Multi-objective Evolutionary Algorithm Research Articles

Enhancing constrained MOEA/D with direct mating using hybrid mating strategies and diverse crossover methods

Abstract The direct mating strategy, which is a constraint-handling method in multi-objective evolutionary algorithms, selects a second parent on the basis of the optimal direction in the objective space, disregarding feasibility. This approach, although effective in early generations, encounters difficulties as solutions better than the current Pareto solutions become scarce, reducing diversity and hindering exploration. Herein, we introduce a hybrid approach that combines direct mating with newly proposed local mating strategies, aiming to generate offspring around the Pareto optimal solutions to improve the solution search performance via a direct mating strategy. Our method addresses the limitations of conventional direct mating, thereby improving its applicability to real-world design problems. Our hybrid strategy employs local mating to select an additional parent close to the initially chosen parent, preserving solution diversity and effectively exploring the solution space. This enhances the effectiveness of direct mating across all generations. In addition, we introduce two types of crossover methods, i.e., simulated binary crossover and differential evolution, for parents selected by direct and local mating, respectively. The synergy among these techniques facilitates a robust search process that can efficiently yield superior solutions. We evaluated the proposed approach using three mathematical problems with distinct Pareto fronts and two practical applications, including an aerospace design problem. The performances of these methods were assessed on the basis of the averages and standard deviations of the hypervolume and inverted generational distance metrics across multiple solution attempts to determine the average performances and the dependencies on initial population variance. The obtained results demonstrate that the hybrid method significantly outperforms the existing methods in the case of constrained multi-objective optimization. Specifically, the hybrid method yielded higher average hypervolumes and lower dependency on initial population variance than the existing methods. The hybrid method also yielded a lower average and less dependency on initial population variance in the inverted generational distance compared to existing methods. This result suggests that the proposed method can obtain high-quality non-dominated solutions, regardless of the initial population.

Revolutionizing population sparsity assessment: machine learning–powered solutions for multi-objective evolutionary algorithms

Decomposed multi-objective evolutionary algorithms have recently gained attention in research, with population sparsity often evaluated through Euclidean distance. However, individuals with high sparsity tend to be located along the edges of the Pareto front, whereas those with low sparsity cluster towards the centre. This article introduces a more accurate method for assessing individual sparsity in the objective space using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The contributions of this work include (1) identifying the limitations of using Euclidean distance for sparsity measurement, (2) mitigating DBSCAN sensitivity to input parameters through adaptive adjustment via a genetic algorithm and (3) integrating DBSCAN with multi-objective algorithms to address the limitations of Euclidean distance by leveraging core and boundary points. Experimental results on three benchmark test problems and an engineering application involving mechanical bearings highlight the proposed algorithm's strong performance and competitiveness.

A bi-subpopulation coevolutionary immune algorithm for multi-objective combinatorial optimization in multi-UAV task allocation

With the development of Unmanned Aerial Vehicle (UAV) technology towards multi-UAV and UAV swarm, multi-UAV cooperative task allocation has more and more influence on the success or failure of UAV missions. From the operational research point of view, such problems belong to high-dimensional combinatorial optimization problems, which makes the solving process face many challenges. One is that the discrete and high-dimensional decision variables make the quality of the solution obtained with acceptable time not guaranteed. Second, the desired solution of real missions often needs to satisfy multiple objective functions, or a set of solutions for decision-making. Therefore, this paper constructs a Multi-objective Combinatorial Optimization in Multi-UAV Task Allocation Problem (MCOTAP) model, and proposes a Bi-subpopulation Coevolutionary Immune Algorithm (BCIA). The two coevolutionary mechanisms improve the lower limit of population diversity, and the evolutionary strategy pool integrating multiple strategies and the adaptive strategy selection mechanism enhance the local search ability in the late evolution. In the experiments, BCIA competes fairly with the mainstream multi-objective evolutionary algorithms (MOEAs), multi-objective immune algorithms (MOIAs) and the recently proposed multi-UAV mission planning algorithms. The experimental results on different test problems (including several multi-objective combinatorial optimization benchmark problems and the proposed MCOTAP model) show that BCIA has superior performance in solving multi-objective combinatorial optimization problems (MCOPs). At the same time, the effectiveness of each design component of BCIA has been comprehensively verified in the ablation study.

Runtime Analysis of Typical Decomposition Approaches in MOEA/D for Many-Objective Optimization Problems.

Decomposition-based multi-objective evolutionary algorithms (MOEAs) are popular methods utilized to address many-objective optimization problems (MaOPs). These algorithms decompose the original MaOP into several scalar optimization subproblems, and solve them to obtain a set of solutions to approximate the Pareto front (PF). The decomposition approach is an important component in them. This paper presents a runtime analysis of a MOEA based on the classic decomposition framework using the typical weighted sum (WS), Tchebycheff (TCH), and penalty-based boundary intersection (PBI) approaches to obtain an optimal solution for any subproblem of two pseudo-Boolean benchmark MaOPs, namely mLOTZ and mCOCZ. Due to the complexity and limitation of the theoretical analysis techniques, the analyzed algorithm employs one-bit mutation to generate offspring individuals. The results indicate that when using WS, the analyzed algorithm can consistently find an optimal solution for every subproblem, which is located in the PF, in polynomial expected runtime. In contrast, the algorithm requires at least exponential expected runtime (with respect to the number of objectives m) for certain subproblems when using TCH or PBI, even though the landscapes of all objective functions in the two benchmarks are strictly monotone. Moreover, this analysis reveals a drawback of using WS: the optimal solutions obtained by solving subproblems are more easily mapped to the same point in the PF, compared to the case of using TCH. When using PBI, a smaller value of the penalty parameter is a good choice for faster convergence to the PF but may compromise diversity. To further understand the impact of these approaches in practical algorithms, numerical experiments on using bit-wise mutation to generate offspring individuals are conducted. The findings of this study may be helpful for designing more efficient decomposition approaches for MOEAs in future research.

Many-Objective Truss Structural Optimization Considering Dynamic and Stability Behaviors

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss).

Human-robot cooperation two-sided partial disassembly line balancing problem

Considering the complexities, risks, and uncertainties of disassembling large end-of-life (EOL) products such as cars and buses, a two-sided human-robot disassembly line can utilise both sides of the workstations to enhance efficiency, improve safety, and increase revenue. This paper develops a human-robot cooperation two-sided partial disassembly line balancing model (TPDLB-HRC) to minimise energy consumption and maximise net revenue by addressing four interrelated sub-problems: planning disassembly sequences, selecting disassembly tasks, assigning tasks to mated-stations, and allocating human-robot resources. In addition, a new reinforcement-learning multi-objective evolutionary algorithm based on decomposition (NRL-MOEA/D) is developed, integrating an encoding/decoding scheme, reinforcement learning, problem characteristics, and coevolution between sub-problems to address the above challenges. The effectiveness and superiority of the designed NRL-MOEA/D in solving various cases are tested by comparing it with eleven algorithms. Finally, the applicability of the proposed method is verified by a series of EOL examples, and trade-offs are made under different recycling profits to guide decision-makers in constructing disassembly schemes in real situations.

A Decomposition-Based Evolutionary Algorithm with Neighborhood Region Domination.

The decomposition-based multi-objective optimization algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) introduces the concept of neighborhood, where each sub-problem requires optimization through solutions within its neighborhood. Due to the comparison being only with solutions in the neighborhood, the obtained set of solutions is not sufficiently diverse, leading to poorer convergence properties. In order to adequately acquire a high-quality set of solutions, this algorithm requires a large number of population iterations, which in turn results in relatively low computational efficiency. To address this issue, this paper proposes an algorithm termed MOEA/D-NRD, which is based on neighborhood region domination in the MOEA/D framework. In the improved algorithm, domination relationships are determined by comparing offspring solutions against neighborhood ideal points and neighborhood worst points. By selecting appropriate solution sets within these comparison regions, the solution sets can approach the ideal points more and faster, thereby accelerating population convergence and enhancing the computational efficiency of the algorithm.

Comprehensive benefit evaluation of mineral resources development based on dual population constrained multi-objective evolutionary algorithm

With the increasing global demand for mineral resources, the comprehensive benefit evaluation of mineral resources development is playing an increasingly important role in the field of mineral resources development. However, there are few attempts to use multi-objective evolutionary algorithms (MOEAs) to study the comprehensive benefit evaluation problem of mineral resources development. To effectively solve this problem, this study established a multi-objective optimization model for comprehensive benefit evaluation of mineral resources development and proposed a dual-population constrained multi-objective evolutionary algorithm (CMOEA). The algorithm uses two populations to organically combine the efficient convergence of the non-dominated sorting genetic algorithm II (NSGA-II) with the advantage of the adaptive geometry estimation based multi-objective evolutionary algorithm (AGE-MOEA) in estimating the shape of the Pareto front, named co-evolution based on non-dominated sorting genetic algorithm and adaptive geometry estimation (C-NSGA-AGE). 3 test suites are used to verify the performance of the proposed algorithm. Experimental results show that compared with competing algorithms, C-NSGA-AGE has strong competitiveness in most test functions. The proposed method is used to solve the model, and five optimal comprehensive benefit evaluation schemes are given for different objectives. Among them, the maximum benefit is obtained when each objective is developed in a balanced way, which reaches 0.837181.

ParetoTracker: Understanding Population Dynamics in Multi-objective Evolutionary Algorithms through Visual Analytics.

Multi-objective evolutionary algorithms (MOEAs) have emerged as powerful tools for solving complex optimization problems characterized by multiple, often conflicting, objectives. While advancements have been made in computational efficiency as well as diversity and convergence of solutions, a critical challenge persists: the internal evolutionary mechanisms are opaque to human users. Drawing upon the successes of explainable AI in explaining complex algorithms and models, we argue that the need to understand the underlying evolutionary operators and population dynamics within MOEAs aligns well with a visual analytics paradigm. This paper introduces ParetoTracker, a visual analytics framework designed to support the comprehension and inspection of population dynamics in the evolutionary processes of MOEAs. Informed by preliminary literature review and expert interviews, the framework establishes a multi-level analysis scheme, which caters to user engagement and exploration ranging from examining overall trends in performance metrics to conducting fine-grained inspections of evolutionary operations. In contrast to conventional practices that require manual plotting of solutions for each generation, ParetoTracker facilitates the examination of temporal trends and dynamics across consecutive generations in an integrated visual interface. The effectiveness of the framework is demonstrated through case studies and expert interviews focused on widely adopted benchmark optimization problems.

A multi-objective multi-task evolutionary algorithm based on source task transfer

A multi-objective multi-task evolutionary algorithm based on source task transfer

Holt-based Prediction Correction Dynamic Multi-Objective Evolutionary Algorithm for IoT with UAV in Aerial Edge Computing

Holt-based Prediction Correction Dynamic Multi-Objective Evolutionary Algorithm for IoT with UAV in Aerial Edge Computing

A repulsive-distance-based maximum diversity selection algorithm for multimodal multiobjective optimization

Multimodal multiobjective optimization problems (MMOPs) are a challenging class of problems. Several advanced evolutionary algorithms have been developed to solve MMOPs, but these algorithms still have some limitations, such as having many parameters, slow convergence speed, and unsatisfactory performance. To solve these problems, we propose a repulsive-distance-based maximum diversity selection algorithm (RMDS) which aims, during environmental selection, to select individuals with the best comprehensive diversity through the repulsive distance. The repulsive distance is the comprehensive Euclidean distance between an individual and selected individuals with the consideration of distribution of individuals in both the decision and objective spaces. RMDS has the following advantages: first, the repulsive distance allows rational selection of well-distributed solutions in the non-parameterized case. Second, the repulsive distance acts both in the decision and objective spaces, so it provides a good balance between the distribution of the solution set in these two spaces. Third, RDMS has a straightforward principle. Experimental results show that RMDS has superior performance incomparison with other well-known multimodal multiobjective evolutionary algorithms on 31 test functions.

Knowledge-aware evolutionary graph neural architecture search

Graph neural architecture search (GNAS) can customize high-performance graph neural network architectures for specific graph tasks or datasets. However, existing GNAS methods begin searching for architectures from a zero-knowledge state, ignoring the prior knowledge that may improve the search efficiency. The available knowledge base (e.g. NAS-Bench-Graph) contains many rich architectures and their multiple performance metrics, such as the accuracy (#Acc) and number of parameters (#Params). This study proposes exploiting such prior knowledge to accelerate the multi-objective evolutionary search on a new graph dataset, named knowledge-aware evolutionary GNAS (KEGNAS). KEGNAS employs the knowledge base to train a knowledge model and a deep multi-output Gaussian process (DMOGP) in one go, which generates and evaluates transfer architectures in only a few GPU seconds. The knowledge model first establishes a dataset-to-architecture mapping, which can quickly generate candidate transfer architectures for a new dataset. Subsequently, the DMOGP with architecture and dataset encodings is designed to predict multiple performance metrics for candidate transfer architectures on the new dataset. According to the predicted metrics, non-dominated candidate transfer architectures are selected to warm-start the multi-objective evolutionary algorithm for optimizing the #Acc and #Params on a new dataset. Empirical studies on NAS-Bench-Graph and five real-world datasets show that KEGNAS swiftly generates top-performance architectures, achieving 4.27% higher accuracy than advanced evolutionary baselines and 11.54% higher accuracy than advanced differentiable baselines. In addition, ablation studies demonstrate that the use of prior knowledge significantly improves the search performance.

Surrogate-assisted decomposition multi-objective evolutionary algorithm for parameters optimization in polyester fiber polymerization process

Surrogate-assisted decomposition multi-objective evolutionary algorithm for parameters optimization in polyester fiber polymerization process

Multi-Objective Optimization of the Layout of Tall Building Sites in Dense Urban Configurations for Improved Sustainability Outcomes

Multi-objective evolutionary algorithms have long been used by architects to find objective solutions to complex building problems involving trade-offs implicit in sustainable building design. At a larger scale, urban designers have created a variety of tools to improve sustainability in urban-and-larger scale design. However, to date, fewer studies have focused on improving sustainability outcomes at the “in between” scale of the neighborhood and urban site. Existing scholarship on optimization at this scale has tended to take a narrow view of sustainability. We seek to expand the implementation of multi-objective evolutionary algorithms to this sometimes overlooked scale while taking a broad view of sustainability which includes social, environmental, and economic design factors. In doing so, we argue this optimization method is uniquely well suited to help designers balance the sometimes competing demands of multiple axes of sustainability which are applicable to design at this larger-than-building scale. In demonstrating the application of such an algorithm to a hypothetical problem in Chicago, we find the method offers a promising way of narrowing potential design solutions. Finally, we discuss the suitability of the solutions generated, the virtues and shortcomings of the method, and offer areas for future study.

OPTIMIZING DISTRIBUTED DATA STORAGE IN MULTI-CLOUD ENVIRONMENTS: ALGORITHMIC APPROACH

Background. Multi-cloud environments present complex challenges in optimal resource allocation and provider selection. Previous research has established a comprehensive ontological model and evaluation criteria for distributed data storage, however efficient provider selection remains a significant challenge due to the dynamic nature of cloud services and the multitude of interdependent factors affecting performance and cost-effectiveness. Objective. The purpose of the paper is to develop and validate a sophisticated optimization function for cloud provider selection in multi-cloud environments, incorporating both Reinforcement Learning (RL) and Multi-Objective Evolutionary Algorithms (MOEAs) to address the complexity of provider selection while considering multiple competing objectives and constraints. Methods. The research employs an ontological approach to formalize domain concepts, relationships, and properties in multi-cloud environments. Additionally, an optimization function is developed incorporating multiple weighted criteria derived from the established ontological model. The study focuses on the implementation of the RL algorithm to adapt to dynamic changes in cloud provider characteristics and integration of MOEAs to handle multiple competing objectives as well as providing a comparative analysis with traditional selection methods and alternative optimization approaches for multi-cloud storage settings. Results. The proposed ontological model successfully formalizes the domain's concepts, relationships, and properties in multi-cloud environments. The optimization function demonstrates effectiveness in selecting the most suitable public cloud provider based on the proposed features, enhancing data management practices automation and decision-making processes. Conclusions. The developed optimization function and suggested methodology significantly advance the state-of-the-art in distributed multi-cloud data storage. The integration of RL and MOEAs provides a robust framework for addressing the complexity of multi-cloud environments while offering superior performance compared to existing approaches. The methodology successfully balances multiple objectives while adapting to dynamic changes in cloud provider characteristics.

A Hybrid Food Recommendation System Based on MOEA/D Focusing on the Problem of Food Nutritional Balance and Symmetry

With the improvement of people’s living standards, the issue of dietary health has received extensive attention. In order to simultaneously meet people’s demands for dietary preferences and nutritional balance, we have conducted research on the issue of personalized food recommendations. For this purpose, we have proposed a hybrid food recommendation model, which can provide users with scientific, reasonable, and personalized dietary advice. Firstly, the collaborative filtering (CF) algorithm is adopted to recommend foods to users; then, the improved Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is used to adjust the nutritional balance and symmetry of the recommended foods. In view of the existing problems in the current nutritional balance algorithm, such as slow convergence speed and insufficient local search ability, the autonomous optimization (AO) adjustment strategy, the self-adaptive adjustment strategy, and the two-sided mirror principle to optimize boundary strategy are introduced in the MOEA/D. According to the characteristics of the food nutrition regulation problem, an adaptive food regulation (AFR) adjustment strategy is designed to achieve more accurate nutritional regulation. Based on the above improvements, a food nutritional recommendation algorithm based on MOEA/D (FNR-MOEA/D) is proposed. Experiments show that compared with MOPSO, MOABC, and RVEA, FNR-MOEA/D performs more superiorly in solving the problem of nutritional balance in food recommendation.

Division-selection transfer learning for prediction based dynamic multi-objective optimization

Dynamic multi-objective optimization problems (DMOPs) are challenging as they require capturing the Pareto optimal front (POF) and Pareto optimal set (POS) during the optimization process. In recent years, transfer learning (TL) has emerged the empirical knowledge and is an effective approach to solve DMOPs. However, negative transfer can occur when the transfer method is not suitable for the transfer task. It may deviate the search path and seriously reduce the efficiency, so how to reduce the occurrence of negative transfer to save the running time of dynamic multi-objective evolutionary algorithm (DMOEA) is an important issue to be addressed. A division-selection transfer learning evolutionary algorithm for dynamic multi-objective optimization (DST-DMOEA) is designed towards this aim. Specifically, individuals with high Spearman correlation are relatively stable in different environments, selecting them to train the Support Vector Regression (SVR) model ensures a more accurate capture of solution features, predicting the objective values of historical solutions based on the model, and thus divide historical solutions into elite and non-elite solutions. Subsequently, for the elite solutions, individual TL that incorporates local information for optimization and transfer is used, while the non-elite solutions are handled with manifold TL method to obtain the overall data distribution and understand the internal structure. Then, merge the predicted individuals generated by two parts of TL will constitute as the initial population in the optimization process. Compared with other algorithms, the initial solution of DST-DMOEA is closer to the real POF, effectively reducing negative transfer. In addition, in 51 test instances, DST-DMOEA has shown superior performance in over 30 instances.

Efficiency multi-agent model assisted Moea/D algorithm for optimization design for building taking into account annual energy consumption and annual user discomfort hours

Recently, with the continuous consumption of energy, building energy conservation has been popular in the energy field. In response to the high computational cost, slow convergence speed, and low accuracy of existing optimization design methods for building energy efficiency, this study first built a multi-objective optimization model for building energy efficiency on the ground of the annual energy consumption of buildings and the quantity of uncomfortable hours for users. Then it introduces a multi-agent model auxiliary mechanism to improve the decomposition based multi-objective evolutionary optimization algorithm, and then solves the multi-objective optimization model for building energy efficiency. In order to select the optimal decision variable of the algorithm, the decision parameters were analyzed and found that the performance was optimal when the number of samples, aggregation number and base model were set to 25.3 and 20. The improved multi-objective evolutionary optimization algorithm on the ground of decomposition has average supervolume and running time values of 32416.13 and 1774.58 seconds under office buildings, and 7899.13 and 3616.96 seconds under residential buildings, respectively. In addition, the annual user discomfort time of office buildings is 555.28h, which is lower than other comparison algorithms. In summary, the optimal performance of the algorithm when the decision variable is set to 25.3 and 20. The algorithm proposed by the research institute has superior performance and has certain application value in selecting the optimal solution for building energy-saving design.

PASS: Portfolio Analysis of Selecting Strategies on quantitative trading via NSGA-II

Quantitative trading, driven by technological advancements, utilizes machine learning and mathematical models to develop trading strategies. Evaluating strategy performance through backtesting is common, but ensuring sufficient funding and stability is crucial. Portfolio construction mitigates risk and promotes sustained profit growth. This article introduces the portfolio analysis of selecting strategies (PASS) model, integrating a stability indicator, ‘drawdown duration’ (DDD) and multi-objective evolutionary algorithms (MOEAs). Results demonstrate that PASS reduces DDD risk by 73.9% and increases profit by 4.1% compared to other MOEAs. The model is applied successfully to trading markets like the New York Mercantile Exchange (NYMEX), the West Texas Intermediate (WTI) and the Mini Dow Jones Industrial Average (YM), aiding investors in crafting profitable strategies and managing risk in leveraged trades.