Dynamic Multi-objective Optimization Research Articles

A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization

Dynamic multi-objective big data optimization problems (DMBDOPs) are challenging because of the difficulty of dealing with large-scale decision variables and continuous problem changes. In contrast to classical multi-objective optimization problems, DMBDOPs are still not intensively explored by researchers in the optimization field. At the same time, there is lacking a software framework to provide algorithmic examples to solve DMBDOPs and categorize benchmarks for relevant studies. This paper presents a metaheuristic software framework for DMBDOPs to remedy these issues. The proposed framework has a lightweight architecture and a decoupled design between modules, ensuring that the framework is easy to use and has enough flexibility to be extended and modified. Specifically, the framework now integrates four basic dynamic metaheuristic algorithms, eight test suites of different types of optimization problems, as well as some performance indicators and data visualization tools. In addition, we have proposed an experience reuse method, speeding up the algorithm’s convergence. Moreover, we have implemented parallel computing with Apache Spark to enhance computing efficiency. In the experiments, algorithms integrated into the framework are tested on the test suites for DMBDOPs on an Apache Hadoop cluster with three nodes. The experience reuse method is compared to two restart strategies for dynamic metaheuristics.

Decoupled MPC Power Balancing Strategy for Coupled Inductor Flying Capacitor DC–DC Converter

A decoupled model predictive control (MPC) power balancing strategy for a coupled inductor-based flying capacitor DC–DC converter (FCDC) is a proposed to solve the power imbalance caused by the parameter differences in the coupled inductor. The decoupled mathematical model of coupled inductor FCDC is firstly derived by analyzing the converter operation state under various modes. On this basis, the control relationship between inductor current and flying capacitor (FC) voltage is redefined and an MPC power balance strategy based on the inductor current with single-step optimization is proposed. The proposed MPC strategy not only achieves decoupled power balancing control but also solves multi-objective dynamic optimization control of the inductor current and FC voltage, greatly reducing the computation load. A detailed theoretical analysis of the proposed strategy is presented and the balancing performance is effectively verified through the experiments.

Effective response strategies based on adaptive selection for dynamic multi-objective evolutionary optimization

Dynamic multiobjective optimization problems (DMOPs) change over time, which require Evolutionary algorithms (EA) track Pareto-optimal solution (PS) or/and Pareto-optimal front (PF) in a constantly change environment. Prediction-based algorithms are the most common method to solve DMOPs. However, a single elaborate predictor is not always suitable for extracting changing pattern of different DMOPs, and not to mention DMOPs with unpredictable changes. To overcome these limitations, a simple yet effective algorithm, response strategies based on adaptive selection (RSAS), are proposed in this paper. When a change occurs, RSAS provides diversified solutions by different proposed strategies, that is, a center-guided self-correcting prediction, an individual-based prediction, and a precision-controllable mutation. Based on the quality of their generated solution set, an adaptive selection mechanism can adjust the selection probability of these three strategies. Since RSAS consists of not merely two different prediction strategies but also a mutation strategy, which can be more responsive to predictable and unpredictable changes. To validate the performance of RSAS, DMOP benchmarks in CEC2018 with recommended configurations are adopted. Compared to four state-of-the-art algorithms, the experimental results show that RSAS is effective and efficient.

Dynamic multi-objective evolutionary algorithm based on decomposition with hybrid prediction

The proposed dynamic multi-objective evolutionary algorithm, DMOEA/D-HP, addresses temporal variations in both the Pareto Front (PF) and Pareto Set (PS) for dynamic multi-objective optimization problems (DMOPs). Utilizing a hybrid prediction approach, the algorithm adapts to the dynamic nature of the problem. The population is divided into three segments for prediction: individuals with a distance greater than a threshold in PS for central prediction, those with a distance less than a threshold in PS for differential evolutionary prediction, and the remaining individuals for cross-mutation to maintain diversity. To assess DMOEA/D-HP’s effectiveness, it is compared with three advanced algorithms in DMOP by using the DF test set. Experimental results demonstrate that DMOEA/D-HP outperforms in terms of distribution and convergence when solving DMOPs.

Deterministic mathematical modeling, sensitivity analysis, and dynamic optimization of cross-flow ultrafiltration systems for concentration of monoclonal antibody solutions

This manuscript proposes a general new framework for mathematical modeling, extended sensitivity analysis and dynamic optimization of tangential flow filtration (TFF) systems for concentration of monoclonal antibody (mAb) products and, potentially, other biologics. This framework is comprised of four major components: (I) a new first-principles-inspired TFF model; (II) dedicated parameter estimation strategies for automated model training; (III) new extended sensitivity analysis techniques for enhancing TFF phenomenological understanding and providing general guidance on TFF process development; and (IV) novel mono-objective and multi-objective dynamic optimization strategies for optimal TFF design and operation. The application of this framework to Bovine immunoglobulin γ (IgG) – a mAb analog in terms of physicochemical properties – shows the potential benefits it may offer in terms of overall TFF performance and rapid TFF development for new mAb candidates, compared to the current state of the art.

Scalable benchmarks and performance measures for dynamic multi-objective optimization

Dynamic multi-objective optimization problems (DMOPs) can be utilized to model certain real-world problems that have a dynamic nature. Algorithms for solving DMOPs can be evaluated and improved by comparing their performance on different benchmarks. However, some existing benchmarks for DMOPs have the limitation of non-uniform weights for decision variables. Additionally, dynamic many-objective optimization problems (DMaOPs) involve more than three objectives, but only a few existing benchmarks can be extended to accommodate DMaOPs. Furthermore, some existing performance measures for DMOPs may not effectively compare the relative performance differences between multiple algorithms or evaluate the search uniformity among different objectives. In this paper, we propose improvements to an existing benchmark for DMOPs by expanding the impact range of decision variables. Moreover, a benchmark framework that can be extended to accommodate DMaOPs is proposed, thus addressing a research gap between the optimization of DMOPs and DMaOPs. Additionally, a set of performance measures for DMOPs are proposed, which can evaluate the relative performance and search uniformity of multi-objective optimization algorithms. By comparing the performance of state-of-the-art and commonly used algorithms on test problems, we can gain a better understanding of the characteristics and strengths and weaknesses of the algorithms and test problems.

A novel population robustness-based switching response framework for solving dynamic multi-objective problems

In this paper, a novel population robustness-based switching response framework (PR-SRF) is proposed to develop effective dynamic multi-objective optimization algorithm (DMOA), which integrates different response strategies to comprehensively cope with the dynamic behaviors. In particular, the population robustness is described by the quantification of how severely the environmental changes affect current population, which is timely graded as three levels of weak, strong, and normal to enable the adaptive switch of three different responses of diversity-enhancement, diversity-maintenance, and the knowledge-transfer, respectively. In this way, associations between the adopted responses and the changing environments are successfully established, thereby facilitating more intelligent decision when handling the dynamic behaviors. According to the benchmark evaluation results, the proposed PR-SRF-DMOA yields better comprehensive performance than several other DMOAs with popular response strategies, and it also outperforms another three DMOAs with hybrid responses, which demonstrates the great competitiveness of our algorithm. In addition, ablation study proves that the proposed PR-SRF can sufficiently exploit the merits of different responses, which effectively alleviates the negative knowledge transfer in extremely fluctuating environments, thereby providing valuable references for the development of evolutionary transfer optimization (ETO) algorithms.

A prediction method for dynamic multiobjective optimization based on joint subspace and correlation alignment

Dynamic multiobjective optimization is a significant challenge in accurately capturing changes in Pareto optimal sets (PS), encompassing both location and manifold changes. Existing approaches primarily focus on tracking changes in the location of the PS, often overlooking the potential impact of changes in the PS manifold, which can be decomposed into rotation and distortion changes. Such oversights can lead to a reduction in the overall performance of an algorithm. To address this issue, a prediction method based on joint subspace and correlation alignment (PSCA) is proposed. PSCA leverages a subspace alignment strategy to effectively capture rotation change in the PS manifold while employing a correlation alignment strategy to capture distortion change. By integrating these two strategies, a quasi-initial population is generated that embodies the captured rotation and distortion change patterns in a new environment. Then, the promising individuals are selected from this quasi-initial population based on their nondominated relations and crowding degree to form the initial population in the new environment. To evaluate the effectiveness of PSCA, we conduct experiments on fourteen benchmark problems. The experimental results demonstrate that PSCA achieves significant improvements over several state-of-the-art algorithms.

Multi-Objective Dynamic Reconstruction of Distributed Energy Distribution Networks Based on Stochastic Probability Models and Optimized Beetle Antennae Search

In the dynamic optimization problem of the distribution network, a dynamic reconstruction method based on a stochastic probability model and optimized beetle antennae search is proposed. By implementing dynamic reconstruction of distributed energy distribution networks, the dynamic regulation and optimization capabilities of the distribution network can be improved. In this study, a random probability model is used to describe the uncertainty in the power grid. The beetle antennae search is used for dynamic multi-objective optimization. The performance of the beetle antennae search is improved by combining it with the simulated annealing algorithm. According to the results, the optimization success rate of the model was 98.7%. Compared with the discrete binary particle swarm optimization algorithm and bacterial foraging optimization algorithm, it was 9.3% and 26.1% faster, respectively. For practical applications, this model could effectively reduce power grid transmission losses, with a reduction range of 16.7–18.6%. Meanwhile, the charging and discharging loads were effectively reduced, with a reduction range of 16.2–19.7%. Therefore, this method has significant optimization effects on actual power grid operation. This research achievement contributes to the further development of dynamic reconstruction technology for distribution networks, improving the operational efficiency and stability of the power grid. This has important practical significance for achieving green and intelligent operation of the power system.

A Mahalanobis Distance-Based Approach for Dynamic Multiobjective Optimization With Stochastic Changes

In recent years, researchers have made significant progress in handling dynamic multi-objective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multi-objective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This paper presents a Mahalanobis Distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. MDA has been tested on stochastic DMOPs with 2 to 4 objectives. The results show that MDA performs significantly better than the other latest algorithms in this paper, suggesting that MDA is effective for DMOPs with stochastic changes.

Dynamic Multiobjective Evolutionary Optimization via Knowledge Transfer and Maintenance

Dynamic Multiobjective Evolutionary Optimization via Knowledge Transfer and Maintenance

A new framework of change response for dynamic multi-objective optimization

Combining response strategies into multi-objective evolutionary algorithms (MOEAs) for dynamic multi-objective optimization problems (DMOPs) is very popular. However, most of them hardly focus on DMOPs via enhancing the operator’s searching ability of MOEAs. We present a new framework of change response called MOEA/D-HSS. When a change is detected, MOEA/D-HSS updates and assesses saved historical information, computing the intensity of change on the decision variables and the similarity between the current environment and historical ones. Hybrid search strategies (HSS) adaptively adjust the searching range of the population in each generational cycle based on the knowledge above, which has a great chance of discovering new promising regions. HSS is integrated into the variation operator of MOEA based on decomposition (MOEA/D-DE) to enhance its search ability. We take into account that the historical information may be useless references in the later stage of the evolution. Thus, the frequency of HSS usage is gradually decreased in every time interval to balance the population’s convergence and diversity. Experimental results demonstrate that MOEA/S-HSS is very competitive on most benchmark problems compared with other state-of-the-art algorithms.

Dynamic Operation Optimization of Complex Industries Based on a Data-Driven Strategy

As industrial practices continue to evolve, complex process industries often exhibit characteristics such as multivariate correlation, dynamism, and nonlinearity, making traditional mechanism modeling inadequate in terms of addressing the intricacies of complex industrial problems. In recent years, with advancements in control theory and industrial practices, there has been a substantial increase in the volume of industrial data. Data-driven dynamic operation optimization techniques have emerged as effective solutions for handling complex industrial processes. By responding to dynamic environmental changes and utilizing advanced optimization algorithms, it is possible to achieve dynamic operational optimization in industrial processes, thereby reducing costs and emissions, improving efficiency, and increasing productivity. This correlates nicely with the goals set forth by conventional process operation optimization theories. Nowadays, this dynamic, data-driven strategy has shown significant potential in complex process industries characterized by multivariate correlations and nonlinear behavior. This paper approaches the subject from a data-driven perspective by establishing dynamic optimization models for complex industries and reviewing the state-of-the-art time series forecasting models to cope with changing objective functions over time. Meanwhile, aiming at the problem of concept drift in time series, this paper summarizes new concept drift detection methods and introduces model update methods to solve this challenge. In addressing the problem of solving dynamic multi-objective optimization problems, the paper reviews recent developments in dynamic change detection and response methods while summarizing commonly used as well as the latest performance measures for dynamic multi-objective optimization problems. In conclusion, a discussion of the research progress and challenges in the relevant domains is undertaken, followed by the proposal of potential directions for future research. This review will help to deeply understand the importance and application prospects of data-driven dynamic operation optimization in complex industrial fields.

A dynamic multi-objective evolutionary algorithm based on genetic engineering and improved particle swarm prediction strategy

Evolutionary and particle swarm optimisation (PSO) algorithms are widely used to solve various optimisation problems. However, both methods have limitations when applied to dynamic multi-objective optimisation problems. Therefore, we propose a dynamic multi-objective evolutionary algorithm based on genetic engineering and improved particle swarm prediction. Genetic engineering encompasses gene sequencing and editing, whereas improved particle swarm prediction involves enhancing information utilisation and dynamic performance. The improved PSO can be better combined with dynamic multi-objective optimization problems (DMOPs) for predicting changing populations, which we call improved particle swarm prediction. Gene sequencing clarifies the functions of different genes during the evolution process, and gene editing enables the algorithm to effectively avoid local optima. Expanding on this foundation, we redefined the notions of particle and global bests in the PSO strategy to improve the information utilisation. Additionally, we innovatively introduced the concept of acceleration, which greatly enhances the dynamic performance of the PSO. Finally, we conducted two experiments to verify the accuracy of our gene sequencing strategy and the performance of our optimisation algorithm. The results indicate that gene sequencing can effectively classify genes, and the developed optimisation algorithm significantly outperforms similar, state-of-the-art, and classical algorithms in terms of distribution and dynamics on 25 test problems.

A learnable population filter for dynamic multi-objective optimization

In this paper, a novel learnable population filter is proposed to solve the dynamic multi-objective problems (DMOPs), whose main idea is to pick out potential valuable individuals in the changing situation via the trained filter to facilitate the population convergence in a new environment. In particular, by selecting training samples from three different optional pools, rich information in the previous searching experiences can be sufficiently used to cope with the dynamic behaviors in DMOPs, thereby handling the imperfect history data availability caused by the environmental uncertainty to some extents. Then, the screened population in the new environment, which is regarded to have reliable quality that benefits accelerating the evolution, is used to initialize the static optimizer. In addition, partial random solutions are employed as supplement to the initial population to further enhance the diversity. It is shown from the benchmark evaluations that the proposed method outperforms some other popular algorithms on both convergence and diversity by seamlessly combining the mainstream strategies in dealing with the dynamic behaviors, which is a competitive method that conforms to the novel evolutionary transfer optimization (ETO) trend. Moreover, effectiveness of the core components is validated through extensive ablation studies, which brings a new sight in developing the learnable DMOP solvers.

Optimization design of load-sharing and light weight of the twin rotors concentric face gear power-split transmission system based on gear tooth matching condition

To improve the dynamic load-sharing performance and achieve lightweight, the twin rotors concentric face gear power-split transmission system (TRFGPSTS) was optimized. The gear tooth matching conditions of the system based on the design characteristics of power flow closed-loop and virtual constraint configuration of the system are established, and the basic parameters of each gear meet the requirements of the system load-sharing layout and synchronous meshing of each branch movement are calculated. Based on the lumped mass parameter method, combined with the calculation results of gear tooth matching, the 45-DOF bending torsional coupling dynamic model of the system was established considering time-varying meshing stiffness, support stiffness, manufacturing and installation errors, and other factors, and the influence of each factor on the dynamic load-sharing performance of the system was analyzed. Combined with the influence law of various factors, a multi-objective dynamic load-sharing optimization design model was established with the best dynamic load-sharing performance and the minimum system quality as the objective function. Through the weighted combination method, the global optimal solution of the system optimization design was determined, and the influence of each parameter on the optimization objective function was analyzed. The correctness of the results was verified by using the genetic algorithm based on Pareto frontier distribution. The results show that the dynamic load-sharing characteristics of the system become worse with the increase of error and torsional stiffness, and are more sensitive to the influence of various error parameters. The optimization process focuses on the geometric parameters such as the Module, the teeth Number, the Pressure angle, and the Tooth width of each gear, which can reflect the degree of influence on the dynamic load-sharing and lightweight of the system. After optimization, the dynamic load sharing coefficient (DLSC) was reduced to 1.017, and the overall geometric volume was reduced to 1.473 × 108 mm3. It provides a theoretical basis for the design and research of a new type of helicopter power transmission system with a compact structure, good maneuverability, and high reliability.

Double-space environmental change detection and response strategy for dynamic multi-objective optimize problem

Dynamic multi-objective optimization problems (DMOPs) which contain various Pareto-optimal front (PF) and Pareto-optimal set (PS) have gained much attention. Accurate environmental change detection reveals the change degree of DMOPs and contributes the algorithm to quickly respond to the environment changes. In order to fully detect environmental changes and efficiently track front, a double-space environmental change detection and response strategy (DSDRS) is proposed. It could detect whether the environment has changed while explore the change intensity of PF and PS, respectively. Moreover, different response strategies are implemented for PF and PS. For PF environmental changes, a multiple knee points-guided evolutionary strategy (MKGES) is proposed, which is driven by front shape information and adaptively responds to different PF change intensities. For PS environmental changes, a knowledge guided memory strategy (KGMS) is proposed, which guides population evolution based on environmental information. The effectiveness of DSDRS is confirmed by comparison with five evolutionary algorithms on 20 dynamic multiobjective benchmark functions. Simulation results demonstrate that the performance of proposed algorithm is outstanding on test functions with complex changing PF and PS.

A Novel Dynamic Multiobjective Optimization Algorithm With Non-Inductive Transfer Learning Based on Multi-Strategy Adaptive Selection.

In this article, a novel multi-strategy adaptive selection-based dynamic multiobjective optimization algorithm (MSAS-DMOA) is proposed, which adopts the non-inductive transfer learning (TL) paradigm to solve dynamic multiobjective optimization problems (DMOPs). In particular, based on a scoring system that evaluates environmental changes, the source domain is adaptively constructed with several optional groups to enrich the knowledge. Along with a group of guide solutions, the importance of historical experiences is estimated via the kernel mean matching (KMM) method, which avoids designing strategies to label individuals. The proposed MSAS-DMOA is comprehensively evaluated on 14 DMOPs, and the results show an overwhelming performance improvement in terms of both convergence and diversity as compared with other four popular DMOAs. In addition, ablation studies are also conducted to validate the superiority of the applied strategies in MSAS-DMOA, which can effectively alleviate the negative transfer phenomenon. Without the conventional labeling procedure, the proposed method also yields satisfactory results, which can provide valuable reference for designing other evolutionary transfer optimization (ETO) algorithms.

A Cooperative Evolutionary Computation Algorithm for Dynamic Multiobjective Multi-AUV Path Planning

Multiple autonomous underwater vehicles (AUVs) are popular for executing submarine missions, which involve multiple targets distributed in a large and complex underwater environment. The path planning of multiple AUVs is a significant and challenging problem, which determines the location of surface points for AUV launch and plans the paths of AUVs for target traveling. Most existing works model the problem as a single-objective static optimization problem. However, the target missions may change over time, and multiple optimization objectives are usually expected for decision making. Thus, this paper models the problem as a dynamic multiobjective optimization problem and proposes a cooperative evolutionary computation algorithm to provide diverse and high-quality solutions for decision makers. In the proposed method, solutions are represented using a bi-layer encode scheme, in which the first layer indicates the surface location points and the second layer represents the traveling sequences of target missions. Multiple populations for multiple objectives (MPMO) framework is adopted to efficiently solve the dynamic multiobjective AUV optimization problem. In addition, a recombination-based sampling strategy is developed to improve convergence by fusing the information of multiple populations. Once a change occurs, an incremental response strategy is adopted to generate high-quality solutions for population evolution. Based on the dataset of New Zealand bathymetry, six complex underwater scenarios are constructed with a size of 50 km×50 km×10 km and 400 target missions for tests. Experimental results show that the proposed method outperforms the state-of-the-art algorithms in terms of solution diversity and optimality.

Learning to Expand/Contract Pareto Sets in Dynamic Multi-Objective Optimization With a Changing Number of Objectives

Learning to Expand/Contract Pareto Sets in Dynamic Multi-Objective Optimization With a Changing Number of Objectives