Evolutionary Multiobjective Optimization Algorithms Research Articles

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

A dual-sampling based evolutionary algorithm for large-scale multi-objective optimization

The vast search space in large-scale multi-objective optimization represents a significant challenge for evolutionary algorithms to converge towards the Pareto Front. As an effective search strategy, direction-guided sampling technique could improve the search efficiency by exploring along the approximated directions to approach the Pareto set. However, the approximated directions may fail to interact with the true Pareto set and result in inefficient search. To address this issue, a dual-sampling method is proposed in this paper. In addition to the samples along the directions approximated by direction-guided sampling, fuzzy Gaussian sampling is applied to adjust the search direction and generate more accurate and evenly distributed solutions. Moreover, a convergence-and-diversity-based mating selection is introduced to balance the exploration and exploitation. The experiments on 72 test benchmarks with bi- and tri-objectives and 500 to 5000 decision variables show the superiority of the proposed algorithm compare with the state-of-the-art algorithms.

Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are characterized by having multiple global or local Pareto solution sets. In most of multimodal multi-objective evolutionary algorithms, the distribution of population in objective space and decision space cannot be taken into account, simultaneously. In this paper, an innovative evolutionary algorithm based on dual-space distribution metric for multimodal multi-objective optimization (DsDMEA) is designed to solve this problem. Specifically, the two enhanced performance metrics are coupled together as a single dual-space distribution metric (DsDM) serving as the criterion for environmental selection. DsDMEA explores solutions on Pareto front and Pareto solutions sets that are not associated with the reference point, which show limited contributions to the distribution in dual spaces. Then DsDMEA removes any bi-noncontributing solutions using DsDM during environmental selection until the population size is met. This achieves a balance between the distribution of solutions and convergence in decision space. At the same time, this paper introduces a novel fitness computation method, enabling the precise localization of local Pareto fronts within the population. Finally, eight state-of-the-art multimodal multi-objective evolutionary algorithms are adopted to make a comparison on two types of benchmark to verify the performance of the DsDMEA. The experimental results demonstrated the DsDMEA effectiveness in solving MMOPs with local problems and traditional MMOPs.

Conditional Generative Adversarial Network-Based Bilevel Evolutionary Multiobjective Optimization Algorithm

Conditional Generative Adversarial Network-Based Bilevel Evolutionary Multiobjective Optimization Algorithm

Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization

The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors.

Performance optimization of latent heat storage device based on surrogate-assisted multi-objective evolutionary algorithm and CFD method

The design of fin structures and the formulation of heat conductivity enhancers have always been critical factors influencing the performance of latent heat storage devices. However, achieving the optimal parameters of fin structures and the fraction of heat conductivity enhancers when adjusting multiple parameters simultaneously remains a time-consuming and labor-intensive task. In this paper, a combination of machine learning methods and computational fluid dynamics (CFD) was employed to optimize the parameters of fin structures and the mass fraction of expanded graphite with minor computational resources and time costs, thereby obtaining a set of Pareto optimal latent heat storage (LHS) devices that simultaneously considers energy storage power and energy storage capacity. The combination essentially is a surrogate assistant multi-objective evolutionary optimization algorithm, which utilizes batch recommendation strategies to recommend multiple high-quality candidate solutions that achieve a balance between two conflicting optimization objectives in CFD simulations. This method significantly reduces the number of model iterations and saves the time and computational resources required for multi-objective optimization. The results showed that the proposed algorithm only required 80 cases of CFD calculations to obtain two well-fitted Gaussian process models, leading to a 91 % improvement in computational efficiency. According to the recommendations from the algorithm, the LHS device with 78 fins of 2.0 mm thickness and 20 % mass fraction of expanded graphite could achieve the optimal trade-off of energy storage power and energy storage capacity. Compared to the prototype, the energy storage power and total energy storage capacity increased by 46.7 % and 22.1 %, respectively. The method proposed in this study can provide guidance for the optimal configuration design of LHS devices.

Developing a crash severity model based on multi objective evolutionary feature selection approaches

The main purpose of this article is assessing the capability of multiobjective optimisation evolutionary algorithms (MOEAs) along with machine learning method on predicting the crash injury severity with the approach of reducing input variables. Dataset of crashes which were occurred in Iran was analysed over the period of 2016–2020. The data were classified into two classes in terms of injury severity: fatal and non-fatal datasets. At first, general prediction models were created by inserting 31 available input variables into support vector machine (SVM) method based on two imbalanced and obtained balanced datasets. A cluster based under sampling technique was used to obtained balanced data. Then evolutionary algorithms of two objectives optimisation algorithms namely non-dominated sorting genetic algorithm (NSGA-II), multi-objective evolutionary algorithm based on decomposition (MOEA/D), and pareto envelope-based selection algorithm (PESA-II) along with SVM were used to select features that significantly affect the severity of crashes and developed the simplified models. Then the simplified developed model was compared to the model which was prepared with random forest (RF) method in feature selection. It is shown that the simplified model developed by combined MOEAs and SVM is more appropriate to accurately predict the crash severity, considering the number of input variables in comparison to RF.

Micro Multiobjective Evolutionary Algorithm With Piecewise Strategy for Embedded-Processor-Based Industrial Optimization.

In some industrial applications, it is required to do off-line multiobjective optimization in embedded systems. Due to their limited computing and memory capability, embedded processor may not be able to run conventional multiobjective optimization evolutionary algorithms (MOEAs). This article proposes a micro MOEA with piecewise strategy (μ MOEA) for industrial optimization in embedded processor. μ MOEA introduces an improved piecewise strategy based on the MOEA/D framework, which serially optimizes subclusters to be compatible with embedded processor under limited computing power. For the purpose of further enhancing μ MOEA, a dynamic and flexible weight vector update trigger mechanism is proposed, so that the algorithm can save and utilize the computing resources of the embedded processor as much as possible. Abundant artificial test problems are carrying out to test the performance of μ MOEA. Through various experiments, it can be found that μ MOEA has outstanding performance in ZDT, DTLZ, SMOP, and MaF problems. Last and most importantly, μ MOEA is successfully applied to two specific application scenarios of industrial optimization on embedded processor for simulation, such as two different types of semi-autogenous grinding optimization problems and micro-grid energy optimization problem, which prove the feasibility of applying MOEA to embedded processor.

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

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

ATM-R: An Adaptive Tradeoff Model With Reference Points for Constrained Multiobjective Evolutionary Optimization.

The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and well-distributed feasible solutions. To achieve this goal, a delicate tradeoff must be struck among feasibility, diversity, and convergence. However, balancing these three elements simultaneously through a single tradeoff model is nontrivial, mainly because the significance of each element varies in different evolutionary phases. As an alternative approach, we adapt distinct tradeoff models in various phases and introduce a novel algorithm named adaptive tradeoff model with reference points (ATM-R). In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence." This transition is instrumental in discovering an adequate number of feasible regions and accelerating the search for feasible Pareto optima in succession. In the feasible phase, ATM-R places an emphasis on balancing diversity and convergence to obtain a set of feasible solutions that are both well-converged and well-distributed. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a diverse set of benchmark test functions and real-world problems demonstrate that ATM-R is effective. When compared to eight state-of-the-art constrained multiobjective optimization evolutionary algorithms, ATM-R consistently demonstrates its competitive performance.

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

Automatic grouping of wind turbine types via multi-objective formulation for nonuniform wind farm layout optimization using an analytical wake model

This study introduces a novel methodology that aims to minimize the number of different wind turbine types used in nonuniform wind farms. This approach involves a trade-off to tackle the logistical challenges associated with installing, operating, and maintaining such wind farms. To accomplish this, a Gaussian analytical wake model is used in conjunction with evolutionary algorithms (NSGA-II and SMS-EMOA) for multi-objective optimization. A multi-objective problem is formulated, regarding wind farm capacity factor (CF) and levelized cost of energy (LCOE), and addressed using two distinct approaches. In the first approach, proposed here, the number of different wind turbine types is limited and treated as an additional objective. In contrast, the second approach allows for flexibility in choosing any number of different turbine types. Comparing the results obtained, it was observed that the methodology presented here yielded a reduced number of different turbine types without compromising CF and LCOE objectives. A multi-criteria decision maker was applied to extract the final non-dominated solutions from the obtained Pareto set. Finally, economic indicators show the profitability of these solutions.

A Co-evolutionary Multi-population Evolutionary Algorithm for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) widely appear in various real-world applications and have attracted increasing attention worldwide. However, how to obtain both good population diversity and fast convergence speed to efficiently solve DMOPs are two challenging issues. Inspired by that the multiple populations for multiple objectives (MPMO) framework can provide algorithms with good population diversity and fast convergence speed, this paper proposes a new efficient algorithm called a co-evolutionary multi-population evolutionary algorithm (CMEA) based on the MPMO framework together with three novel strategies, which are helpful for solving DMOPs efficiently from two aspects. First, in the evolution control aspect, a convergence-based population evolution strategy is proposed to select the suitable population for executing the evolution in different generations, so as to accelerate the convergence speed of the algorithm. Second, in the dynamic control aspect, a multi-population-based dynamic detection strategy and a multi-population-based dynamic response strategy are proposed to help the algorithm maintain the population diversity, which are efficient for detecting and responding to the dynamic changes of environments. Integrating with the above strategies, the CMEA is proposed to solve the DMOP efficiently. The superiority of the proposed CMEA is validated in experiments on widely-used DMOP benchmark problems.

Energy Consumption Prediction in Residential Buildings—An Accurate and Interpretable Machine Learning Approach Combining Fuzzy Systems with Evolutionary Optimization

This paper addresses the problem of accurate and interpretable prediction of energy consumption in residential buildings. The solution that we propose in this work employs the knowledge discovery machine learning approach combining fuzzy systems with evolutionary optimization. The contribution of this work is twofold, including both methodology and experimental investigations. As far as methodological contribution is concerned, in this paper, we present an original designing procedure of fuzzy rule-based prediction systems (FRBPSs) for accurate and transparent energy consumption prediction in residential buildings. The proposed FRBPSs are characterized by a genetically optimized accuracy–interpretability trade-off. The trade-off optimization is carried out by means of multi-objective evolutionary optimization algorithms—in particular, by our generalization of the well-known strength Pareto evolutionary algorithm 2 (SPEA2). The proposed FRBPSs’ designing procedure is our original extension and generalization (for regression problems operating on continuous outputs) of an approach to designing fuzzy rule-based classifiers (FRBCs) we developed earlier and published in 2020 in this journal. FRBCs operate on discrete outputs, i.e., class labels. The experimental contribution of this work includes designing the collection of FRBPSs for residential building energy consumption prediction using the data set published in 2024 and available from Kaggle Database Repository. Moreover, the comparison with 20 available alternative approaches is carried out, demonstrating that our approach significantly outperforms alternative methods in terms of interpretability and transparency of the energy consumption predictions made while remaining comparable or slightly superior in terms of the accuracy of those predictions.

Virtual Sound Image Reconstruction Method for Multi-objective Optimization of Folk Music Based on Evolutionary Algorithm

At present, the exchanges in various fields such as culture, economy, and politics are becoming more and more close in the world. From the perspective of the relationship between national music and cultural development, the development of national music has also received more and more attention, and it has become an inevitable trend in the development of today's era. The purpose of this paper was to perform virtual reconstruction of the sound image of folk music through multiple objective optimizations, and to model the virtual sound image of folk music as a multi-objective optimization problem. According to the research on sound image positioning, the relevant noise factors were removed, so as to achieve the playback of ethnic music that enhanced the surround effect and visual enjoyment. The evolutionary algorithm in this paper was mainly based on the multi-objective optimized sound image localization technology. For the music virtual sound image, an improved FCM algorithm and an evolutionary multi-objective optimization algorithm combining local and non-local information of the sound image were proposed, respectively. Through the analysis of the traditional sound image algorithm method, the accuracy of the sound image localization on the horizontal plane could be effectively improved. After the conversion, the audience could feel the better stereo image and surround feeling of the folk music. Through experimental analysis, it can be seen that the system can not only perform virtual conversion of audio-visual signals of different frequencies, but also provide data for different audio playback systems. The feature point registration error is low, and the reconstruction effect is good, especially the random delay processing in the range of 0∼20m, and the performance is better than the traditional method. Finally, virtual left and right surround sound image signals were obtained, which effectively improved the three-dimensional surround feeling of folk music.

A multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy

Multimodal multi-objective optimization problems (MMOPs), which aim to identify as many optimal solutions as possible and exhibit multiple equivalent Pareto optimal solution sets (PSs) that correspond to the same Pareto optimal front (PF), commonly arise in a wide range of optimization problems in the real world. However, some dominated solutions that exhibit greater diversity in the decision space may be substituted by non-dominated solutions with a higher level of decision space crowding. To tackle this issue, this paper proposes a multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy (MMODE_SPDN), which can balance convergence, objective space diversity and decision space diversity. Specifically, two archives are initially updated serially followed by the overall update of the parallel structure, in which the serial-first approach can enhance population diversity and the parallel structure can greatly reduce the amount of calculation. In addition, a dynamic neighbor strategy which utilizes adaptive selection among neighbors to generate difference vectors in the decision space and objective space and then adopts the main and auxiliary parent method during the mutation process is proposed. Furthermore, the utilization of an auxiliary archive and the clustering-based special crowding distance (CSCD) method are employed to facilitate the updating of the archive, thereby enhancing diversity. MMODE_SPDN is compared with other multimodal multi-objective optimization evolutionary algorithms (MMOEAs) on numerous test problems and the experimental results demonstrate that MMODE_SPDN exhibits superior performance.

A dynamic multi-objective optimization evolutionary algorithm with adaptive boosting

Dynamic multi-objective optimization problems (DMOPs) are prevalent in the real world, where the challenge in solving DMOPs is how to track the time-varying Pareto-optimal front (PF) and Pareto-optimal set (PS) quickly and accurately. However, balancing convergence and diversity is challenging as a single strategy can only address a particular type of DMOP. To solve this issue, a dynamic multi-objective optimization evolutionary algorithm with adaptive boosting (AB-DMOEA) is proposed in this paper. In the AB-DMOEA, an adaptive boosting response mechanism will increase the weights of high-performing strategies, including those based on prediction, memory, and diversity, which have been improved and integrated into the mechanism to tackle various problems. Additionally, the dominated solutions reinforcement strategy optimizes the population to ensure the effective operation of the above mechanism. In static optimization, the static optimization boosting mechanism selects the appropriate static multi-objective optimizer for the current problem. AB-DMOEA is compared with the other seven state-of-the-art DMOEAs on 35 benchmark DMOPs. The comprehensive experimental results demonstrate that the overall performance of the AB-DMOEA is superior or comparable to that of the compared algorithms. The proposed AB-DMOEA is also successfully applied to the smart greenhouses problem.

DpEA: A dual-population evolutionary algorithm for dynamic constrained multiobjective optimization

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are very difficult to solve because both of the objectives and constraints may change over time. The existing approaches for solving DCMOPs mainly develop dynamic response techniques and constraint handling techniques. But they do not focus on the search capability of the static optimizer in each environment, which ignores the intrinsic requirement of quickly locating Pareto-optimal Front (PF) in each environment when solving DCMOPs. To this end, this paper proposes a dual-population evolutionary algorithm for solving DCMOPs, called as DpEA, which maintains a population without considering constraints (called UP) for exploration and a population with considering constraints (called CP) for exploitation in each environment. In each iteration of a new environment, UP firstly adopts a stratified mutation strategy (SMS) and a dominated solution repairment strategy (DSR) to enhance the exploration ability of finding promising regions where the PF may reside. SMS uses solutions from different nondominated fronts to generate offspring, while DSR repairs the single-optimal variables of the dominated solutions by sampling from the distribution of those variables of nondominated solutions. Secondly, this paper uses an adaptive offspring ratio adjustment strategy to control the offspring number generated by UP and CP according to the normalized Hausdorff distance between nondominated solution sets from the two latest generations of UP. This strategy is helpful to balance the intensity between exploration and exploitation and thereby ensures efficient search. Experimental results on CEC 2023 DCF test suite show that DpEA has a superior performance over six state-of-the-art algorithms.

Accelerating surrogate assisted evolutionary algorithms for expensive multi-objective optimization via explainable machine learning

A series of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed to handle expensive multi-objective optimization problems (EMOPs). However, the surrogate of these SAEAs is underutilized to a large extent, which limits the search efficiency of these algorithms. To be specific, existing algorithms do not sufficiently exploit the estimated solution quality information from the surrogate models during offspring generation. To address this issue, this paper proposes an SAEA framework named EXO-SAEA (EXplanation Operator based Surrogate-Assisted Evolutionary Algorithm). First, it divides the current population into two populations according to the a priori knowledge from the surrogate model. Then, for each solution in the first population, EXO-SAEA employs the SHapley Additive exPlanations (SHAP) model to estimate the contribution of each decision variable to the fitness values. After that, the Shapley values are then normalized for the offspring generation of the first population, while the second population uses generic GA operators. Two representative surrogate-assisted evolutionary algorithms are used to instantiate the proposed framework. Experimental results on the synthetic benchmark problems and three real-world problems involving six state-of-the-art algorithms demonstrate the effectiveness of the proposed framework.

Two-stage sparse multi-objective evolutionary algorithm for channel selection optimization in BCIs.

Channel selection has become the pivotal issue affecting the widespread application of non-invasive brain-computer interface systems in the real world. However, constructing suitable multi-objective problem models alongside effective search strategies stands out as a critical factor that impacts the performance of multi-objective channel selection algorithms. This paper presents a two-stage sparse multi-objective evolutionary algorithm (TS-MOEA) to address channel selection problems in brain-computer interface systems. In TS-MOEA, a two-stage framework, which consists of the early and late stages, is adopted to prevent the algorithm from stagnating. Furthermore, The two stages concentrate on different multi-objective problem models, thereby balancing convergence and population diversity in TS-MOEA. Inspired by the sparsity of the correlation matrix of channels, a sparse initialization operator, which uses a domain-knowledge-based score assignment strategy for decision variables, is introduced to generate the initial population. Moreover, a Score-based mutation operator is utilized to enhance the search efficiency of TS-MOEA. The performance of TS-MOEA and five other state-of-the-art multi-objective algorithms has been evaluated using a 62-channel EEG-based brain-computer interface system for fatigue detection tasks, and the results demonstrated the effectiveness of TS-MOEA. The proposed two-stage framework can help TS-MOEA escape stagnation and facilitate a balance between diversity and convergence. Integrating the sparsity of the correlation matrix of channels and the problem-domain knowledge can effectively reduce the computational complexity of TS-MOEA while enhancing its optimization efficiency.