Many-objective Evolutionary Algorithms Research Articles

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.

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.

A Pareto dominance relation based on reference vectors for evolutionary many-objective optimization

Pareto dominance based approach is a classical method for solving multi-objective optimization problems (MOPs). However, as the number of objectives increases, the selection pressure drops sharply. Solutions with good convergence and diversity are hardly obtained. To tackle these issues, this paper proposes a Pareto dominance relation based on reference vectors (called PRV-dominance) for evolutionary many-objective optimization. In PRV-dominance, solutions in the population are divided into several subregions according to a set of uniform reference vectors. To enhance the convergence, a new convergence metric based on the ranking of objective function values is designed to determine the dominance relationship between two solutions. Then, the density in different subregions is considered to maintain the diversity. In order to verify the performance of our approach, WFG and MaF benchmark problems with 3, 5, 8, and 15 objectives are utilized. Experimental results demonstrate that the proposed PRV-dominance outperforms eight existing dominance relations in balancing convergence and diversity. An improved NSGA-II is suggested based on the proposed PRV-dominance, which shows the competitive performance when compared with six other state-of-the-art algorithms in solving many-objective optimization problems (MaOPs). The effectiveness of the proposed PRV-dominance is also verified on two other existing many-objective evolutionary algorithms.

A many-objective evolutionary algorithm based on learning assessment and mapping guidance of historical superior information

Abstract Multi-objective optimization algorithms have shown effectiveness on problems with two or three objectives. As the number of objectives increases, the proportion of non-dominated solutions increases rapidly, resulting in insufficient selection pressure. Nevertheless, insufficient selection pressure usually leads to the loss of convergence, too intense selection pressure often results in a lack of diversity. Hence, balancing the convergence and diversity remains a challenging problem in many-objective optimization problems. To remedy this issue, a many-objective evolutionary algorithm based on learning assessment and mapping guidance of historical superior information, referred to here as MaOEA-LAMG, is presented. In the proposed algorithm, an effective learning assessment strategy according to historical superior information based on an elite archive updated by indicator ${I}_{\varepsilon + }$ is proposed, which can estimate the shape of the Pareto front and lay the foundation for subsequent fitness and acute angle-based similarity calculations. From this foundation, to balance the convergence and diversity dynamically, a mapping guidance strategy based on the historical superior information is designed, which contains clustering, associating, and proportional selection. The performance of the proposed algorithm is validated and compared with ten state-of-the-art algorithms on 24 test instances with various Pareto fronts and real-world water resource planning problem. The empirical studies substantiate the efficacy of the results with competitive performance.

Many-objective joint optimization of computation offloading and service caching in mobile edge computing

The computation offloading problem in mobile edge computing (MEC) has received a lot of attention, but service caching is also a research topic that cannot be ignored in MEC. Due to the limited resources available on the Edge Server (ES), a wise computation offloading and service caching policy must be formulated in order to maximize system offload efficiency. In this paper, a many-objective joint optimization computation offloading and service caching model (MaJOCOSC) is designed. The model takes into account the limited computing and storage resources of ES, the delay and energy consumption constraints of different types of tasks, and multiple processing modes of user tasks, and sets delay, energy consumption, task hit service rate, service cache balancing, and load balancing as the five optimization objectives of MaJOCOSC. Meanwhile, a non-dominated sorting genetic algorithm (NSGAIII-ASF&WD) based on achievement scalar function (ASF) and the k-nearest neighbor weighted distance mating selection strategy is proposed for better solving the model. The ASF ensures that the given strategy performs well for each objective value, and the k-nearest neighbor weighted distance provides the user with a diversity of strategies. Simulation results show that NSGAIII-ASF&WD can obtain better objective values when solving the model compared with other many-objective evolutionary algorithms, and a suitable computation offloading and service caching strategy is obtained.

Cognitive radio resource scheduling using an adaptive multiobjective evolutionary algorithm

With the proliferation of IoT devices and the increasing popularity of location-oriented services in cyber-physical-social systems, the cognitive engines of these systems have taken on a multitude of parameters across various dimensions, making it impractical and time-consuming to search for the exact optimal solution. To address this challenge, the use of nature-inspired or evolutionary algorithms to find satisfactory solutions in a timely manner has gained significant attention, with reference point-based algorithms being one of the prominent approaches. However, when dealing with nonuniform, degenerate, and discrete Pareto fronts in the target space, using a considerable number of reference points may become ineffective, leading to a loss of diversity in exploration and exploitation during the problem-solving process. Consequently, the distribution of the solutions is adversely affected. To overcome this challenge, this paper presents a strategy to estimate the eigenvalues of the Pareto front in a timely manner. When encountering nonuniform, degenerate, and discrete Pareto fronts, a combination of radial space partitioning and angle selection mechanisms is employed to address these issues. Subsequently, an adaptive selection-based many-objective evolutionary algorithm (ASMaOEA) is proposed. Extensive comparisons with several competing methods on 31 representative benchmark problems demonstrate that ASMaOEA can provide a flexible configuration for decision engines in three typical scenarios involving cyber-physical-social systems. Furthermore, the analysis confirms that ASMaOEA can reduce the bit error rate and improve the system’s throughput, thereby offering substantial benefits to the overall performance of the system.

Resource-aware multi-criteria vehicle participation for federated learning in Internet of vehicles

Federated learning (FL), as a safe distributed training mode, provides strong support for the edge intelligence of the Internet of Vehicles (IoV) to realize efficient collaborative control and safe data sharing. However, due to the resource limitation and the instability of training environment in the complex IoV, ideal performance of FL cannot be achieved. Since considering the actual resource constraints and federated task requirements, the diversified device selection criteria make the resource-aware vehicle selection problem become a multi-criteria selection problem. To effectively support FL for IoV, the resource-aware multi-criteria vehicle selection problem was described as a many-objective optimization problem, and a resource-aware many-objective vehicle selection model (RA-MaOVSM) is proposed to optimize resource efficiency. The RA-MaOVSM considering heterogeneous resources (like computation resources, communication resources, energy resources and data resources) of on-board devices in IoV, and realizes the joint optimization of learning efficiency, energy cost and global performance. Additionally, a novel probability distribution combination game strategy is applied to many-objective evolutionary algorithm (MaOEA) for improving the model solving performance. Simulation results demonstrate that RA-MaOVSM can effectively optimize the IoV resources and FL model performance, and the designed algorithm exhibits good convergence and distribution, achieving a good balance among multiple device selection criteria.

Dominance relation selection and angle-based distribution evaluation for many-objective evolutionary algorithm

In many-objective optimization, most existing evolutionary algorithms struggle to effectively balance the convergence and diversity of population. Given the failure of Pareto-dominance-based selection mechanism in high-dimensional spaces and the growing recognition of the advantages of angle-based similarity evaluation, we propose a Many-objective Evolutionary Algorithm using Dominance Relation Selection and Angle-based Distribution Evaluation (DSAE). Firstly, based on both traditional Pareto dominance and a newly proposed Angle-dominance with higher selection pressure, a Dominance Relation Selection (DRS) strategy is designed, which dynamically adjusts the selection pressure by assessing the overall proximity between parent and offspring populations. Then, an Angle-based Distribution Evaluation is proposed to determine the distribution levels of solutions, so as to adaptively maintain promising distribution performance of population in objective space. Furthermore, a Pareto-dominance-based global optimal solution set is introduced to save solutions with the best diversity throughout the iteration as the final output. Finally, DSAE is compared with 7 state-of-the-art algorithms by using benchmark test suites DTLZ and WFG with 5, 8 and 10 objectives, and the experimental results demonstrate that DSAE has the most advanced performance.

Evolving many-objective dispatching rule pairs for unrelated parallel machine scheduling with sequence-dependent setup times

The real-world problem of unrelated parallel machine scheduling problem with sequence-dependent setup times (UPMSPSST) is investigated and focuses on two key aspects: fast solution and many-objective optimization. While dispatching rules (DRs) are effective in meeting demand, the manual design of many-objective DRs (MaODRs) is challenging. An alternative approach, based on the automatic evolution of MaODRs using hyper-heuristics, shows promise. However, limited literature exists on the automatic evolution of MaODRs specifically for UPMSPSST. In this study, a many-objective genetic programming (MaOGP) algorithm is formed by combining many-objective evolutionary algorithms (MaOEAs) with genetic programming (GP) algorithms. This enables the automatic evolution of MaODRs, leveraging the respective advantages of each approach. The exploration results demonstrate that the evolved MaODRs outperform manually designed DRs reported in prior literature. Furthermore, when considering combinations of objectives with different correlations, the MaODRs exhibit outstanding performance across multiple objectives simultaneously, surpassing even the performance of DRs trained separately for individual objectives. These findings highlight the potential of the proposed MaOGP approach in efficiently and effectively solving the UPMSPSST problem, opening avenues for further research and practical applications in related industries.

A many-objective evolutionary algorithm based on reference vector guided selection and two diversity and convergence enhancement strategies

Achieving the balance between convergence and diversity is a key and challenging issue in many-objective optimization. Reference vector guided selection is an exemplary method for decomposition-based many-objective evolutionary algorithms (MaOEAs). However, there are some problems with it such as insufficient number of obtained solutions and inefficient convergence evaluation metric. Aiming at solving or alleviating these problems, this paper proposes a many-objective evolutionary algorithm based on reference vector guided selection and two diversity and convergence enhancement strategies. The proposed algorithm introduces two new strategies namely adaptive sparse region detection and convergence-only selection. The former is to adaptively detect sparse regions of current elite population, while the latter is to prevent the elimination of solutions with prominent convergence performance. Together with a newly proposed elite retention strategy, these two strategies can achieve diversity and convergence enhancement on the basis on reference vector guided selection. Besides, A new selection criterion for reference vector guided selection is proposed to better measure the convergence of solutions in high dimensionality. Experimental results on widely used test problem suites up to 15 objectives indicate that the proposed algorithm is highly competitive in comparison with seven state-of-the-art MaOEAs.

A Knee Point-Driven Many-Objective Evolutionary Algorithm with Adaptive Switching Mechanism

The Pareto dominance-based evolutionary algorithms can effectively address multiobjective optimization problems (MOPs). However, when dealing with many-objective optimization problems with more than three objectives (MaOPs), the Pareto dominance relationships cannot effectively distinguish the nondominated solutions in high-dimensional spaces. With the increase of the number of objectives, the proportion of dominance-resistant solutions (DRSs) in the population rapidly increases, which leads to insufficient selection pressure. In this paper, to address the challenges on MaOPs, a knee point-driven many-objective evolutionary algorithm with adaptive switching mechanism (KPEA) is proposed. In KPEA, the knee points determined by an adaptive strategy are introduced for not only mating selection but also environmental selection, which increases the probability of generating excellent offspring. In addition, to remove dominance-resistant solutions (DRSs) in the population, an interquartile range method is adopted, which enhances the selection pressure. Moreover, a novel adaptive switching mechanism between angle-based selection and penalty for selecting solutions is proposed, which is aimed at achieving a balance between convergence and diversity. To validate the performance of KPEA, it is compared with five state-of-the-art many-objective evolutionary algorithms. All algorithms are evaluated on 20 benchmark problems, i.e., WFG1-9, MaF1, and MaF4-13 with 3, 5, 8, and 10 objectives. The experimental results demonstrate that KPEA outperforms the compared algorithms in terms of HV and IGD in most of the test instances.

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.

Neuro-evolution-based generic missile guidance law for many-scenarios

Designing efficient aerial interceptors is an important task. Using Pareto-optimality, this paper presents a novel approach for generating guidance laws that are generic for many aerial pursuit-evasion scenarios. In particular, the pure-proportional navigation law is combined with a neural network to create adaptive guidance laws, which adapt according to the current state of the system. First, a many-objective optimization problem is formulated in which each objective aims at the best performance in one of the scenarios. Next, using simulations with a many-objective evolutionary algorithm, a population of guidance laws is evolved towards the Pareto-optimal ones. The obtained guidance laws from multiple runs are statistically analyzed and compared with a set of Pareto-optimal pure-proportional navigation laws. The results suggest that the proposed approach provides a significant improvement as compared with the pure-proportional navigation law over the entire set of scenarios.

An adaptive parental guidance strategy and its derived indicator-based evolutionary algorithm for multi- and many-objective optimization

The indicator-based multi-objective evolutionary algorithms have demonstrated their superiority in handling diverse types of multi- and many-objective optimization problems. However, these evolutionary algorithms still face significant challenges in balancing convergence and diversity of the evolutionary population, despite numerous auxiliary mechanisms designed to improve their performance. To address this issue, an adaptive parental guidance strategy (APGS) is proposed in this paper. On the one hand, APGS leverages the current population to evaluate the quality of the newly generated offspring. On the other hand, it employs an adaptive threshold to select offspring individuals with better convergence and diversity. This approach enhances the convergence and diversity of the candidate solution set throughout the evolutionary process, thereby ensuring high-quality obtained solutions. By incorporating the APGS, this paper proposes a new indicator-based evolutionary algorithm with parental guidance (IEAPG). Simulation results on several test suites and real-world problem show that compared to PREA, SPEA/R, GrEA, TS-NSGA-II, HEA and MaOEA/IGD, the proposed IEAPG has better performance and robustness in dealing with different types of multi- and many-objective optimization problems. Furthermore, further investigation reveals that the incorporation of the APGS can significantly improve the performance of different categories of multi- and many-objective evolutionary algorithms.

A many-objective evolutionary algorithm assisted by ideal hyperplane

In many-objective optimization problems (MaOPs), balancing convergence and diversity while rapidly converging to the Pareto front is an arduous task for evolutionary algorithms. In addition, with the increase of the number of targets, the number of non-dominant solutions increases exponentially, and the individual selection pressure is insufficient. For this problem, we propose a many-objective evolution algorithm assisted by an ideal hyperplane (MaOEA-IH). To begin, the ideal hyperplane is built from the extremums of each dimension of objective space, guiding the individual to the Pareto front of search. Second, a parallel p-norm mating selection strategy based on the ideal hyperplane is proposed to improve convergence. In addition, two other factors are taken into account: (1) different p-norms are used to measure different spatial scales; and (2) individual selection uncertainty is defined by incorporating a probabilistic perturbation mechanism. Following that, the sum of objectives is applied to shift-based density estimation, which serves as an evaluation criterion in the environmental selection operation. This method increases the chances of solutions with high convergence and diversity entering the next generation, thereby increasing selection pressure. On three benchmark problems of DTLZ, WFG, and MaF, we compare MaOEA-IH with seven excellent algorithms. The results demonstrate that the MaOEA-IH proposed is highly competitive in solving MaOPs.

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.

An adaptive many-objective evolutionary algorithm based on decomposition with two archives and an entropy trigger

ABSTRACTThis article proposes two novel mechanisms to improve the performance of many-objective evolutionary algorithms based on Chebyshev scalarization. One mechanism improves the efficiency and effectiveness of the adaptation of the descent directions in criteria space, while the other ensures that extreme solutions are preserved. Weight adaptation via WS-transformation has shown promising results, but its performance is dependent on the choice of the start of the adaptation process. In order to overcome this limitation, in this article an efficient entropy-based trigger is proposed with fast calculation of the entropy that scales favourably with the number of dimensions. The novel entropy-based method is complemented by a dual-archiving mechanism that preserves extreme solutions. The dual-archiving strategy mitigates the possibility to discard those critical individuals whose loss affects the whole evolutionary process. The new algorithm proposed in this article (called aMOEA/D-2A-ET) is compared against a set of state-of-the-art MOEAs and shown to have competitive performance.

Multipopulation-Based Differential Evolution for Large-Scale Many-Objective Optimization.

In recent years, numerous efficient many-objective optimization evolutionary algorithms have been proposed to find well-converged and well-distributed nondominated optimal solutions. However, their scalability performance may deteriorate drastically to solve large-scale many-objective optimization problems (LSMaOPs). Encountering high-dimensional solution space with more than 100 decision variables, some of them may lose diversity and trap into local optima, while others may achieve poor convergence performance. This article proposes a multipopulation-based differential evolution algorithm, called LSMaODE, which can solve LSMaOPs efficiently and effectively. In order to exploit and explore the exponential decision space, the proposed algorithm divides the population into two groups of subpopulations, which are optimized with different strategies. First, the randomized coordinate descent technique is applied to 10% of individuals to exploit the decision variables independently. This subpopulation maintains diversity in the decision space to avoid premature convergence into local optimum. Second, the remaining 90% of individuals are optimized with the nondominated guided random interpolation strategy, which interpolates individual among three nondominated solutions randomly. The strategy can guide the population convergent toward the nondominated solutions quickly, meanwhile, maintain good distribution in objective space. Finally, the proposed LSMaODE is evaluated on the LSMOP test suites from the scalability in both decision and objective dimensions. The performance is compared against five state-of-the-art large-scale many-objective evolutionary algorithms. The experimental results show that LSMaODE provides highly competitive performance.

A Constraint-Handling Technique for Decomposition-Based Constrained Many-Objective Evolutionary Algorithms

A Constraint-Handling Technique for Decomposition-Based Constrained Many-Objective Evolutionary Algorithms