Multi-objective Differential Evolution Research Articles

Reinforcement learning-based differential evolution algorithm for constrained multi-objective optimization problems

Many real-world problems can be established as Constrained Multi-objective Optimization Problems (CMOPs). It is still challenging to automatically set efficient parameters for Constrained Multi-Objective Evolutionary Algorithms (CMOEAs) to solve these CMOPs. A Reinforcement Learning-based Multi-Objective Differential Evolution (RLMODE) algorithm is proposed, in which the main parameters are dynamically adjusted. During the evolution process, the offspring generated is evaluated and compared with its corresponding parents, the relationship between the offspring and parent can adjust the parameters of RLMODE by the Reinforcement Learning (RL) technique. The feedback mechanism can produce the most appropriate parameters for RLMODE, which pushes the population towards feasible regions. The proposed RLMODE is evaluated on thirty functions and compared with some popular CMOEAs. The performance indicator IGD has revealed that the proposed RLMODE is competitive. Then, they are applied to solve the UAV path planning problem with three objectives and a constraint. The real application has further demonstrated the superiority of the proposed RLMODE.

A recursive framework for improving the performance of multi-objective differential evolution algorithms for gene selection

Gene selection is a pivotal process in machine-learning-driven medical diagnostics, where the goal is to identify a subset of genes from microarray expression profiles that can enhance the predictive accuracy of classifiers for disease diagnosis. The two key objectives of gene selection are to reduce the dimensionality of the data and to improve the accuracy of disease diagnosis, which is typically a multi-objective optimization problem. In recent years, multi-objective evolutionary algorithms (MOEAs) have gained wide attention in feature selection research, and several related algorithms have been produced. However, most algorithms tend to get stuck in local optimality when searching for solutions from a high-dimensional space. To solve the gene selection problem effectively, this study introduces a recursive multi-objective differential evolution algorithm with elite recursive strategy (RMODE-E) and a recursive multi-objective differential evolution algorithm with Pareto front recursive strategy (RMODE-P). RMODE-E amalgamates the features selected by the top E elite individuals, RMODE-P consolidates the features selected by the Pareto front set, and the combined features then serve as the foundation for subsequent recursive rounds of searching. The proposed feature subspace combination strategy not only reduces the recursive search space but also improves the capacity to find globally optimal feature subsets. Extensive experiments were conducted to compare our proposed algorithms with eight state-of-the-art evolutionary algorithms to validate their effectiveness. Experimental results demonstrate that RMODE-P has better global search capability as it achieves better best classification accuracy, mean classification accuracy, and minimal gene subset size.

Scheduling of Continuous Annealing With a Multi-Objective Differential Evolution Algorithm Based on Deep Reinforcement Learning

This paper studies a multi-objective scheduling problem in a continuous annealing operation of the steel industry, which is to simultaneously determine the production batch sizes for coils and their schedules so as to minimize the cost of setup, earliness, and tardiness. A large batch can reduce the setup costs but lead to a cost increase in earliness and tardiness. Thus, the conflict objectives of minimizing setup cost, earliness, and tardiness can be formulated separately. In this paper, we formulate a multi-objective optimization model for the problem and develop an adaptive multi-objective differential evolutionary based on deep reinforcement learning (AMODE-DRL) for effectively obtaining the Pareto solutions. In the proposed AMODE-RDL, DRL is integrated into the MODE algorithm as a controller, which can adaptively select mutation operators and parameters according to different search domains. Computational results on randomly generated instances and the practical problem instances show that DRL can effectively guide MODE to select mutation operators and parameters. The proposed algorithm can obtain better solutions compared to other powerful multi-objective evolutionary and adaptive MODE algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Setup usually leads to a decrease in production capacity and an increase in production costs. Similarly, earliness and tardiness costs are also crucial. These costs correspond to production, customer demand, and inventory, which are common objectives in production systems. However, the three objectives are generally conflicting, and it is very hard for practitioners to make appropriate decisions with manual experience. The multi-objective optimization methods can provide different scheduling for practitioners who may choose the suitable one according to current working conditions. Accordingly, the proposed model and algorithm can extend to other fields with similar characteristic problems.

Multi-objective optimization of syngas production for Fischer-Tropsch synthesis based on biogas catalytic reforming and upgrading

The conversion of biogas into synthesis gas, for its subsequent application in Fischer-Tropsch synthesis, is one of the most studied processes for the production of liquid biofuels. However, this conversion still has economic and environmental disadvantages. This study evaluated the technical feasibility of a syngas production plant from biogas upgrading and reforming, through water scrubbing and bi-reforming processes. Aspen Plus modeling and a multi-objective optimization (MOO) were used to minimize CO2 emissions and maximize profitability. The multi-objective differential evolution with tabu list method was used to resolve the MOO design problem. The results reveal inherent trade-offs between both objectives. In particular, certain process parameters exerted a notable influence on the outcomes. Keeping a low water flow in the absorption column is essential to reduce environmental impact, but this also results in a lesser removal of impurities from biogas. Conversely, a higher water flow in the reactor promotes methane conversion, but concurrently raises the environmental impact. Nevertheless, the profitability of the Pareto front ranged from 5,200 to 6,500 k$ with a 1,000 Nm³/h biogas feed and the calculated CO2 equivalent net flow values varied between -11,900 and -11,550 kg/h. Therefore, it was successfully validated that calculated solutions of the Pareto allowed to demonstrate the feasibility of the proposed process.

An improved differential evolution algorithm for multi-modal multi-objective optimization.

Multi-modal multi-objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the Multi-modal multi-objective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non-dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain well-distributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.

Manifold assistant multi-modal multi-objective differential evolution algorithm and its application in actual rolling bearing fault diagnosis

The fault diagnosis of rotating mechanical systems is crucial for ensuring the reliability of industrial equipment. In actual industrial scenarios, different combinations of fault features may yield the same diagnostic accuracy, but the difficulty and cost of obtaining different features generally vary. Therefore, in the feature extraction process, if multiple optimal feature combinations can be provided to decision-makers, it would be beneficial to select the feature subsets with lower computational cost or measurement difficulty that achieve the same fault diagnosis performance. Therefore, we model the fault feature selection task as a multi-modal multi-objective optimization problem (MMOP). To better solve MMOPs, a manifold assistant multi-modal multi-objective differential evolution (MA-MMODE) algorithm is proposed. It can establish a regularity model based on the distribution of the population to generate offspring and approximate the true Pareto set. Subsequently, this paper presents a preselection strategy that considers the distributions of both the decision space and objective space. The proposed preselection strategy can ensure that individuals with more promising solutions enter the mating pool to generate new offspring, thus exploring the search space more comprehensively. Using the CEC 2019 test set, the proposed MA-MMODE is compared with state-of-the-art algorithms, and the experimental results illustrate the effectiveness of the proposed algorithm. Moreover, based on two real rolling bearing testbeds, the proposed MA-MMODE is applied for feature selection in actual fault diagnosis. The experimental results show that the proposed MA-MMODE can provide multiple equivalent feature subsets to decision-makers while effectively improving the fault diagnosis accuracy for rolling bearings.

Three-stage multi-modal multi-objective differential evolution algorithm for vehicle routing problem with time windows

In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.

Automatic Crowd Navigation Path Planning in Public Scenes Through Multiobjective Differential Evolution

Crowd navigation path planning is important in public scenes. Existing strategies are mainly based on manual design, which is not flexible or effective enough. This article proposes an evolutionary framework for automatic crowd navigation path planning in public scenes. The proposed framework contains a new fitness evaluation mechanism that can quantitatively evaluate the quality of a path planning strategy by considering both crowd safety and flow speed. Based on the fitness evaluation mechanism, a framework based on multiobjective differential evolution (DE) is developed to efficiently evolve path planning strategies. Simulation results on two synthetic scenes and a real-world metro station scene show that the proposed framework can provide good path planning strategies.

Reinforcement learning-based multi-objective differential evolution algorithm for feature selection

Feature Selection (FS) can be used to determine the optimal subset of features from a raw dataset by reducing dimensionality and improving accuracy. In this study, a reinforcement learning-based multi-objective differential evolution algorithm (RLMODE) for FS is proposed, which is modeled as a multi-objective optimization problem. First, a reinforcement learning-based offspring generation strategy is designed. The offspring generation strategy is based on the Q-learning framework, which considers each individual in the population as an agent. The dominance relationship between an agent and its predecessor is used to encode the state. A well-chosen action set containing three typical differential evolution mutation operators is available for each agent. The reward is used to update the exclusive Q-table. Moreover, a novel Pareto front (PF) relearning strategy is devised to allow adequate communication between individuals on the PF. The PF relearning strategy reevaluates the potential value of all individuals on the PF as a whole. This promotes the propagation of excellent solutions and improves PF diversity. The proposed RLMODE initially demonstrates its strength in benchmarks. The excellent results for 17 datasets demonstrate RLMODE’s merits in terms of dimensionality reduction and accuracy improvement. Therefore, the proposed RLMODE method is a promising FS technique.

Reliability-based design of high-performance hydrocyclones: Multi-objective optimization, fabrication using 3D-printing and experimental analysis

In the literature, several works aim to improve the performance of hydrocyclones using geometry optimization. However, these approaches do not consider the uncertainties in the models, design variables, and parameters, which can lead to solutions that do not correspond to the expected results when applied to real systems. Considering that, the present work proposed a reliability-based optimization of the hydrocyclone dimensions using the Advanced Mean Value (AMV) technique associated with the Multi-Objective Differential Evolution (MODE) algorithm. For that purpose, the maximization of total efficiency and minimization of underflow-to-throughput ratio and Euler number were taken as objectives and constraints were set to ensure an acceptable performance of the hydrocyclone in the main aspects of the process. Some of the obtained devices were selected to be fabricated through an additive manufacturing technique (3D printing) and, after that, be experimentally tested. The optimization results showed that the reliability-based optimization affected the Pareto curves in two different ways: a shortening or a displacement of the curve in relation to the nominal one, depending on which constraints are being activated. The experimental results demonstrated that the hydrocyclones obtained by the reliable approach had a greater tendency to meet the set constraints in practice. Finally, hydrocyclones with great experimental performance were obtained considering separation efficiency, concentration capacity, and energy consumption.

An [formula omitted]-constrained multiobjective differential evolution with adaptive gradient-based repair method for real-world constrained optimization problems

Over the past decade, incorporating information from the objective function into the constraint-handling process has garnered considerable attention in evolutionary algorithm research. Stemming from this, multiobjective optimization has emerged as a promising approach that simultaneously optimizes the objective function and constraints. However, the challenges associated with optimizing objective functions and satisfying constraints exhibit significant variability. Some constraints and/or objective functions can be exceptionally challenging, necessitating specific methods to identify the optimal solution within a limited feasible region. This study proposes an adaptive gradient descent-based repair method to enhance the search capability for both objective function optimization and constraint satisfaction. This method leverages objective function information to rectify infeasible solutions using gradient descent, thereby reducing the limitations of a purely constraint-based approach and automating the application of the repair method. Furthermore, an enhanced variant of the ɛ-constrained multiobjective differential evolution algorithm is developed for solving constrained optimization problems. The efficacy of the proposed approach is assessed using 57 benchmark test functions derived from real-world applications. Empirical results demonstrate that our approach is capable of locating high-quality solutions, outperforming several selected state-of-the-art algorithms.

Economic Emission Dispatch with Stochastic Renewable Power and Voltage Source Converters via Reinforcement Learning Multi-Objective Differential Evolution

Economic Emission Dispatch with Stochastic Renewable Power and Voltage Source Converters via Reinforcement Learning Multi-Objective Differential Evolution

Evaluation of an effective solving method based on cooperative multi-objective differential evolution for multi-objective optimization problems

Evaluation of an effective solving method based on cooperative multi-objective differential evolution for multi-objective optimization problems

Blockchain event ordering algorithm based on high-dimensional multi-objective differential evolution

Abstract Since the birth of Bitcoin, blockchain technology has been widely used in many fields, such as finance, supply chain management, smart contracts, etc.and has been highly valued for its decentralized and tamper-proof characteristics. With the expansion of application scenarios, blockchain faces inefficient data processing challenges, particularly in event sequencing and processing. Developing efficient event sequencing algorithms is a research priority to enhance the performance of blockchain systems. This study addresses the efficiency problem in blockchain event sequencing by introducing a high-dimensional multi-objective differential evolution strategy to improve blockchain technology’s performance in various fields. This paper uses the NSGA-III-WA algorithm to efficiently sort blockchain events by combining differential evolution strategies. Compared to the traditional sorting algorithm, this algorithm reduces latency by 30% and improves memory usage by about 20% when dealing with events of the same size, ensuring sorting accuracy. By optimizing the weight vector adjustment strategy, the convergence speed and distribution uniformity of the algorithm and the solution can be optimized. In this paper, the algorithm can effectively improve the efficiency and performance of blockchain event processing, which is critical in optimizing blockchain systems.

Multiobjective Differential Evolution Algorithm Balancing Multiple Stakeholders for Low-Carbon Order Scheduling in E-Waste Recycling

Order scheduling is an important part of the e-waste recycling process, which can influence the quantity and efficiency of the recycling. With the sustainable development of e-waste recycling, low-carbon order scheduling becomes a significant and challenging reverse logistics scheduling problem. However, it is difficult to obtain an effective low-carbon order schedule considering the conflicting interests of the multiple stakeholders, including enterprises, drivers, customers, and governments. To address this issue, a multi-objective order scheduling model (MOOSM) and a multi-objective differential evolution algorithm balancing multiple stakeholders (MODE-MS) are proposed in this paper. First, to embody the interests of different stakeholders, three time-dependent key variables are calculated by the road congestion and vehicle load, including the velocity, travelling time and carbon emission. Second, with the above key variables, a five-objective order scheduling model is formulated to describe the low-carbon order scheduling problem in e-waste recycling. Third, for solving the MOOSM, a multi-objective differential evolution algorithm based on an adaptive evolutionary search strategy is developed to obtain the low-carbon and stakeholders satisfied scheduling schemes. The experimental results validate the feasibility of MOOSM and the effectiveness of MODE-MS. By comparing with four state-to-art algorithms, the advantages of the proposed MODE-MS are further demonstrated in solving the low-carbon order scheduling.

A multitasking multi-objective differential evolution gene selection algorithm enhanced with new elite and guidance strategies for tumor identification

A key preprocessing step in tumor recognition based on microarray expression profile data and machine learning is to identify tumor marker genes. Gene selection aims to select the most relevant gene subset from the original ultra-high dimensional microarray expression profile data to improve tumor identification performance. Inspired by evolutionary multitasking (EMT) and multi-objective optimization, this paper puts forward a novel multitasking multi-objective differential evolution gene selection algorithm (MMODE) which uses new elite and guidance strategies to select the best gene subsets. MMODE initializes two different populations according to different filtering criteria to increase the diversity of the search. These two populations guide their respective populations to search in the optimal direction through knowledge transfer in the evolutionary process. In addition, MMODE employs new elite and guidance strategies that enables individuals to narrow the search range and jump out of local optima. The proposed algorithm is validated on 13 publicly available microarray expression datasets in comparison with state-of-the-art gene selection algorithms. The experimental results show that MMODE can find smaller gene subsets and achieve higher classification accuracy compared with other algorithms.

English Speech Emotion Classification Based on Multi-Objective Differential Evolution

Speech signals involve speakers’ emotional states and language information, which is very important for human–computer interaction that recognizes speakers’ emotions. Feature selection is a common method for improving recognition accuracy. In this paper, we propose a multi-objective optimization method based on differential evolution (MODE-NSF) that maximizes recognition accuracy and minimizes the number of selected features (NSF). First, the Mel-frequency cepstral coefficient (MFCC) features and pitch features are extracted from speech signals. Then, the proposed algorithm implements feature selection where the NSF guides the initialization, crossover, and mutation of the algorithm. We used four English speech emotion datasets, and K-nearest neighbor (KNN) and random forest (RF) classifiers to validate the performance of the proposed algorithm. The results illustrate that MODE-NSF is superior to other multi-objective algorithms in terms of the hypervolume (HV), inverted generational distance (IGD), Pareto optimal solutions, and running time. MODE-NSF achieved an accuracy of 49% using eNTERFACE05, 53% using the Ryerson audio-visual database of emotional speech and song (RAVDESS), 76% using Surrey audio-visual expressed emotion (SAVEE) database, and 98% using the Toronto emotional speech set (TESS). MODE-NSF obtained good recognition results, which provides a basis for the establishment of emotional models.

A fuzzy multi-objective optimization model for sustainable healthcare supply chain network design

Healthcare supply chains play a crucial role, which enables the implementation of optimization strategies that have rapidly emerged as highly effective means for improving the overall structure of pharmaceutical and healthcare supply chains.. In the healthcare industry, parameters such as increasing the quality of service, as well as optimizing costs, environmental, and social factors play a unique role in supply chain management. To improve the healthcare supply chain network, this study proposed a novel optimization model to optimize multiple objectives, including minimizing the total costs and environmental impacts, while maximizing the social factors by creating jobs simultaneously. To address the effects of uncertain parameters, a fuzzy optimization method alongside the multi-objective gray wolf optimizer (MOGWO), non-dominated sorting genetic algorithm II (NSGA-II), multi-objective differential evolution algorithm (MODEA), and ε-constraint are applied to optimize the model. Also, a case study of the pharmaceutical industry demonstrates the model's efficacy in a real-life context. The numerical results show the MOGWO manages to create high-quality Pareto solutions with a good spread at the Pareto boundary within a short time compared to the ε-constraint approach. Further, it has shown a more robust performance compared to MODEA and NSGA-II, indicating the efficiency of MOGWO, among other solution methods and other objective indicators.

A hybrid electricity load prediction system based on weighted fuzzy time series and multi-objective differential evolution

With advances in science and technology, the demand for electricity is increasing dramatically. Consequently, reliable short-term power load prediction is critical to ensure the safety, efficiency, and cost-effectiveness of electricity grids. However, owing to the volatility and randomness of power load time series, traditional forecasting models have struggled to meet the current power system requirements for load prediction precision and stability. In light of this, this study proposes a new hybrid short-term electricity load prediction system that combines the variational modal decomposition (VMD) technique, multi-objective differential evolutionary algorithm (MODE), and weighted fuzzy time series (WFTS) prediction model to increase load prediction precision and stability. Four Belgian datasets (spring, summer, autumn, and winter) were used for short-term power load prediction experiments and were compared with prevalent prediction methods. The experimental results indicate that the designed system obtains MAPESpring=0.6670%, MAPESummer=0.5835%, MAPEAutumn=0.7049%, MAPEWinter=0.7123% and STDSpring=60.2575, STDSpring=62.6573, STDSpring=72.7393, STDSpring=71.5549, which are obviously superior to the comparison models in terms of prediction accuracy and stability.

Decomposition–based multi-objective differential evolution for extractive multi-document automatic text summarization

The central challenge in Automatic Text Summarization (ATS) involves efficiently generating machine-generated text summaries through optimization algorithms. An ATS is a critical component for systems dealing with textual information processing. However, the current approach faces a significant hurdle due to the computational intensity of the process, particularly when employing complex optimization techniques like swarm intelligence optimization alongside a costly ATS repair operator. While the current approach yields impressive Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metrics for the generated summary, it struggles with inefficiencies, mainly attributed to the substantial optimization time consumed by the ATS repair operator scheme. In order to address this, a novel solution called Decomposition-based Multi-Objective Differential Evolution (MODE/D) is proposed. It is built upon the foundation of Differential Evolution for Multi-Objective Optimization (DEMO) and the weighted sum method (WS), coupled with an innovative ATS repair operator scheme. Through experimentation on Document Understanding Conferences (DUC) datasets, the novel approach of MODE/D – WS is validated by evaluating the results using ROUGE metrics. The outcomes are twofold: a remarkable reduction in serial execution time and a noteworthy enhancement over existing techniques in the scholarly domain, as evidenced by improved ROUGE-1, ROUGE-2, and ROUGE-L scores.