes the diversity and then considers the convergence. Thus, DSFMO can drive individuals to approach the Pareto front from various directions, and further achieve the balance between convergence and diversity of the population. In this framework, we first construct a candidate pool by selecting these individuals with small crowded degree (i.e., good diversity), in which the crowded degree is evaluated by the global diversity measure based on the objective transferring. Then, the individual in the constructed candidate pool that has the best convergence is selected to enter the next generation, where the convergence is evaluated by the conditional convergence measure that considers the importance of boundary individuals and evolution status. The above two steps are repeatedly executed until the next generation population is formed. In addition, a space projection assisted mating selection is developed to select high-quality parents for variation and further enhance the exploration and exploitation ability of DSFMO. Experiments on 88 test instances have shown that DSFMO can perform best on most test instances. In other words, DSFMO outperforms its seven competitors in balancing convergence and diversity of the population.

Many-objective evolutionary algorithm based on parallel distance for handling irregular Pareto fronts

In recent years, various many-objective evolutionary algorithms (MaOEAs) have been proved to be successful in solving many-objective optimization problems (MaOPs). However, the performance of most MaOEAs is seriously affected when handling MaOPs with irregular Pareto fronts (PFs). In this paper, a new MaOEA variant based on parallel distance (called PDMaOEA) is proposed to solve MaOPs with irregular PFs. Firstly, two new metrics based on parallel distance are designed. The first one termed diversity metric can adapt to irregular PFs. The second one called comprehensive selection metric can consider both diversity and convergence simultaneously. Based on the two metrics, a mating selection method and an environmental selection strategy are proposed. In the mating selection, solutions with good convergence or diversity are chosen to improve the quality of offspring population. In the environmental selection, the selection pressure is significantly enhanced by the two metrics. Experimental study is validated on 19 irregular problems with different shapes of PFs. Performance of the proposed PDMaOEA is compared with six state-of-the-art algorithms. Statistical analysis shows that the proposed approach is competitive in handling MaOPs with irregular PFs.