Many-objective Optimization Research Articles

Research on Multi-Objective Evolutionary Algorithms Based on Large-Scale Decision Variable Analysis

Large-scale high-dimensional many-objective optimization problems (LaMaOPs) are prevalent in fields such as autonomous driving, cloud resource scheduling, and smart grids. LaMaOPs involve a large number of decision variables and multiple conflicting objectives that need to be optimized simultaneously. The challenges posed by the curse of dimensionality due to the vast number of decision variables, and the conflict between convergence and diversity caused by the numerous objective variables, make traditional optimization methods inadequate. To address these issues, this paper proposes a two-population cooperative evolutionary algorithm based on large-scale decision variable analysis (DVA-TPCEA). This algorithm integrates quantitative analysis methods for decision variables to deeply examine their impact on each objective and introduces a contribution-based objective detection method. Additionally, a dual-population cooperative evolution mechanism is employed, with targeted optimization strategies designed for convergence and diversity populations, achieving synergistic and complementary optimization between the two populations. To validate the algorithm’s effectiveness in practical applications, a large-scale container resource scheduling strategy based on the DVA-TPCEA algorithm is also proposed. The experimental results indicate that the proposed algorithm demonstrates significant advantages in both general datasets DTLZ, WFG, and LSMOP, and practical models.

Symmetrical Generalized Pareto Dominance and Adjusted Reference Vector Cooperative Evolutionary Algorithm for Many-Objective Optimization

Symmetrical Generalized Pareto Dominance and Adjusted Reference Vector Cooperative Evolutionary Algorithm for Many-Objective Optimization

Many-objective optimization algorithm based on the similarity principle and multi-mechanism collaborative search

Many-objective optimization algorithm based on the similarity principle and multi-mechanism collaborative search

A many-objective optimization approach to design office building façade considering energy-daylight balance concept within prevalent climate types of Iran

The concept of energy-daylight balance in architectural design aims to maximize daylighting while reducing energy consumption. Many parameters influence this concept, although they are not necessarily of equal importance in different climates. This study aims to identify the appropriate weight distribution sets (WDSs) for the most influential parameters of the energy-daylight balance concept, namely energy efficiency, daylighting, visual comfort, and thermal comfort, under the prevalent climate types of Iran. To this end, a many-objective optimization algorithm (NSGA-III) is applied to a parametric design procedure involving design variables related to the window system and a proposed shading system, leading to the identification of the most optimal façade designs for office buildings in each climate. Next, a weighted sum method (WSM) evaluates the Pareto-optimal solutions of each climate type based on nine different WDSs. Analyzing the absolute Pareto-optimal solutions, which are the solutions with the highest WSM scores within each WDS in each climate, reveals that, depending on the climate, prioritizing daylighting, thermal comfort, or energy efficiency objectives leads to the highest overall performances within these solutions. Furthermore, the Friedman test results show that in the design of office buildings in Bandar Abbas, Isfahan, Rasht, or Tehran, the most optimal trade-off between the objectives generally occurs by prioritizing energy efficiency, whereas in Dezful, it is generally achieved by prioritizing daylighting. However, pairwise comparisons of the WDSs reveal that in each climate, there are a number of pairs of sets that are not significantly different.

Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

In order to better balance the convergence and diversity of MOEA/D for many objective optimization problems (MaOPs) with various Pareto fronts (PFs), an adaptive decomposition-based evolutionary algorithm for MaOPs with two-stage dual-density judgment is proposed. To solve the problem that weighted Tchebycheff decomposition may produce weakly Pareto optimal solutions when the solution is not unique or the uniqueness is difficult to guarantee, an augmented weighted Tchebycheff decomposition is adopted. To balance the convergence and diversity of non-dominated solutions in the external archive, different sparsity-level evaluations using vector angles or Euclidean distances are used to measure the distribution of solutions at different stages. To improve the diversity of solution sets obtained by MOEA/D for various PFs, an adaptive weight vector adjustment method based on two-stage dual-density judgment is presented. For weight vector addition, the potential search area is found according to the two-stage density judgment, and then a two-stage sparsity level judgment on the solutions of this area is performed for a second density judgment. For weight vector deletion, the degree of crowding is used to delete the weight vectors with a high crowding degree. Compared with nine advanced multi-objective optimization algorithms on DTLZ and WFG problems, the results demonstrate that the performance of the proposed algorithm is significantly better than other algorithms.

An adaptive transfer strategy guided by reference vectors for many-objective optimization problems

An adaptive transfer strategy guided by reference vectors for many-objective optimization problems

Multi-indicator collaborative evolutionary algorithm for many-objective optimization

Multi-indicator collaborative evolutionary algorithm for many-objective optimization

Advancing SWAT Model Calibration: A U-NSGA-III-Based Framework for Multi-Objective Optimization

In recent years, remote sensing data have revealed considerable potential in unraveling crucial information regarding water balance dynamics due to their unique spatiotemporal distribution characteristics, thereby advancing multi-objective optimization algorithms in hydrological model parameter calibration. However, existing optimization frameworks based on the Soil and Water Assessment Tool (SWAT) primarily focus on single-objective or multiple-objective (i.e., two or three objective functions), lacking an open, efficient, and flexible framework to integrate many-objective (i.e., four or more objective functions) optimization algorithms to satisfy the growing demands of complex hydrological systems. This study addresses this gap by designing and implementing a multi-objective optimization framework, Py-SWAT-U-NSGA-III, which integrates the Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III). Built on the SWAT model, this framework supports a broad range of optimization problems, from single- to many-objective. Developed within a Python environment, the SWAT model modules are integrated with the Pymoo library to construct a U-NSGA-III algorithm-based optimization framework. This framework accommodates various calibration schemes, including multi-site, multi-variable, and multi-objective functions. Additionally, it incorporates sensitivity analysis and post-processing modules to shed insights into model behavior and evaluate optimization results. The framework supports multi-core parallel processing to enhance efficiency. The framework was tested in the Meijiang River Basin in southern China, using daily streamflow data and Penman–Monteith–Leuning Version 2 (PML-V2(China)) remote sensing evapotranspiration (ET) data for sensitivity analysis and parallel efficiency evaluation. Three case studies demonstrated its effectiveness in optimizing complex hydrological models, with multi-core processing achieving a speedup of up to 8.95 despite I/O bottlenecks. Py-SWAT-U-NSGA-III provides an open, efficient, and flexible tool for the hydrological community that strives to facilitate the application and advancement of multi-objective optimization in hydrological modeling.

A population hierarchical-based evolutionary algorithm for large-scale many-objective optimization

In large-scale many-objective optimization problems (LMaOPs), the performance of algorithms faces significant challenges as the number of objective functions and decision variables increases. The main challenges in addressing this type of problem are as follows: the large number of decision variables creates an enormous decision space that needs to be explored, leading to slow convergence; and the high-dimensional objective space presents difficulties in selecting dominant individuals within the population. To address this issue, this paper introduces an evolutionary algorithm based on population hierarchy to address LMaOPs. The algorithm employs different strategies for offspring generation at various population levels. Initially, the population is categorized into three levels by fitness value: poorly performing solutions with higher fitness (Ph), better solutions with lower fitness (Pl), and excellent individuals stored in the archive set (Pa). Subsequently, a hierarchical knowledge integration strategy (HKI) guides the evolution of individuals at different levels. Individuals in Pl generate offspring by integrating differential knowledge from Pa and Ph, while individuals in Ph generate offspring by learning prior knowledge from Pa. Finally, using a cluster-based environment selection strategy balances population diversity and convergence. Extensive experiments on LMaOPs with up to 10 objectives and 5000 decision variables validate the algorithm’s effectiveness, demonstrating superior performance.

Zone-based many-objective building decarbonization considering outdoor temperature and occupation uncertainty

Operational building decarbonization is challenging due to complex weather conditions and occupation uncertainty. This paper introduces a precise optimization framework integrating the building information modelling technique and intelligent algorithms to dynamically predict multi-scenario building carbon emissions and optimize the building emissions performance considering building zones and weather conditions. Firstly, the on-site data and building information modeling-supported building emissions simulation data are collected for model training. Secondly, using intelligent algorithms, zone-based hourly carbon emissions and multi-scenario carbon emissions prediction are conducted simultaneously. Thirdly, the optimal decarbonization strategies are conducted using intelligent algorithms under various weather conditions. This framework has been verified for decarbonization in a high-rise operational building. The results reveal that: (1) The carbon emissions prediction is highly consistent with the ground truth after considering the sub-zone correlations; the R2 for the west, south, and east zones are 0.900, 0.900, and 0.942, respectively; (2) The surrogate models can accurately predict carbon emissions and thermal comforts with all R2 are higher than 0.912. The optimization rate of the building reaches 59.2 % while the outdoor temperature is above 35 °C. (3) In the many-objective optimization model, considering occupation uncertainty makes the strategy close to the actual situation, reaching the decarbonization by 6815.23 kg compared to the empirical operation for the cooling period. This work provides a new path for operational building precise management and control-oriented optimization decarbonization.

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

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

An Improved NSGA-III with a Comprehensive Adaptive Penalty Scheme for Many-Objective Optimization

Pareto dominance-based algorithms face a significant challenge in handling many-objective optimization problems. As the number of objectives increases, the sharp rise in non-dominated individuals makes it challenging for the algorithm to differentiate their quality, resulting in a loss of selection pressure. The application of the penalty-based boundary intersection (PBI) method can balance convergence and diversity in algorithms. The PBI method guides the evolution of individuals by integrating the parallel and perpendicular distances between individuals and reference vectors, where the penalty factor is crucial for balancing these two distances and significantly affects algorithm performance. Therefore, a comprehensive adaptive penalty scheme was proposed and applied to NSGA-III, named caps-NSGA-III, to achieve balance and symmetry between convergence and diversity. Initially, each reference vector’s penalty factor is computed based on its own characteristic. Then, during the iteration process, the penalty factor is adaptively adjusted according to the evolutionary state of the individuals associated with the corresponding reference vector. Finally, a monitoring strategy is designed to oversee the penalty factor, ensuring that adaptive adjustments align with the algorithm’s needs at different stages. Through a comparison involving benchmark experiments and two real-world problems, the competitiveness of caps-NSGA-III was demonstrated.

Sustainable Operation Strategy for Wet Flue Gas Desulfurization at a Coal-Fired Power Plant via an Improved Many-Objective Optimization

Coal-fired power plants account for a large share of the power generation market in China. The mainstream method of desulfurization employed in the coal-fired power generation sector now is wet flue gas desulfurization. This process is known to have a high cost and be energy-/materially intensive. Due to the complicated desulfurization mechanism, it is challenging to improve the overall sustainability profile involving energy-, cost-, and resource-relevant objectives via traditional mechanistic models. As such, the present study formulated a data-driven many-objective model for the sustainability of the desulfurization process. We preprocessed the actual operation data collected from the desulfurization tower in a domestic ultra-supercritical coal-fired power plant with a 600 MW unit. The extreme random forest algorithm was adopted to approximate the objective functions as prediction models for four objectives, namely, desulfurization efficiency, unit power consumption, limestone supply, and unit operation cost. Three metrics were utilized to evaluate the performance of prediction. Then, we incorporated differential evolution and non-dominated sorting genetic algorithm-III to optimize the multiple parameters and obtain the Pareto front. The results indicated that the correlation coefficient (R2) values of the prediction models were greater than 0.97. Compared with the original operation condition, the operation under optimized parameters could improve the desulfurization efficiency by 0.25% on average and reduce energy, cost, and slurry consumption significantly. This study would help develop operation strategies to improve the sustainability of coal-fired power plants.

Aiding decision makers in articulating a preference closeness model through compensatory fuzzy logic for many-objective optimization problems

One of the main challenges in applying preference-based approaches to many-objective optimization problems is that decision makers (DMs) initially have only a vague notion of the solution they want and can obtain. In this paper, we propose an interactive approach that aids DMs in articulating a preference model in a progressive way. The quality of a solution is determined in terms of its “preference closeness” to an aspiration point, which is a subjective concept that can be outlined by the DM. Our proposal is based on compensatory fuzzy logic, which allows for the construction of predicates that are expressed in language that is close to natural. One main advantage is that the model can be optimized via metaheuristics, and we utilize an ant colony optimization algorithm for this. Our model complies with the principles of hybrid augmented intelligence, not only because the algorithm is enriched with knowledge from the DM, but also because the DM also learns the concept of “preference closeness” throughout the process. The proposed model is validated on benchmarks with five and 10 objective functions, and is compared with two state-of-the-art algorithms. Our approach allows for better convergence to the best compromise solutions. The advantages of our approach are supported by statistical tests of the results.

An agent-based cooperative co-evolutionary framework for optimizing the production planning of energy supply chains under uncertainty scenarios

Nowadays, energy and power companies compete to get the raw materials and equipment they need on time, as project times lengthen, costs spiral, stock-out continues to plague plans to a decarbonized energy future. The risks reflect the impact of uncertainty and volatility on the resilience of the supply chains. Therefore, there is a need for the enhancement of the production planning in Energy Supply Chains (ESCs), as it enables affordable energy supplies and supports the companies transition to a clean, secure and sustainable energy mix. This study aims to understand the interactive behavior among individuals and optimize their production planning under uncertainty scenarios. In particular, we propose a novel framework to couple an Agent-based Modelling (ABM) and a Co-evolutionary Algorithm (CEA), to realize its capacity to solve a Many-objective Optimization Problem (MaOP) where the profits of multiple agents are concurrently maximized in their interactive transaction processes under normal conditions and uncertain disruption events.For demonstration, we illustrate the proposed approach by considering a five-layer oil and gas ESC model, where uncertainties from multiple sources and the structural dynamics challenge the balance between supply and demand. The results obtained by an integration of a Cooperative Co-evolutionary Particle Swarm Optimizer (CCPSO) algorithm into ABM show the pricing and orders of the target agents are optimized while the loss of ESC resilience is minimized under uncertainty scenarios, proving its capacity of improving the diversity and the convergence, compared to the classic evolutionary algorithms.

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

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

Wind power forecasting based on ensemble deep learning with surrogate-assisted evolutionary neural architecture search and many-objective federated learning

Deep neural networks (DNN) have been widely used in wind power forecasting (WPF), however, they still encounter difficulties such as delayed variable selection, DNN architecture design, and network weight optimization. Therefore, an ensemble cascaded DNN (ECDNN) with surrogate-assisted evolutionary neural architecture search (SEANS) and many-objective federated learning (MOFL) is proposed and referred to as ECDNN-SENAS-MOFL. SEANS is proposed to determine the delayed variables and network architecture efficiently, which allows significantly enhancing the evolutionary search efficiency than traditional evolutionary neural architecture search (ENAS) approaches by employing a surrogate model to achieve fast fitness evaluations. Meanwhile, MOFL is developed by embedding the federated learning into many-objective optimization to obtain more reliable network weights based on the distributed modeling data than traditional centralized learning and federated learning, as well as solving the problems of data privacy protection and data islands. Furthermore, selective ensemble learning is introduced to build high-performance ensemble WPF model by combining the merits of multiple highly influential Pareto solutions. The effectiveness and superiority of the proposed ECDNN-SENAS-MOFL method are verified using an actual wind power dataset. The application results show that the proposed method can provide new insights into data-driven WPF modeling and has a great potential for practical applications.

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

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

Many-Objective Grasshopper Optimization Algorithm (MaOGOA): A New Many-Objective Optimization Technique for Solving Engineering Design Problems

In metaheuristic multi-objective optimization, the term effectiveness is used to describe the performance of a metaheuristic algorithm in achieving two main goals—converging its solutions towards the Pareto front and ensuring these solutions are well-spread across the front. Achieving these objectives is particularly challenging in optimization problems with more than three objectives, known as many-objective optimization problems. Multi-objective algorithms often fall short in exerting adequate selection pressure towards the Pareto front in these scenarios and difficult to keep solutions evenly distributed, especially in cases with irregular Pareto fronts. In this study, the focus is on overcoming these challenges by developing an innovative and efficient a novel Many-Objective Grasshopper Optimisation Algorithm (MaOGOA). MaOGOA incorporates reference point, niche preserve and information feedback mechanism (IFM) for superior convergence and diversity. A comprehensive array of quality metrics is utilized to characterize the preferred attributes of Pareto Front approximations, focusing on convergence, uniformity and expansiveness diversity in terms of IGD, HV and RT metrics. It acknowledged that MaOGOA algorithm is efficient for many-objective optimization challenges. These findings confirm the approach effectiveness and competitive performance. The MaOGOA efficiency is thoroughly examined on WFG1-WFG9 benchmark problem with 5, 7 and 9 objectives and five real-world (RWMaOP1- RWMaOP5) problem, contrasting it with MaOSCA, MaOPSO, MOEA/DD, NSGA-III, KnEA, RvEA and GrEA algorithms. The findings demonstrate MaOGOA superior performance against these algorithms.

Optimal Design Study of Metal-as-Insulation HTS Synchronous Motor With Multiple Operating Points for EVs Based on Many-Objective Optimization

Optimal Design Study of Metal-as-Insulation HTS Synchronous Motor With Multiple Operating Points for EVs Based on Many-Objective Optimization