Many-objective Optimization Method Research Articles

Many-objective artificial hummingbird algorithm: an effective many-objective algorithm for engineering design problems

Abstract Many-objective optimization presents unique challenges in balancing diversity and convergence of solutions. Traditional approaches struggle with this balance, leading to suboptimal solution distributions in the objective space especially at higher number of objectives. This necessitates the need for innovative strategies to adeptly manage these complexities. This study introduces a Many-Objective Artificial Hummingbird Algorithm (MaOAHA), an advanced evolutionary algorithm designed to overcome the limitations of existing many-objective optimization methods. The objectives are to improve convergence rates, maintain solution diversity, and achieve a uniform distribution in the objective space. MaOAHA implements information feedback mechanism (IFM), reference point-based selection and association, non-dominated sorting, and niche preservation. The IFM utilizes historical data from previous generations to inform the update process, thereby improving the algorithm’s the exploration and exploitation capabilities. Reference point-based selection, along with non-dominated sorting, ensures solutions are both close to the Pareto front and evenly spread in the objective space. Niche preservation and density estimation strategies are employed to maintain diversity and prevent overcrowding. The comprehensive experimental analysis benchmarks MaOAHA against four leading algorithms viz. Many-Objective Gradient-Based Optimizer, Many-Objective Particle Swarm Optimizer, Reference Vector Guided Evolutionary Algorithm, and Nondominated Sorting Genetic Algorithm III. The DTLZ1–DTLZ7 benchmark sets with four, six, and eight objectives and five real-world problems (RWMaOP1–RWMaOP5) are considered for performance assessment of the selected algorithms. The results demonstrate that internal parameter-free MaOAHA significantly outperforms its counterparts, achieving better generational distance by up to 52.38%, inverse generational distance by up to 38.09%, spacing by up to 56%, spread by up to 71.42%, hypervolume by up to 44%, and runtime by up to 52%. These metrics affirm the MaOAHA’s capability to enhance the decision-making processes through its adept balance of convergence, diversity, and uniformity.

A Mutual Information-Based Many-Objective Optimization Method for EEG Channel Selection in the Epileptic Seizure Prediction Task

A Mutual Information-Based Many-Objective Optimization Method for EEG Channel Selection in the Epileptic Seizure Prediction Task

Multi-and many-objective optimization: present and future in de novo drug design.

de novo Drug Design (dnDD) aims to create new molecules that satisfy multiple conflicting objectives. Since several desired properties can be considered in the optimization process, dnDD is naturally categorized as a many-objective optimization problem (ManyOOP), where more than three objectives must be simultaneously optimized. However, a large number of objectives typically pose several challenges that affect the choice and the design of optimization methodologies. Herein, we cover the application of multi- and many-objective optimization methods, particularly those based on Evolutionary Computation and Machine Learning techniques, to enlighten their potential application in dnDD. Additionally, we comprehensively analyze how molecular properties used in the optimization process are applied as either objectives or constraints to the problem. Finally, we discuss future research in many-objective optimization for dnDD, highlighting two important possible impacts: i) its integration with the development of multi-target approaches to accelerate the discovery of innovative and more efficacious drug therapies and ii) its role as a catalyst for new developments in more fundamental and general methodological frameworks in the field.

Many-objective Optimization Method Based on Dimension Reduction for Operation of Large-scale Cooling Energy Systems

Many-objective Optimization Method Based on Dimension Reduction for Operation of Large-scale Cooling Energy Systems

Many-objective rapid optimization of reactor shielding design based on NSGA - III

In this paper, a many-objective optimization method for reactor shielding design coupled with NSGA - III and neural network is proposed. By establishing the many-objective optimization model, using Monte Carlo method to calculate samples to train neural network, and the prediction results of neural network are used as the parameters of fitness function for many-objective optimization. The coupling between neural network and NSGA - III is realized, and the Pareto optimal solution of many-objective optimization of reactor shielding design is obtained. The results show that the method of neural network coupling NSGA - III performs well in solving the many-objective optimization problem, and can be applied to the many-objective optimization engineering design of reactor radiation shielding.

A novel binary many-objective feature selection algorithm for multi-label data classification

For Multi-label classification, redundant and irrelevant features degrade the performance of classification. To select the best features based on several conflicting objectives, feature selection can be modeled as a large-scale optimization problem. However, most existing multi-objective feature selection methods select the features based on minimizing two well-known objectives, the number of features and classification error, additional objectives can be considered to improve the classification performance. In this study, for the first time, a many-objective optimization method is proposed to select the efficient features for multi-label classification based on not only two mentioned objectives, but also maximizing the correlation between features and labels and minimizing the computational complexity of features. Maximizing the correlation could lead to increasing the accuracy of classification. On the other hand, selecting less complex features decreases the computational complexity of feature extraction phase. The most important aim of this paper is to tackle the multi-label feature selection based on the number of features, classification error, correlation between features and labels, and computational complexity of features, simultaneously. The conducted many-objective feature selection problem is solved using a proposed binary version of NSGA-III algorithm. The binary operator improves the exploration power of optimizer to search the large-scale space. In order to evaluate the proposed algorithm (called binary NSGA-III), a benchmarking experiments is conducted on eight multi-label datasets in terms of several multi-objective assessment metrics, including Hypervolume indicator, Pure Diversity, and Set-coverage. Experimental results show significant improvements for proposed method in comparison with other algorithms.

Study on Large-Scale Many-Objective Optimization Method for Aerodynamics and Underhood Cooling Airflow Using Detailed Vehicle Model

Study on Large-Scale Many-Objective Optimization Method for Aerodynamics and Underhood Cooling Airflow Using Detailed Vehicle Model

Review of the Research Landscape of Multi-Criteria Evaluation and Benchmarking Processes for Many-Objective Optimization Methods: Coherent Taxonomy, Challenges and Recommended Solution

Evaluation and benchmarking of many-objective optimization (MaOO) methods are complicated. The rapid development of new optimization algorithms for solving problems with many objectives has increased the necessity of developing performance indicators or metrics for evaluating the performance quality and comparing the competing optimization algorithms fairly. Further investigations are required to highlight the limitations of how criteria/metrics are determined and the consistency of the procedures with the evaluation and benchmarking processes of MaOO. A review is conducted in this study to map the research landscape of multi-criteria evaluation and benchmarking processes for MaOO into a coherent taxonomy. Then contentious and challenging issues related to evaluation are highlighted, and the performance of optimization algorithms for MaOO is benchmarked. The methodological aspects of the evaluation and selection of MaOO algorithms are presented as the recommended solution on the basis of four distinct and successive phases. First, in the determination phase, the evaluation criteria of MaOO are collected, classified and grouped for testing experts’ consensus on the most suitable criteria. Second, the identification phase involves the process of establishing a decision matrix via a crossover of the ‘evaluation criteria’ and MaOO’, and the level of importance of each selective criteria and sub-criteria from phase one is computed to identify its weight value by using the best–worst method (BWM). Third, the development phase involves the creation of a decision matrix for MaOO selection on the basis of the integrated BWM and VIKOR method. Last, the validation phase involves the validation of the proposed solution.

Design of a 70T Quasi-Continuous High Magnetic Field System with a Dual-Coil Magnet

As a significant research method, quasi-continuous high magnetic field (QCHMF) can meet scientific experimental requirements for higher magnetic intensity, longer flat-top pulsed width and lower ripple in physics, biology and other scientific fields. In this paper, a QCHMF system designed by many-objective optimization method is presented to obtain the magnetic intensity of 70T. The magnet system consists of two coils, the inner coil is energized by the 100 MVA/100 MJ generator-rectifier power supply and the outer coil is powered by a 22 MJ capacitor power supply. To reduce the adjusting difficulty of the QCHMF, a decoupling transformer is designed. Moreover, a self-adaptive PI controller is used to reduce the ripple of the QCHMF. The MATLAB/Simulink and COMSOL Multiphysics are adopted to establish the equivalent model of QCHMF system and the simulation result presents the system can generate 70T/100 ms flat-top pulse has the ripple less than 1300 ppm.

Energy, economic, environmental and engineering quantity optimization of industrial energy recovery network

The industrial energy recovery network has a large energy-saving potential. The retrofit of the original heat exchanger network (HEN) plays an important role in reducing energy consumption in existing process industries. However, a single economic or energy target is no longer sufficient to meet the retrofit needs of existing process industries. Therefore, an improved retrofit method that comprehensively considers many-objective is worthy of exploration. In this study, a many-objective optimization model with energy, economic, environmental and engineering quantity (4E) indexes for heat exchanger network retrofit is proposed, which avoids the one-sided analysis brought by single-objective optimization. The non-dominated sorting genetic algorithm based on reference point (NSGA-III) is applied to solve the proposed retrofit model. Three typical cases are used to verify and analyze the effectiveness and superiority of the proposed method. The case results show that the many-objective optimization method provides diverse retrofit options and flexibility to decision makers. Retrofit schemes with comparative energy, economic or environmental performance may take on notable difference in engineering quantity. Compared with the original networks, the retrofitted networks in the case studies can achieve a decrease in energy consumption up to 49.6%, a decrease in the total annual cost up to 22.2%, and a decrease in environmental impact up to 32.8%. Compared with the literature, the proposed method obtains optimization solutions with less energy consumption, capital cost, environmental impact and payback period.

A Novel Many-Objective Recommendation Algorithm for Multistakeholders

Most traditional recommender systems focus specifically on increasing consumer satisfaction by providing a list of relevant content to consumers. However, the perspectives of other multisided marketplace stakeholders are also equally important, i.e., the exposure for suppliers or providers and profit for the platform. The suppliers want their products to be presented to users, and the objective of the platform is to maximize their profit. Nevertheless, because consumers' preferences and the objectives of providers as well as the platform may conflict with each other, it degrades the utility of the recommendation methods by only considering users' views. Therefore, in this work, we use a many-objective optimization method to maintain a tradeoff among five objectives for three stakeholders and obtain multiple Pareto front solutions in a single run. We first combine customer lifetime value and user purchase preference to create a new similarity model (Sim_RFMP) to increase the recommendation accuracy of the recommendation list. Furthermore, we propose a many-objective model (NBHXMAOEA) for multistakeholder recommendation. In NBHXMAOEA, we present a novel N-block heuristic crossover operator (NBHX) that recombines blocks of chromosomes based on heuristics. Through extensive experiments, the results demonstrate that our proposed NBHXMAOEA achieves superior performance in terms of average accuracy, diversity, novelty, provider coverage, and platform profit to its competing methods.

VisualUVAM: A Decision Support System Addressing the Curse of Dimensionality for the Multi-Scale Assessment of Urban Vulnerability in Spain

Many-objective optimization methods have proven successful in the integration of research attributes demanded for urban vulnerability assessment models. However, these techniques suffer from the curse of the dimensionality problem, producing an excessive burden in the decision-making process by compelling decision-makers to select alternatives among a large number of candidates. In other fields, this problem has been alleviated through cluster analysis, but there is still a lack in the application of such methods for urban vulnerability assessment purposes. This work addresses this gap by a novel combination of visual analytics and cluster analysis, enabling the decision-maker to select the set of indicators best representing urban vulnerability accordingly to three criteria: expert’s preferences, goodness of fit, and robustness. Based on an assessment framework previously developed, VisualUVAM affords an evaluation of urban vulnerability in Spain at regional, provincial, and municipal scales, whose results demonstrate the effect of the governmental structure of a territory over the vulnerability of the assessed entities.

Many-objectives multilevel thresholding image segmentation using Knee Evolutionary Algorithm

Image segmentation is one of the popular tasks in image processing that can be used in several applications. For that, there are several methods have been proposed for image segmentation; in which, these methods aim to minimize or maximize single objective (SO) function to find the optimal threshold to separate the image into the optimal number of regions. While a few of the image segmentation methods consider multi-objective functions which aim to find the optimal solutions that can reduce the conflict among the different objectives. However, these methods have some limitations as decreasing their performance when the number of objectives is increasing. Due to increasing the number of non-dominated solutions, so, there isn’t pressure towards the Pareto front. Therefore, this paper proposes an alternative image segmentation method using many-objective optimization (MaOP) algorithms considering seven objective functions. One of the most competitive MaOPs is called the Knee Evolutionary Algorithm (KnEA) which used to find the set of Pareto optimal solutions for seven objective functions to improve the image segmentation. The proposed KnEA is evaluated using a set of six images tested at six different levels of threshold, and its performance is compared with other MaOP methods. The experimental results show that the KnEA method has a better approximation to the optimal Pareto fronts (PFs) than the other MaOPs method in terms of the quality of the segmented image such as the peak signal-to-noise ratio (PSNR), the structural similarity index (SSIM), and the computational time. As well as, the quality of PFs is measuring using the hypervolume, coverage and spacing indicators.

A Development of Evolutionary Many-objective Optimization Method for Decision Aid on Distribution System Reconfiguration

A Development of Evolutionary Many-objective Optimization Method for Decision Aid on Distribution System Reconfiguration

A Probabilistic and Multi-Objective Analysis of Lexicase Selection and -Lexicase Selection.

Lexicase selection is a parent selection method that considers training cases individually, rather than in aggregate, when performing parent selection. Whereas previous work has demonstrated the ability of lexicase selection to solve difficult problems in program synthesis and symbolic regression, the central goal of this article is to develop the theoretical underpinnings that explain its performance. To this end, we derive an analytical formula that gives the expected probabilities of selection under lexicase selection, given a population and its behavior. In addition, we expand upon the relation of lexicase selection to many-objective optimization methods to describe the behavior of lexicase selection, which is to select individuals on the boundaries of Pareto fronts in high-dimensional space. We show analytically why lexicase selection performs more poorly for certain sizes of population and training cases, and show why it has been shown to perform more poorly in continuous error spaces. To address this last concern, we propose new variants of -lexicase selection, a method that modifies the pass condition in lexicase selection to allow near-elite individuals to pass cases, thereby improving selection performance with continuous errors. We show that -lexicase outperforms several diversity-maintenance strategies on a number of real-world and synthetic regression problems.

An angle based constrained many-objective evolutionary algorithm

Having successfully handled many-objective optimization problems with box constraints only by using VaEA, a vector angle based many-objective evolutionary algorithm in our precursor study, this paper extended VaEA to solve generic constrained many-objective optimization problems. The proposed algorithm (denoted by CVaEA) differs from the original one mainly in the mating selection and the environmental selection, which are made suitable in the presence of infeasible solutions. Furthermore, we suggest a set of new constrained many-objective test problems which have different ranges of function values for all the objectives. Compared with normalized problems, this set of scaled ones is more applicable to test an algorithm’s performance. This is due to the nature property of practical problems being usually far from normalization. The proposed CVaEA was compared with two latest constrained many-objective optimization methods on the proposed test problems with up to 15 objectives, and on a constrained engineering problem from practice. It was shown by the simulation results that CVaEA could find a set of well converged and properly distributed solutions, and, compared with its competitors, obtained a better balance between convergence and diversity. This, and the original VaEA paper, together demonstrate the usefulness and efficiency of vector angle based algorithms for handling both constrained and unconstrained many-objective optimization problems.

An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach

In the precursor paper, a many-objective optimization method (NSGA-III), based on the NSGA-II framework, was suggested and applied to a number of unconstrained test and practical problems with box constraints alone. In this paper, we extend NSGA-III to solve generic constrained many-objective optimization problems. In the process, we also suggest three types of constrained test problems that are scalable to any number of objectives and provide different types of challenges to a many-objective optimizer. A previously suggested MOEA/D algorithm is also extended to solve constrained problems. Results using constrained NSGA-III and constrained MOEA/D show an edge of the former, particularly in solving problems with a large number of objectives. Furthermore, the NSGA-III algorithm is made adaptive in updating and including new reference points on the fly. The resulting adaptive NSGA-III is shown to provide a denser representation of the Pareto-optimal front, compared to the original NSGA-III with an identical computational effort. This, and the original NSGA-III paper, together suggest and amply test a viable evolutionary many-objective optimization algorithm for handling constrained and unconstrained problems. These studies should encourage researchers to use and pay further attention in evolutionary many-objective optimization.