Dynamic Multi-objective Evolutionary Algorithm Research Articles

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

A dynamic multi-objective evolutionary algorithm with variable stepsize and dual prediction strategies

The prediction strategy is a key method for solving dynamic multi-objective optimization problems (DMOPs), particularly the commonly used linear prediction strategy, which has an advantage in solving problems with regular changes. However, using the linear prediction strategy may have limited advantages in addressing problems with complex changes, as it may result in the loss of population diversity. To tackle this issue, this paper proposes a dynamic multi-objective optimization algorithm with variable stepsize and dual prediction strategies (VSDPS), which aims to maintain population diversity while making predictions. When an environmental change is detected, the variable stepsize is first calculated. The stepsize of the nondominated solutions is expressed by the centroid of the population, while the stepsize of the dominated solutions is determined by the centroids of the clustered subpopulations. Then, the dual prediction strategies combine an improved linear prediction strategy with a dynamic particle swarm prediction strategy to track the new Pareto-optimal front (PF) or Pareto-optimal set (PS). The improved linear prediction strategy aims to enhance the convergence of the population, while the dynamic particle swarm prediction strategy focuses on preserving the diversity of the population. There have also been some improvements made in the static optimization phase, which are advantageous for both population convergence and diversity. VSDPS is compared with six state-of-the-art dynamic multi-objective evolutionary algorithms (DMOEAs) on 28 test instances. The experimental results demonstrate that VSDPS outperforms the compared algorithms in most instances.

A novel preference-driven evolutionary algorithm for dynamic multi-objective problems

Most studies in dynamic multi-objective optimization have predominantly focused on rapidly and accurately tracking changes in the Pareto optimal front (POF) and Pareto optimal set (POS) when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). In particular, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm consists of three key components: an evolutionary direction adjustment strategy based on changing reference points to accommodate shifts in preferences, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy that combines linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in scenarios where preferences remain unchanged. Experimental studies conducted on 30 widely used benchmark problems in which it outperforms contrasting algorithms on 71% of test suits. Empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs.

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.

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.

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.

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.

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 dynamic multi-objective evolutionary algorithm using center and multi-direction prediction strategies.

Dynamic multi-objective optimization problems have been popular because of its extensive application. The difficulty of solving the problem focuses on the moving PS as well as PF dynamically. A large number of efficient strategies have been put forward to deal with such problems by speeding up convergence and keeping diversity. Prediction strategy is a common method which is widely used in dynamic optimization environment. However, how to increase the efficiency of prediction is always a key but difficult issue. In this paper, a new prediction model is designed by using the rank sums of individuals, and the position difference of individuals in the previous two adjacent environments is defined to identify the present change type. The proposed prediction strategy depends on environment change types. In order to show the effectiveness of the proposed algorithm, the comparison is carried out with five state-of-the-art approaches on 20 benchmark instances of dynamic multi-objective problems. The experimental results indicate the proposed algorithm can get good convergence and distribution in dynamic environments.

Dynamic Multi-Objective Evolutionary Algorithms: An Overview

Evolutionary algorithms have been widely explored and applied in optimization problems. The introduction of multi-objective evolutionary algorithms (MOEAs) has facilitated the adaptation and creation of new methods to handle more complex and realistic optimizations, such as dynamic multi-objective optimization problems (DMOPs). A dynamic MOEA (DMOEA) can be constructed by changing the MOEA structure and variation operators used to solve DMOPs. Furthermore, DMOEAs can implement change-detection strategies and mechanisms to handle the dynamics of the environment. DMOEAs are often designed to solve unconstrained DMOPs. However, several studies have been conducted to solve dynamic constrained MOPs and more recently, to solve dynamic many-objective optimization problems. There are many real-world DMOPs; however, few DMOEAs have been evaluated with respect to those problems. Evaluation of algorithm performance is an essential aspect of using DMOEAs. Several measures used to validate MOEAs have been adapted to assess DMOEAs and quantitatively compare them. This paper presents a broad review of DMOEAs. The information is summarized and organized according to current research branches. Furthermore, a more general classification scheme for DMOEAs is proposed, based on the method of incorporating diversity to solve DMOPs.

A Knowledge Guided Transfer Strategy for Evolutionary Dynamic Multiobjective Optimization

The key task in dynamic multiobjective optimization problems (DMOPs) is to find Pareto-optima closer to the true one as soon as possible once a new environment occurs. Previous dynamic multiobjective evolutionary algorithms (DMOEAs) normally focus on DMOPs with regular environmental changes, but neglect widespread random one, limiting their applications in real-world fields. To address this issue, a knowledge guided transfer strategy based DMOEA is proposed in the paper. First, knowledge described as a two-tuple is extracted under each historical environment and preserved to a knowledge pool. Redundant knowledge is recognized and adaptively removed so as to guarantee the diversity of the pool. Second, a knowledge matching strategy is developed to re-evaluate the representative of each stored knowledge under a new environment, with the purpose of finding the most valuable one to promote positive knowledge transfer. Third, an improved knowledge transfer mechanism based on subspace alignment is introduced. By integrating it with knowledge reuse mechanism, a hybrid transfer strategy is constructed to adaptively select the most suitable one in terms of the similarity degree of selected knowledge on the current environment, and then generate a new initial population. Experiments on 20 benchmark problems demonstrate that the knowledge guided transfer strategy outperforms five state-of-the-art algorithms, achieving good versatility in solving DMOPs with both regular and random changes.

Domain Generalization-Based Dynamic Multiobjective Optimization: A Case Study on Disassembly Line Balancing

The objective of disassembly lines is to disassemble End-of-Life products in a remanufacturing field. The disassembly line balancing problem (DLBP) considers how to allocate disassembly operations to operators on the disassembly line to optimize predetermined goals, such as cycle time. In practice, various environmental uncertainties (e.g., uncertain product quality) exist in the disassembly line. These uncertainties entail DLBP essentially a dynamic multi-objective optimization problem. This study presents a dynamic DLBP (D-DLB) to model the effect of environmental uncertainties on the assignment of disassembly operations. Furthermore, a prediction-based dynamic optimization algorithm, termed domain generalization-based dynamic multi-objective evolutionary algorithm (DG-DMOEA), combining meta-learning with multi-objective optimization, is proposed to solve D-DLB. In DG-DMOEA, a meta-learning algorithm is employed to learn the parameters of a solution-generative model from the Pareto-optimal sets in all historical environments. Subsequently, the solution-generative model is applied to generate a high-quality initial population that can assist multi-objective optimization algorithms in finding the Pareto-optimal set in the new environment faster. Since no information in the new environment is required, learning can begin before the new environment arrives, significantly reducing computational time. Moreover, different solution-generative models can be designed for different DMOPs. Therefore, DG-DMOEA can thoroughly combine real-world problem properties to represent knowledge. The experimental results show that, compared with state-of-the-art methods, DG-DMOEA can considerably improve the quality of solutions and significantly enhance the ability to react quickly to environmental changes.

Dynamic adaptive multi-objective optimization algorithm based on type detection

Dynamic multi-objective optimization problems (DMOPs) are multi-objective problems that are influenced by dynamically changing environmental parameters. Most current algorithms for solving DMOPs only respond to dynamic changes in the decision space or objective space and also ignore the impact of the type of DMOPs on the algorithm. The changes in the Pareto-optimal solution (POS) and Pareto-optimal front (POF) may affect the type of change in DMOPs. Therefore, this paper proposed an adaptive dynamic multi-objective evolutionary algorithm for type detection (TDA-DMOEA). First, the dynamic detection operator is designed to identify the types of dynamic problems. The Wilcoxon signed-rank test and Hyper Volume (HV) are used to detect the difference of POS and POF in two adjacent environments respectively. Then, different response strategies are designed to cope with different types of changes in DMOP. In particular, a multi-angle-based transfer learning method (MA-TL) with a closed kernel function is derived when faced with simultaneous changes in POS and POF. Finally, a comprehensive study of the commonly used benchmark set of DMOPs is presented, and the proposed algorithm achieves better performance in optimizing DMOPs.

Multi-strategy dynamic multi-objective evolutionary algorithm with hybrid environmental change responses

Multi-strategy dynamic multi-objective evolutionary algorithm with hybrid environmental change responses

Dynamic multi-objective workflow scheduling for combined resources in cloud

Cloud resource providers offer idle resources to users as spot instances. The price of the instances changes with market supply and demand, and the dynamic price can have a significant impact on workflow scheduling. In this work, we use a combination of spot and on-demand instances as the foundation cloud resource and characterize the dynamic workflow scheduling problem as a dynamic multi-objective optimization problem (DMOP), where the dynamics originate from the dynamic price of spot instances. The scheduling solution is found by considering three objectives: maximizing the reliability of the instances while minimizing the makespan and cost. In addition, we provide an enhanced MOEAD algorithm called MOEA/D-URDI that combines diversity introduction and uniform random sampling, where the uniform random sampling paradigm is used to generate the initial weight vector. The dynamic multi-objective optimization evolutionary algorithm DMOEA/D-URDI is then created by combining the method with a dynamic optimization framework. Our technique beats existing algorithms, according to experimental data based on dynamic benchmark sets and three well-known scientific procedures in terms of metrics on dynamic benchmark sets and better ensures reliability in scheduling scientific workflows while reducing makespan and cost.

Novel strategies based on a gradient boosting regression tree predictor for dynamic multi-objective optimization

Prediction-based dynamic multiobjective optimization evolutionary algorithms have become one of the mainstream methods for solving dynamic multiobjective optimization problems. However, the unknown nonlinear relationships in sequential environments bring great challenge to the construction of prediction model and the inevitable error between the historical obtained solutions and the real pareto-optimal solutions troubles the prediction accuracy. In this paper, a gradient boosting regression tree based dynamic multiobjective optimization evolutionary algorithm is proposed, called MOEA/D-XGB. The time series solutions formed by subspace decomposition are trained in the XGBoost-based predictor to produce a high-quality initial population when environmental change occurs. And a novel population promotion strategy based on generalized additive model is proposed to improve the quality of historical obtained solutions. The performance comparisons with five state-of-the-art algorithms have shown that MOEA/D-XGB achieves best performance in 59 out of 70 experiments on MIGD and 60 out of 70 experiments on MHV, respectively, which demonstrates that the proposed design is capable of significantly improving the performance of dynamic multiobjective optimization.

Dynamic Multi-objective Optimization for Coagulating Process of Carbon Fiber Precursor Based on Lifelong Learning

Process parameter optimization is an essential link in the coagulating process of carbon fiber. In this paper, considering the dynamic factors of the coagulating bath environment, a dynamic multi-objective optimization problem (DMOP) model for the coagulating process is constructed with process parameters as decision variables and performance indicators as optimization objectives. We combine lifelong learning (LLL) and multi-objective optimization to solve this model and propose a lifelong learning-based dynamic multi-objective evolutionary algorithm (LLL-DMOEA). In LLL-DMOEA, the lifelong learning method is used to learn common knowledge in historical environments. After the arrival of the new environment, we use the common knowledge to generate a high-quality initial population and speed up the process of the multi-objective optimization algorithm to find the Pareto-optimal set (POS) in the new environment. At the same time, common knowledge only requires information in historical environments. The response time to environmental changes can be sped up by learning before the new environment arrives. Experimental results show that the proposed algorithm can effectively solve the optimization problem of process parameters in the coagulating process.

Considering spatiotemporal evolutionary information in dynamic multi‐objective optimisation

AbstractPreserving population diversity and providing knowledge, which are two core tasks in the dynamic multi‐objective optimisation (DMO), are challenging since the sampling space is time‐ and space‐varying. Therefore, the spatiotemporal property of evolutionary information needs to be considered in the DMO. In the present study, a sliding‐time‐window‐based population clustering method (SPC) is proposed to effectively solve dynamic multi‐objective optimisation problems (DMOPs). In the SPC, the knowledge is provided by saving historical data in the temporal dimension, and a spectral clustering method is used to divide the saved data into multiple neighbourhood subspaces for preserving population diversity in the spatial dimension. The SPC is incorporated into the RM‐MEDA and is compared with other recently proposed state‐of‐the‐art dynamic multi‐objective evolutionary algorithms (DMOEAs) on 14 DMOPs introduced in IEEE CEC2018. Simulation results demonstrate that the proposed method is capable of enhancing the tracking performance of the RM‐MEDA in the dynamically changing environments. Additionally, the SPC is utilised to solve an actual dynamic multi‐objective translation control problem of an immersed tunnel element. Results show that the proposed SPC outperforms the knee point‐based transfer learning method in terms of both computational cost and tracking performance.

A dynamic multi-objective evolutionary algorithm based on gene sequencing and gene editing

Evolutionary Algorithm is a mature global optimization method with high robustness and wide applicability. It can effectively address complex problems that are difficult to be solved by traditional optimization algorithms. In evolution, it is still uncertain which gene parent can produce offspring through competition and eventually become an excellent individual of the last generation population. Inspired by the fact that gene sequencing can discover biological gene defects, this paper proposes a dynamic multi-objective evolutionary algorithm based on gene sequencing and gene editing (GSGE). The gene sequencing algorithm is designed using support vector machine (SVM), and correlation coefficient, as the result of sequencing, has also been verified. Combining stratified sampling and multi-population strategy, a prediction strategy that can use all chromosome information is designed. The new gene editing strategy edits individual genes to optimize the Pareto optimal front (PF) distribution, for the first time different types of genes can match different optimization strategies, which greatly improves the distribution of the population without affecting the convergence. The comparison experiment between GSGE and the state of the art algorithms is performed on 25 test functions and the Pareto optimal set (PS) curves obtained by dimension reduction fully demonstrate the significant advantages of GSGE.