Reference Vector Guided Evolutionary Algorithm Research Articles

Multi-strategy reference vector guided evolutionary algorithm and its application in multi-objective optimal scheduling of microgrid systems containing electric vehicles

To solve the optimization scheduling problem of microgrids involving Electric Vehicles (EVs), in this paper, the integration of EVs into the microgrid is considered in the microgrid system composed of wind turbine, photovoltaic turbine, micro gas turbine, fuel cell, and storage battery, and the economic dispatch model of the microgrid system containing EVs is established, with the minimization of the operation cost and pollutant treatment cost as the optimization objective. Meanwhile, Chebyshev mapping is introduced into the reference vector guided evolutionary algorithm (RVEA) to initialize the distribution of the population, and then an improved angle-penalized distance (APD) method is used to balance the convergence and diversity of the algorithm. The improved RVEA algorithm is applied to the scheduling model proposed in this paper, Different operational scheduling scenarios are investigated, scheduling results with different optimization objectives are discussed. The results show that the multi-strategy RVEA algorithm proposed in this paper can improve the economical and environmentally friendly protection of the microgrid system, and promote the optimal operation of the microgrid.

Multi-objective optimization for impeller structure parameters of fuel cell air compressor using linear-based boosting model and reference vector guided evolutionary algorithm

As a pivotal part of cathode air supply system, centrifugal air compressors play a central position in ensuring efficient operations of onboard fuel cells. To improve the overall performance of compressors, comprehensive performance tests were conducted and an integrated simulation model was developed by using computational fluid dynamics (CFD) methods. On this basis, the prediction performance of Linear-based Boosting models was investigated, and multi-objective optimization of impeller structural parameters was carried out through the Reference Vector Guided Evolutionary Algorithm (RVEA). Simulation results indicate that the impeller of the original compressor exhibits significant entropy increase, insufficient gas compression and serious energy dissipation, highlighting considerable room for design optimization. The eXtreme Gradient Boosting (XGBoost) model with 29 estimators has superior generalization ability and prediction performance, making it the preferred Boosting model for the compressor. Multi-objective optimizations have strong universality and rationality, resulting in a well-distributed and diversified final non-dominated solution set. The isentropic efficiency and pressure ratio of the Max_σ solution are improved by 18.7% and 70.1%, while those of the Max_ηc solution are enhanced by 23.0% and 48.9%, respectively. After optimization, the gas experiences reduced shock loss, diminished entropy increase and enhanced flow stability. These findings can provide data support, theoretical basis and directional guidance for performance improvement of centrifugal air compressors.

Efficient constrained large-scale multi-objective optimization based on reference vector-guided evolutionary algorithm

Efficient constrained large-scale multi-objective optimization based on reference vector-guided evolutionary algorithm

NSGA-II/SDR-OLS: A Novel Large-Scale Many-Objective Optimization Method Using Opposition-Based Learning and Local Search

Recently, many-objective optimization problems (MaOPs) have become a hot issue of interest in academia and industry, and many more many-objective evolutionary algorithms (MaOEAs) have been proposed. NSGA-II/SDR (NSGA-II with a strengthened dominance relation) is an improved NSGA-II, created by replacing the traditional Pareto dominance relation with a new dominance relation, termed SDR, which is better than the original algorithm in solving small-scale MaOPs with few decision variables, but performs poorly in large-scale MaOPs. To address these problems, we added the following improvements to the NSGA-II/SDR to obtain NSGA-II/SDR-OLS, which enables it to better achieve a balance between population convergence and diversity when solving large-scale MaOPs: (1) The opposition-based learning (OBL) strategy is introduced in the initial population initialization stage, and the final initial population is formed by the initial population and the opposition-based population, which optimizes the quality and convergence of the population; (2) the local search (LS) strategy is introduced to expand the diversity of populations by finding neighborhood solutions, in order to avoid solutions falling into local optima too early. NSGA-II/SDR-OLS is compared with the original algorithm on nine benchmark problems to verify the effectiveness of its improvement. Then, we compare our algorithm with six existing algorithms, which are promising region-based multi-objective evolutionary algorithms (PREA), a scalable small subpopulation-based covariance matrix adaptation evolution strategy (S3-CMA-ES), a decomposition-based multi-objective evolutionary algorithm guided by growing neural gas (DEA-GNG), a reference vector-guided evolutionary algorithm (RVEA), NSGA-II with conflict-based partitioning strategy (NSGA-II-conflict), and a genetic algorithm using reference-point-based non-dominated sorting (NSGA-III).The proposed algorithm has achieved the best results in the vast majority of test cases, indicating that our algorithm has strong competitiveness.

Comparison of multi-objective genetic algorithms for optimization of cascade reservoir systems

Abstract Multi-objective genetic algorithms (MOGAs) are widely used for multi-reservoir systems’ optimization due to their high efficiency and fast convergence. However, the computational cost grows exponentially with the expansion of multi-reservoir systems and the increased dimensions of optimization problems, posing a great challenge to multi-reservoir operations. Therefore, it is important to find a suitable and efficient multi-objective algorithm for multi-reservoir system optimization. In this study, three representative MOGAs were selected, namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Non-Dominated Sorting Genetic Algorithm III (NSGA-III), and Reference Vector Guided Evolutionary Algorithm (RVEA), and three multi-objective optimization models were then developed accordingly. Numerical experiments were conducted to evaluate the performance of these three algorithms for the optimization of a cascaded reservoir system. The results show that for the two-objective model, the non-dominant size generation rate (NDSGR) of NSGA-II is 1.66 and 4.01 times that of NSGA-III and RVEA, respectively. NSGA-II is more suitable for solving the optimization operation problem with two objectives. Based on the comprehensive evaluation, NSGA-III seems to be more appropriate for more than two objectives. These results emphasize the importance of using appropriate algorithms and provide further insights into the choice of algorithms for the optimization of hydropower systems.

Recommendation Based on Large-Scale Many-Objective Optimization for the Intelligent Internet of Things System

Recommender systems are of great significance for mining the data generated by the Internet of Things (IoT) and are important for the intelligent IoT systems. The traditional recommendation algorithms only consider the accuracy as the optimization objective. In this article, a many-objective optimization model consisting of the F1 measure, recommendation novelty, recommendation coverage, customer satisfaction, landmark similarity, and overfitting is constructed for recommendation. Then, to improve the recommendation performance, we propose to use a large-scale many-objective optimization algorithm based on problem transformation (LSMaOA) to optimize the matrix factorization model for the recommender system in the intelligent IoT systems. The experimental results show that LSMaOA is robust and can effectively optimize the model’s six objectives. Compared with the knee point-driven evolutionary algorithm (KnEA), the grid-based evolutionary algorithm (GrEA), the large-scale multiobjective optimization framework (LSMOF), and the reference vector guided evolutionary algorithm (RVEA), the proposed algorithm can promote the F1 measure by 7.78%, 13.63%, 21.85%, and 28.63%, respectively.

An Ensemble Surrogate-Based Framework for Expensive Multiobjective Evolutionary Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have become very popular for tackling computationally expensive multiobjective optimization problems (EMOPs), as the surrogate models in SAEAs can approximate EMOPs well, thereby reducing the time cost of the optimization process. However, with the increased number of decision variables in EMOPs, the prediction accuracy of surrogate models will deteriorate, which inevitably worsens the performance of SAEAs. To deal with this issue, this article suggests an ensemble surrogate-based framework for tackling EMOPs. In this framework, a global surrogate model is trained under the entire search space to explore the global area, while a number of surrogate submodels are trained under different search subspaces to exploit the subarea, so as to enhance the prediction accuracy and reliability. Moreover, a new infill sampling criterion is designed based on a set of reference vectors to select promising samples for training the models. To validate the generality and effectiveness of our framework, three state-of-the-art evolutionary algorithms [nondominated sorting genetic algorithm III (NSGA-III), multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) and reference vector-guided evolutionary algorithm (RVEA)] are embedded, which significantly improve their performance for solving most of the test EMOPs adopted in this article. When compared to some competitive SAEAs for solving EMOPs with up to 30 decision variables, the experimental results also validate the advantages of our approach in most cases.

Communication-efficient federated recommendation model based on many-objective evolutionary algorithm

The federated recommendation system (FedRS), which is the application of the recommendation system (RS) in federated learning, has been creatively developed as increasing attention has been paid to user privacy protection. However, traditional federated learning consumes excessive communication time and resource, which seriously limits the development of the FedRS. To reduce the communication cost and improve the recommendation performance of FedRS, an improved many-objective federated recommendation model with a novel parameter reduction strategy is proposed in this paper. The model aims to optimize the number of parameters shared between the server and client to improve communication efficiency in the federated process. Optimal parameter selection solutions can be obtained using the many-objective evolutionary algorithm (MaOEA), which can optimize the recommendation accuracy, novelty, diversity, and communication efficiency of FedRS simultaneously. Furthermore, the reference vector guided evolutionary algorithm (RVEA) was adopted to evaluate the proposed model. Experiments were performed on two famous recommendation datasets to examine the superiority of RVEA for the evaluation. The performance results indicated that the proposed model can not only provide accurate, diverse, and novel recommendations for the client, but can also realize efficient communication.

Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone.

Optimization of subsurface models with multiple criteria using Lexicase Selection

Seismic History Matching (SHM) is a key problem in the geosciences community, requiring optimal parameters of a subsurface model that match the observed data from multiple in-situ measurements. Therefore, the SHM problems are usually solved with Multi-Objective Evolutionary Algorithms (MOEAs). This group of algorithms optimize multiple objectives simultaneously, considering the trade-off between objectives. However, SHM requires the solutions that are good on all objectives rather than a trade-off. In this study, we propose a Differential Evolution algorithm using Lexicase Selection to solve the SHM problems. Unlike the MOEAs, this selection method pushes the solutions to perform well on all objectives. We compared this method with two MOEAs, namely Non-dominated Sorting Genetic Algorithm II and Reference Vector-guided Evolutionary Algorithm, on two SHM problems. The results show that this method generates more solutions near the ground truth.

An Adaptive Reference Vector Adjustment Strategy and Improved Angle-Penalized Value Method for RVEA

Decomposition-based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector-guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle-penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, and 10-objective MaF1–MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.

Modeling and parameter identification of seated human body with the reference vector guided evolutionary algorithm

The low frequency vibration of the vehicle in motion has a great influence on the ride comfort of occupants. The research on the vibration response characteristics of human body plays a great role in analyzing and improving ride comfort. The purpose of this study was to investigate the parameter identification of seated human body dynamic model. A seven-degree-of-freedom (DOF) lumped parameter model was established to describe the vibration response characteristics of human body. The derivation processes of apparent mass (AM) and seat to head transmissibility (STHT) were performed. After the theoretical calculation of the human body vibration characteristics, we used several different evolutionary algorithms to identify the 23 parameters of the model, including the mass, stiffness and damping parameters. By comparing the results of the five optimization algorithms and comprehensively analyzing the convergence and distribution of the non-dominated solution set, we found that the reference vector guided evolutionary algorithm (RVEA) shows good competitiveness in solving many-objective optimization problem (MaOP), that is, parameter identification of seated human body model in this paper. The AM and STHT calculated by model identification were compared with their measured by experiment. The result shows that the selected seven-DOF model can well describe the vertical vibration characteristics of seated human body and the identification method used in this paper can accurately identify the parameters of lumped parameter model, which provides convenience for the establishment of a complete “road-vehicle-seat-human body” system dynamic model.

Neighborhood samples and surrogate assisted multi-objective evolutionary algorithm for expensive many-objective optimization problems

Many surrogate-assisted meta-heuristic algorithms have been proposed for single-objective expensive optimization problems, however, not so much attention has been paid to multi-objective expensive problems, especially for those with more than four objectives. In this paper, we use reference vector guided evolutionary algorithm (RVEA) to select suitable individuals, and radial basis function (RBF) networks are used to estimate the fitness of the original objective function to reduce the computational cost. These suitable individuals are optimized by the RBF network for several iterations. Then in surrogate model management, an infill strategy is proposed to select promising individuals for exact evaluations. Euclidean distance to origin or uncertainty is adaptively considered, according to the convergence degree of the current population in the infill strategy. The approximation uncertainty of each solution is calculated according to its distance to the modeling samples in the decision space. The experimental results on a number of many-objective optimization problems showed that the proposed method is competitive to three state-of-the-art algorithms for solving computationally expensive many-objective optimization problems.

Reliability-Based Robust Design Optimization in Consideration of Manufacturing Tolerance by Multi-Objective Evolutionary Optimization with Repair Algorithm

There are inherently various uncertainties in practical engineering, and reliability-based design optimization (RBDO) and robust design optimization (RDO) are two well-established methodologies when considering the uncertainties. Naturally, reliability-based robust design optimization (RBRDO) is a methodology developed recently by combining RBDO and RDO, in which the tolerances of random design variables are always assumed as constants. However, the tolerance of random design variables is a key factor for the objective robustness and manufacturing cost, and the tolerance allocation is the core problem in mechanical manufacturing. Inspired by the cost–tolerance relationship in mechanical manufacturing, this paper presents an integrated framework to simultaneously find the optimal design variable and the corresponding tolerance in the multi-objective RBRDO, with the trade-off between objective robustness and manufacturing cost. The failure mechanism of the constraint handling strategy of the constrained reference vector-guided evolutionary algorithm (C-RVEA) is discussed to solve the multi-objective optimization formulation. Then the robust repair operator and reliability-based repair operator are proposed to transform unfeasible solutions to the feasible ones under reliability constraints. Numerical results reveal that the proposed repair algorithm is effective. By solving the integrated multi-objective optimization problem, the Pareto front with the compromised solutions between the objective robustness and manufacturing cost could be obtained, from which decision makers can select the satisfying solution conveniently according to the preferred requirements.

A New Decomposition-Based Many-Objective Algorithm Based on Adaptive Reference Vectors and Fractional Dominance Relation

Decomposition-based evolutionary multi-objective algorithms (MOEAs) and many-objective algorithms (MaOEAs) divide a multi-objective problem (MOP) or a many-objective problem (MaOP) into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto Fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector guided evolutionary algorithm (RVEA) by designing an adaptive reference vectors adjustment strategy and strengthening the poor selection pressure. By adding the adaptive strategy, the predefined reference vectors will be dynamically adjusted according to the distribution of promising solutions with good overall performance and the subspaces where the PF lies may be further divided so as to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increasing of objective size. Motivated by that, an improved angle-penalized distance (APD) method based on a newly proposed fractional dominance relation is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, 10- objective MaF1-MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.

An Adaptive Reference Vector-Guided Evolutionary Algorithm Using Growing Neural Gas for Many-Objective Optimization of Irregular Problems.

Most reference vector-based decomposition algorithms for solving multiobjective optimization problems may not be well suited for solving problems with irregular Pareto fronts (PFs) because the distribution of predefined reference vectors may not match well with the distribution of the Pareto-optimal solutions. Thus, the adaptation of the reference vectors is an intuitive way for decomposition-based algorithms to deal with irregular PFs. However, most existing methods frequently change the reference vectors based on the activeness of the reference vectors within specific generations, slowing down the convergence of the search process. To address this issue, we propose a new method to learn the distribution of the reference vectors using the growing neural gas (GNG) network to achieve automatic yet stable adaptation. To this end, an improved GNG is designed for learning the topology of the PFs with the solutions generated during a period of the search process as the training data. We use the individuals in the current population as well as those in previous generations to train the GNG to strike a balance between exploration and exploitation. Comparative studies conducted on popular benchmark problems and a real-world hybrid vehicle controller design problem with complex and irregular PFs show that the proposed method is very competitive.

Can modern multi-objective evolutionary algorithms discover high-dimensional financial risk portfolio tradeoffs for snow-dominated water-energy systems?

Hydropower generation in the Hetch Hetchy Power System is strongly tied to snowmelt dynamics in the central Sierra Nevada and consequently is particularly financially vulnerable to changes in snowpack availability and timing. This study explores the Hetchy Hetchy Power System as a representative example from the broader class of financial risk management problems that hold promise in helping utilities such as SFPUC to understand the tradeoffs across portfolios of risk mitigation instruments given uncertainties in snowmelt dynamics. An evolutionary multi-objective direct policy search (EMODPS) framework is implemented to identify time adaptive stochastic rules that map utility state information and exogenous inputs to optimal annual financial decisions. The resulting financial risk mitigation portfolio planning problem is mathematically difficult due to its high dimensionality and mixture of nonlinear, nonconvex, and discrete objectives. These features add to the difficulty of the problem by yielding a Pareto front of solutions that has a highly disjoint and complex geometry. In this study, we contribute a diagnostic assessment of state-of-the-art multi-objective evolutionary algorithms’ (MOEAs') abilities to support a DPS framework for managing financial risk. We perform comprehensive diagnostics on five algorithms: the Borg multi-objective evolutionary algorithm, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Non-dominated Sorting Genetic Algorithm III (NSGA-III), Reference Vector Guided Evolutionary Algorithm (RVEA), and the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). The MOEAs are evaluated to characterize their controllability (ease-of-use), reliability (probability of success), efficiency (minimizing model evaluations), and effectiveness (high quality tradeoff representations). Our results show that newer decomposition, reference point, and reference vector algorithms are highly sensitive to their parameterizations (difficult to use), suffer from search deterioration (losing solutions), and have a strong likelihood of misrepresenting key tradeoffs. The results emphasize the importance of using MOEAs with archiving and adaptive search capabilities in order to solve complex financial risk portfolio problems in snow-dependent water-energy systems.

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

Multi-objective optimization (MOO), which involves more than one conflicting objective to be optimized simultaneously, is expected to provide efficient and comprehensive reservoir management (RM) solutions. The multi-objective production optimization problems are considered to be expensive due to the difficulties and cost of operations. Surrogate-assisted evolutionary algorithms (SAEAs), which has proved to be an effective way to solve expensive problems, design computationally cheap function to approximate each objective function. Meanwhile, the optimization process involves a large number of decision variables. However, building a high-quality surrogate model has become difficult due to the “curse of dimensionality”. Base on characterization, an efficient multi-objective optimization framework called SA-RVEA-PCA is proposed to effectively deal with large-scale and computationally expensive simulation-based optimization problems, including three parts:1) Given a set of simulation results, a Gaussian process (GP) model based on Principal Component Analysis (PCA) for each objective function is trained so that the surrogate models can guide the optimization more accurately. 2) A reference vector guided evolutionary algorithm (RVEA) recently developed is employed as a multi-objective optimizer. 3) The information of uncertainty given by GP and angle-penalized penalized (APD) proposed in RVEA are used to update the surrogate models. To the best of our knowledge, the proposed algorithm is applied to a benchmark function, and two typical applications of MOO with synthetic reservoir models. Results show that the proposed method can provide more comprehensive and efficient RM with a higher convergence speed.

The distributed many-objective economic/emission load dispatch benchmark problem

Abstract This paper considers a new kind of economic/emission load dispatch-based problem framework. In the proposed framework, non-synchronous and distant generators are connected to different demanding areas, unlike conventional distributed dispatch problems. Only some of the generators are physically connected to the demanding areas, which are shared by some other generators. Hence, each generator affects other generators. Additionally, the proposed framework is enriched with an over-produced power that can be sold to the neighboring regions. Since many aspects, constraints and objectives are introduced in this new framework, the number of objectives is increased. To solve this experimental problem, many-objective optimization algorithms are applied, and the results are compared with each other. These algorithms are the multi-objective evolutionary algorithm based on decomposition, inverse modeling-based multi-objective evolutionary algorithm, grid-based evolutionary algorithm for many-objective optimization, reference vector-guided evolutionary algorithm, and strength Pareto evolutionary algorithm with shift-based density estimator. Additionally, to evaluate the performances of many-objective optimization algorithms, the multi-objective version of the problem is solved with a constraint-based classical optimization algorithm, achievement scalarization functions, and sequential quadratic programming. The results suggest that as the model converges to a more realistic problem, the number of objectives is increased, and more efficient algorithms are needed to solve these problems.

Decomposition-based sub-problem optimal solution updating direction-guided evolutionary many-objective algorithm

The many-objective optimization problem (MaOP) is a common problem in the fields of engineering and scientific computing. It requires the optimization of multiple conflicting objectives. Due to the complexity of the MaOP, its optimization requires considerable amounts of time and computation resources to execute. Moreover, demand for a general optimization method for different types of MaOPs is becoming increasingly urgent. In this paper, the reference-vector-guided evolutionary algorithm (RVEA) is modified to accelerate the optimization speed and to improve its adaptability. To achieve more rapid convergence, a sub-problem optimal solution updating direction-guided variation strategy is developed to replace the original variation strategy of the RVEA. A comparative experiment on the typical test suites verifies that the proposed method offers preferable performance. Our experiment shows that the performance of the OD-RVEA declines when optimizing MaOPs with irregular Pareto fronts (PFs). To address this issue, an adaptive reference vector adjustment strategy is designed as a means of enhancing the optimization capabilities of MaOPs with irregular PFs by adjusting the distribution of reference vectors. Our comparative experiment on test cases that involve irregular PFs shows that the algorithm that applies this strategy outperforms the algorithm that applies fixed reference vectors.