Multi-objective Evolutionary Algorithm Research Articles

An improved problem transformation algorithm for large-scale multi-objective optimization

Solving Large-Scale Multi-Objective Optimization Problems (LSMOPs) is the major challenge in evolution computation. Due to the large number of decision variables involved, it is not easy for existing multi-objective evolutionary algorithms to search the entire decision variable space with limited computation resources. To address the above problem, a large-scale multi-objective evolutionary algorithm based on problem transformation, called LSMOEA/PT, is presented in this paper. LSMOEA/PT uses an improved problem transformation strategy to transform LSMOPs into small-scale multi-objective problems to accelerate convergence speed and reduce computational resources. Specifically, The transformation strategy selects reference solutions to initialize a weight population by applying the opposite individual method. After optimizing the weight population, a dual line strategy is implemented to combine the weight vectors with the decision variables from the original population, thereby generating a new population. The new population is combined with the original population for environment selection. In LSMOEA/PT, a double learning swarm optimizer is introduced to speed up the convergence of the population. A uniform distribution strategy is conducted to update transformed solutions after the problem transformation process, increasing the diversity of the population. Experimental results show that LSMOEA/PT is competitive with eleven state-of-the-art algorithms on large-scale multi-objective optimization test problems with up to 2000 decision variables.

MOAAA/D: a decomposition-based novel algorithm and a structural design application

When real-world engineering challenges are examined adequately, it becomes clear that multi-objective need to be optimized. Many engineering problems have been handled utilizing the decomposition-based optimization approach according to the literature. The performance of multi-objective evolutionary algorithms is highly dependent on the balance of convergence and diversity. Diversity and convergence are not appropriately balanced in the decomposition technique, as they are in many approaches, for real-world problems. A novel Multi-Objective Artificial Algae Algorithm based on Decomposition (MOAAA/D) is proposed in the paper to solve multi-objective structural problems. MOAAA/D is the first multi-objective algorithm that uses the decomposition-based method with the artificial algae algorithm. MOAAA/D, which successfully draws a graph on 24 benchmark functions within the area of two common metrics, also produced promising results in the structural design problem to which it was applied. To facilitate the design of the "rectangular reinforced concrete column" using MOAAA/D, a solution space was derived by optimizing the rebar ratio and the concrete quantity to be employed.

A dual-population auxiliary multiobjective coevolutionary algorithm for constrained multiobjective optimization problems

The key to solving constrained multiobjective optimization problems (CMOPs) lies in maintaining the feasibility, convergence, and diversity of the population. In recent years, various constraint handling techniques (CHTs) and strategies have been proposed to enhance the performance of constrained multiobjective evolutionary algorithms (CMOEAs). However, most of these algorithms face difficulties in dealing with problems that have large infeasible regions and discontinuous small feasible regions, as they have trouble crossing large infeasible regions while simultaneously maintaining the convergence and diversity of the population. To tackle this issue, this paper proposes a dual-population auxiliary coevolutionary algorithm with an enhanced operator, denoted as DAEAEO. Auxiliary population 1 employs an improved ϵ-constraint handling technique to provide high-quality feasible solutions for the main population. Auxiliary population 2 adopts the non-dominated sorting method to provide favorable objective information for the main population to help it cross the infeasible region. In addition, to further improve diversity, each population adopts an enhanced operator and a genetic operator to generate offspring, respectively. Finally, knowledge transfer between offspring is realized. Compared to six state-of-the-art CMOEAs on DASCMOPs, LIR-CMOPs, DOC test suites, and two real-world problems, the proposed DAEAEO achieved superior performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions.

MOREM: An evolutionary multitasking optimization algorithm for multi-objective recommendations

Multi-objective evolutionary algorithms (MOEAs) have been successfully applied in recommender systems, where the recommendation is modeled as a multi-objective optimization problem by considering both accuracy and non-accuracy metrics. However, to recommend to all users, the population individuals in most of the exiting MOEA-based recommendation algorithms are usually encoded in the form of matrix encoding, and with the increased number of users and items, it will lead to a large search space. To this end, in this paper, we propose a novel evolutionary multitasking algorithm MOREM to tackle the challenge of multi-objective recommendations, where a related auxiliary task is constructed by both user and item reduction to help solving the complex original task by knowledge transfer. Specifically, a task generation strategy for creating auxiliary task is firstly proposed to cluster users by user-rating information (i.e., user reduction), where only a part of important items (i.e., item reduction) are recommended for the central user within each cluster with the aim to greatly reduce the size of the matrix encoding. In addition, a novel knowledge transfer mechanism is proposed, which can effectively achieve knowledge migration between the two tasks. Experimental results on real-world datasets show that MOREM outperforms several state-of-the-art algorithms for multi-objective recommendations.

A multi-objective evolutionary algorithm for robust positive-unlabeled learning

Positive and unlabeled (PU) learning is to learn a binary classifier with good generalization ability from PU data. A variety of PU learning algorithms with promising performance have been proposed. However, most of them assume that PU samples are “clean”, which is not true in real applications due to the existing noisy or redundant samples. Thus, how to obtain a robust PU classifier with better performance is a challenging problem. To this end, we propose a novel multi-objective evolutionary algorithm to tackle it, named BPUSS-MOEA. Specifically, we firstly transform the robust PU learning into a bi-objective PU sample selection (BPUSS) problem, in which two objectives are designed. One is the number of selected “clean” PU samples and the other is the PU accuracy. Then, a dual-coding scheme is designed to represent the selected “clean” PU samples and the labels of U samples. With the dual-coding scheme, a novel offspring generation strategy is developed to achieve the offsprings with high quality. To further improve the performance of BPUSS-MOEA, an effective population initialization strategy is designed. Experiments on 10 datasets with different noise levels show that compared with the state-of-the-arts, the proposed algorithm demonstrates its robustness in terms of the PU accuracy.

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.

Deep Heterogeneous AutoML Trend Prediction Model for Algorithmic Trading in the USD/COP Colombian FX Market Through Limit Order Book (LOB)

This study presents a novel and competitive approach for algorithmic trading in the Colombian US dollar inter-bank market (SET-FX). At the core of this strategy is an advanced predictive model, developed using the Tree-based Pipeline Optimization Tool (TPOT). TPOT, an automated machine learning platform based on strongly-typed genetic programming, incorporates the Non-dominated Sorting Genetic Algorithm II (NSGA-II). This multi-objective evolutionary algorithm is instrumental in identifying machine learning models that strike an optimal balance between high accuracy and low complexity, thereby advancing the field of predictive modeling in financial markets.

A dynamic-speciation-based differential evolution with ring topology for constrained multimodal multi-objective optimization

Constrained multimodal multi-objective optimization problems (CMMOPs) consist of multiple equivalent constrained Pareto sets (CPSs) that have the identical constrained Pareto front (CPF). It is challenging for primary multimodal multi-objective evolutionary algorithms (MMEAs) to solve CMMOPs since they do not consider constraints. To tackle this challenge, a dynamic speciation-based differential evolution with ring topology, termed DSRDE, for solving CMMOPs is developed in this paper. To search for multiple equivalent CPSs in CMMOPs, the dynamic speciation-based niche strategy is developed. The dynamic speciation-based niche strategy divides the population into multiple species, each of which searches for diverse and equivalent CPSs in different regions. Particularly, the species number is dynamically decreased to explore the equivalent CPSs with good convergence. Then, a ring topology is constructed among multiple species and their neighbors to balance the diversity, convergence, and feasibility of solutions. Continuously, each species interacts information with its neighbors and searches for equivalent CPSs. DSRDE adopts the popular constrained dominance principle to handle constraints and uses the differential evolutionary algorithm to locate diverse CPSs in the ring topology. It is compared with several state-of-the-art algorithms in two CMMOPs test suites for evaluating the performance of the proposed DSRDE. The experimental results confirm that DSRDE is competitive and has the ability to find multiple CPSs when tackling CMMOPs. DSRDE is also implemented in a real-world CMMOP and obtains 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.

Multiobjective Evolutionary Component Effect on Algorithm Behaviour

The performance of multiobjective evolutionary algorithms (MOEAs) varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from their components. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still unknown what are the most influential components that lead to performance improvements. This study specifies a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a tuned Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) designed by the iterated racing (irace) configuration package on constrained problems of 3 groups: (1) analytical real-world problems, (2) analytical artificial problems and (3) simulated real-world. We then compare the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the anytime hypervolume values. Looking at the objective space behavior, the MOEAs studied converged before half of the search to generally good HV values in the analytical artificial problems and the analytical real-world problems. For the simulated problems, the HV values are still improving at the end of the run. In terms of decision space behavior, we see a diverse set of the trajectories of the STNs in the analytical artificial problems. These trajectories are more similar and frequently reach optimal solutions in the other problems.

A dynamic multi-objective evolutionary algorithm based on Mahalanobis distance and intra-cluster individual correlation rectification

Responding quickly and accurately to environmental changes is a challenge in addressing dynamic multi-objective optimization problems (DMOPs). Although many dynamic multi-objective evolutionary algorithms (DMOEAs) have demonstrated impressive performance, there is still room for improvement in accurately predicting population behavior. To address this limitation, this paper proposes a prediction strategy based on Mahalanobis distance and intra-cluster individual correlation rectification (MCIR) to deal with DMOPs. First, a manifold clustering method is used to partition the Pareto set of the population into subpopulations, in which individuals with similar movement trends are grouped into clusters. Second, the Mahalanobis distance is introduced to systematically measure the relationships between clusters in adjacent environments. Time series models are established for each cluster center to predict their positions in the neighboring environment. On this basis, the movement characteristics of individuals within clusters are further rectified by calculating the correlation between intra-cluster individuals and the cluster center, facilitating more accurate tracking of the changing Pareto set/Pareto front. Finally, Gaussian noise is introduced to ensure the diversity of new individuals. The effectiveness of the MCIR algorithm is demonstrated by comparing it with four DMOEAs using 18 test instances. Experimental results confirm that MCIR holds great promise in addressing DMOPs.

Integrating transformers and many-objective optimization for drug design

BackgroundDrug design is a challenging and important task that requires the generation of novel and effective molecules that can bind to specific protein targets. Artificial intelligence algorithms have recently showed promising potential to expedite the drug design process. However, existing methods adopt multi-objective approaches which limits the number of objectives.ResultsIn this paper, we expand this thread of research from the many-objective perspective, by proposing a novel framework that integrates a latent Transformer-based model for molecular generation, with a drug design system that incorporates absorption, distribution, metabolism, excretion, and toxicity prediction, molecular docking, and many-objective metaheuristics. We compared the performance of two latent Transformer models (ReLSO and FragNet) on a molecular generation task and show that ReLSO outperforms FragNet in terms of reconstruction and latent space organization. We then explored six different many-objective metaheuristics based on evolutionary algorithms and particle swarm optimization on a drug design task involving potential drug candidates to human lysophosphatidic acid receptor 1, a cancer-related protein target.ConclusionWe show that multi-objective evolutionary algorithm based on dominance and decomposition performs the best in terms of finding molecules that satisfy many objectives, such as high binding affinity and low toxicity, and high drug-likeness. Our framework demonstrates the potential of combining Transformers and many-objective computational intelligence for drug design.

Integration of preferences in multimodal multi-objective optimization

Various existing multimodal multi-objective evolutionary algorithms (MMEAs) efficiently search for an approximation to the Pareto optimal front (PF), which consists of multiple equivalent Pareto optimal sets (PSs), when tackling multimodal multi-objective optimization problems (MMOPs). However, in practical applications, the Decision-maker (DM) often seeks specific portions of the PF, known as the Region of Interest (ROI), corresponding to particular instances rather than the whole PF. Existing MMEAs only focus on the whole PF and lack exploration of the ROI. Consequently, we propose an innovative MMEA that incorporates the DM’s preferences and local convergence quality (MMEA-PLC). The proposed algorithm integrates the DM’s preferences into the traditional Pareto-dominance relationship, enabling the search for multiple equivalent Pareto optimal set subsets (PSSs) within the ROI. Due to the influence of local PFs, accurately representing the ROI can be challenging when expressed across different PFs. Therefore, we design a preference-based Pareto-dominance relationship to accurately convey the preferences on different PFs by mapping solutions onto a hyperplane in the objective space. Then, we further develop a scheme for assessing local convergence quality (LCQ) to ensure that the algorithm can identify multiple equivalent PSSs within the same ROI. To verify the effectiveness of the proposed algorithm, MMEA-PLC was experimentally compared with eight state-of-the-art MMEAs on 28 benchmark functions and a real-life application problem. Experimental results show that MMEA-PLC has significant competitive advantages in different preference scenarios.

Information gain-based multi-objective evolutionary algorithm for feature selection

Feature selection (FS) has garnered significant attention because of its pivotal role in enhancing the efficiency and effectiveness of various machine learning and data mining algorithms. Concurrently, multiobjective feature selection (MOFS) algorithms strive to balance the complexity of multiple optimization objectives during the FS process. These include minimizing the number of selected features while maximizing classification performance. Nonetheless, managing the complexity of feature combinations presents a formidable challenge, particularly in high-dimensional datasets. Evolutionary algorithms (EAs) are increasingly adopted in MOFS owing to their exceptional global search capabilities and robustness. Despite their strengths, EAs face difficulties in navigating expansive solution spaces and achieving a balance between exploration and exploitation. To address these challenges, this study introduces a novel information gain-based EA for MOFS, designated as IGEA. This approach utilizes a clustering method for selecting a diverse parent population, thereby enhancing individual variability and maintaining a high-quality population. Considerably, IGEA employs information gain as a metric to evaluate the contribution of features to classification tasks. This metric informs crucial operations such as crossover and mutation. Moreover, the study extensively examines the actual solutions derived from IGEA, focusing on feature correlation and redundancy. This analysis illuminates IGEA's adept handling of these aspects to refine MOFS. Experimental results on 23 widely used classification datasets confirm IGEA's superiority over five other state-of-the-art algorithms, demonstrating its enhanced effectiveness and efficiency in complex MOFS scenarios.

Enhancing the maintenance strategy and cost in systems with surrogate assisted multiobjective evolutionary algorithms

Digital twins need efficient methodologies to design maintenance strategies for decision-making purposes. Recently, a methodology coupling computational simulation and multiobjective evolutionary algorithms has been proposed for developing maintenance strategies consisting in assigning times for preventive maintenance activities and designing the layout of components of a system, minimizing the unavailability of the system and the strategy cost.Here, surrogate assisted evolutionary algorithms (SAEAs) enhance the multiobjective optimization and improve the drawback of the computational cost of the maintenance strategy assessment based on discrete simulation. Several Kriging surrogates were tested.Two industrial test cases are handled in the experimental section, where the methodology succeed in obtaining nondominated designs improving previous benchmarks, and enhancing state-of-the-art multiobjective optimizers, with up to an order of magnitude in terms of the number of fitness function evaluations. Results show that using multiobjective SAEAs in the development of optimal maintenance strategies could foster and improve digital twins operations.

Scheduling stochastic distributed flexible job shops using an multi-objective evolutionary algorithm with simulation evaluation

The trend of reverse globalisation prompts manufacturing enterprises to adopt distributed structures with multiple factories for improving production efficiency, meeting customer requirements, and responding disturbance events. This study focuses on scheduling a distributed flexible job shop with random job processing time to achieve minimal makespan and minimal total tardiness. First, a stochastic programming model is established to formulate the concerned problems. Second, in accordance with the natures of two objectives and randomness, an evolutionary algorithm incorporating an evaluation method is designed. In it, population-based and external archive-based search processes are developed for searching candidate solutions, and the evaluation method integrates stochastic simulation and discrete event simulation to calculate objective values of acquired solutions. Finally, a mathematical optimisation solver, CPLEX, is employed to validate the developed model and optimisation approach. A set of cases is solved to verify the performance of the proposed method. The comparisons and discussions show the superiority of the proposed method for handling the problems under study.

Merging preferences into the best solution seeking for many-objective optimization problems

Finding out a best solution of the multi-objective optimization problem (MOP) or many-objective optimization problem (MaOP) in the user’s view, is a significant and practical problem. The multi-objective evolutionary algorithms (MOEAs) are applied to solve the MaOPs. Considering many conflicting objectives, they would generate numerous nondominated solutions. Merging the preferences from the user to objectives is an effective way to measure the nondominated solutions and find out the best one (a posterior approach). But the preference relations may be contradictory and highly sparse. In this paper, we propose a process of finding out a best solution with preference relations among attributes (BSPA). In which, we emphasize to test the contradiction and ease the high sparsity of preference relations, then an available preference degree matrix is obtained and merged into the selection of best solution. Based on the proposed process, three methods of NSGA-II-BSPA, P-NSGA-II and P-GA are proposed to solve the best solution of an MOP or MaOP. The experiments are conducted, and the metrics of contradiction probability, feasibility and availability are proposed to measure the BSPA and the vigorous results are obtained. At last, three case studies are adopted to verify the proposed methods’ effectiveness and efficiency. Meanwhile, the hypothesis tests are conducted and the results indicate that the obtained best solutions of proposed methods are satisfiable.

An enhanced NSGA-II and a fast constraint repairing method for combined heat and power dynamic economic emission dispatch

In this paper, an enhanced NSGA-II (ENSGA-II) is presented for the combined heat and power dynamic economic emission dispatch (CHPDEED). ENSGA-II produces offspring individuals by a novel crossover of the Cauchy distribution with adaptive location and scale parameters. It can not only sufficiently explore and exploit the decision space but also remain a relatively high population diversity. Also, ENSGA-II adopts a modified crowding distance to penalize crowded individuals, seeking to evenly distribute the individuals in the objective space. In addition, a fast constraint repairing method (FCRM) is proposed to significantly reduce the constraint violations and guide infeasible individuals to move towards feasible zones rapidly. The proposed ENSGA-II is applied to a number of multi-objective optimization problems and compared with the other eight multi-objective evolutionary algorithms (MOEAs). ENSGA-II is found to produce better results on most problems, such as smaller inverse generational distances, larger hypervolumes, larger coverage rates and smaller spacings. Therefore, ENSGA-II can obtain a satisfactory Pareto set with broad spread, high diversity, strong convergence and good evenness, and it is an efficient alternative for CHPDEED.

Evolutionary Bilevel Optimization via Multiobjective Transformation-Based Lower-Level Search

Nested evolutionary algorithms (EAs) have been regarded as very promising tools for bi-level optimization. Due to the nested structure, the upper level population evaluation requires a set of complete lower level optimizations, thereby reducing the efficiency and practicability of EA methods. In this paper, a multi-objective transformation-based evolutionary algorithm (MOTEA) is proposed to perform multiple lower level optimizations in a parallel and collaborative manner. Specifically, the corresponding multiple lower level optimizations for each generation of the upper level population evaluation are transformed into locating a set of Pareto optimal solutions of a constructed multi-objective optimization problem. By utilizing the built-in implicit parallelism of evolutionary multi-objective optimization, multiple lower level problems can thus be optimized in parallel. Within one multi-objective search population, the collaboration among the parallel lower level optimization can be realized by exploiting and utilizing the implicit similarities among them for better efficiency. The effectiveness and efficiency of the proposed MOTEA are verified by comparing it with four state-of-the-art evolutionary bi-level optimization algorithms on two sets of popular bi-level optimization benchmark test problems and three application problems.

Multitask Learning for Joint Diagnosis of Multiple Mental Disorders in Resting-State fMRI.

Facing the increasing worldwide prevalence of mental disorders, the symptom-based diagnostic criteria struggle to address the urgent public health concern due to the global shortfall in well-qualified professionals. Thanks to the recent advances in neuroimaging techniques, functional magnetic resonance imaging (fMRI) has surfaced as a new solution to characterize neuropathological biomarkers for detecting functional connectivity (FC) anomalies in mental disorders. However, the existing computer-aided diagnosis models for fMRI analysis suffer from unstable performance on large datasets. To address this issue, we propose an efficient multitask learning (MTL) framework for joint diagnosis of multiple mental disorders using resting-state fMRI data. A novel multiobjective evolutionary clustering algorithm is presented to group regions of interests (ROIs) into different clusters for FC pattern analysis. On the optimal clustering solution, the multicluster multigate mixture-of-expert model is used for the final classification by capturing the highly consistent feature patterns among related diagnostic tasks. Extensive simulation experiments demonstrate that the performance of the proposed framework is superior to that of the other state-of-the-art methods. Moreover, the potential for practical application of the framework is also validated in terms of limited computational resources, real-time analysis, and insufficient training data. The proposed model can identify the remarkable interpretative biomarkers associated with specific mental disorders for clinical interpretation analysis.