Dynamic Multi-objective Evolutionary Algorithm Research Articles

A dynamic multi-objective evolutionary algorithm based on Niche prediction strategy

In reality, many multi-objective optimization problems are dynamic. The Pareto optimal front (PF) or Pareto optimal solution (PS) of these dynamic multi-objective problems (DMOPs) changes as the environment change. Therefore, solving such problems requires an optimization algorithm that can quickly track the PF or PS after an environment change. Prediction-based response mechanism is a common method used to deal with environmental changes, which is commonly known as center point-based prediction. However, if the predicted direction of the center point is inaccurate, the predicted population will be biased towards one side. In this paper, we propose a niche prediction strategy based on center and boundary points (PCPB) to solve the dynamic multi-objective optimization problems, which consists of three steps. After environmental changes are detected, the first step is to divide the niche, dividing different individuals in the PS into different niche populations. The second step is to independently predict different niches, and select individuals with good convergence and distribution in the niche to predict the individuals that will produce the next generation. Finally, some different individuals are randomly generated in the next possible PS area to ensure the diversity of the population. To verify whether our proposed strategy is effective and competitive, PCPB was compared with five state-of-the-art strategies. The experimental results show that PCPB performed competitively in solving dynamic multi-objective optimization problems, which proves that our algorithm has good competitiveness.

A dynamic multi-objective evolutionary algorithm based on two-stage dimensionality reduction and a region Gauss adaptation prediction strategy

Dynamic multi-objective optimization evolutionary algorithms (DMOEAs) have attracted increasing attention due to their superior performance in real-world applications. It is challenging to rapidly track the changing Pareto set (PS) and Pareto front (PF) in DMOEAs. However, most existing studies only focus on the position change in the PS. To address this problem, we define a series of new PS region changes. Based on these definitions, we propose a dynamic multi-objective evolutionary algorithm based on two-stage dimensionality reduction and a region Gauss adaptation prediction strategy (DRPS). Specifically, we estimate the possible type of PS changes at the next moment by processing historical information. Afterward, the basic scaling population PSB is generated by dimensionality reduction, while parameters including the scaling factor and density change rate are calculated. Combining these parameters with a Gaussian distribution, the algorithm adaptively adjusts the sampling probability of individuals in PSB, achieving prediction with different types of PS changes. We conducted extensive experiments and compared classical algorithms, the latest algorithms, and algorithms with the same type in 25 test functions. The results demonstrate that the proposed algorithm outperforms the compared algorithms in most cases, while implying that the newly defined PS region change is reasonable.

A Self-Learning Based Dynamic Multi-Objective Evolutionary Algorithm for Resilient Scheduling Problems in Steelmaking Plants

Scheduling is one of the most important missions for plant-wide optimization in steelmaking manufacturing systems. In the context of dynamic scheduling, the decision-maker should simultaneously minimize economic objectives within the decision space and violation penalty out of the decision space. In this study, we introduce a resilient scheduling model in steelmaking plants, which provides flexible decisions, including buffering times in between stages and controllable processing speeds in the casting stage, to enable the solution to absorb random disturbances and recover quickly. We formulate the dynamic steelmaking scheduling problem with resilient responding strategies, which is a variant of dynamic multi-objective optimization problems (DMOP), and propose a resilient scheduling optimization framework to solve it over time. First, we employ a vector with problem-specific knowledge to map the whole decision space to sub-schedules in the casting stage, which contains casting priority, casting speed and scaling ratio. Next, we form a multi-objective linear programming model to evaluate these problem-specific vectors. Last but not least, we develop a self-learning based dynamic multi-objective differential evolutionary algorithm to solve the variant DMOP, in which a hypothesis-testing technique is used to detect and identify environmental changes. The sensitivity analysis and algorithm comparisons are performed on a wide range of problem instances under dynamic environments. Experimental evidence validates that the proposed resilient model and the optimization framework is effective to solve the dynamic scheduling problem in steelmaking plants. Note to Practitioners—This paper investigates a dynamic scheduling problem that comes from steelmaking manufacturing systems and is extensively studied in existing works. Because a decision-maker only has incomplete knowledge about the realistic environments, this paper simultaneously considers that both the decision and objective space of a scheduling problem dynamically changed over time. We develop a resilient scheduling model which can absorb the different types or scales of disturbances caused by unforeseen events, and recover rapidly to the original state. We formulate the resilience scheduling model and propose a dynamic multi-objective algorithm based on the self-learning differential evolutionary algorithm to solve it. The effectiveness of the proposed model and algorithm is validated via sensitivity analysis and comparison to other well-known algorithms. Furthermore, the resilient scheduling model and its optimization framework can also be applied to dynamic scheduling problems in other industries.

A dynamic multi-objective evolutionary algorithm using adaptive reference vector and linear prediction

A dynamic multi-objective evolutionary algorithm using adaptive reference vector and linear prediction

Dynamic multi-objective evolutionary optimization algorithm based on two-stage prediction strategy

Tracking pareto-optimal set or pareto-optimal front in limited time is an important problem of dynamic multi-objective optimization evolutionary algorithms (DMOEAs). However, the current DMOEAs suffer from some deficiencies. In the early optimization process, the algorithms may suffer from random search. In the late optimization process, the knowledge which can accelerate the convergence rate is not fully utilized. To address the above issue, a DMOEA based on the two-stage prediction strategy (TSPS) is proposed. TSPS divides the optimization progress into two stages. At the first stage, multi-region knee points are selected to capture the pareto-optimal front shape, which can accelerate the convergence and maintaining good diversity at the same time. At the second stage, improved inverse modeling is applied to search the representative individuals, which can improve the diversity of the population and is beneficial to predicting the moving location of the pareto-optimal front. Experimental results on dynamic multi-objective optimization test suites show that TSPS is superior to the other six DMOEAs. In addition, the experimental results also show that the proposed method has the ability to respond quickly to environmental changes.

Dynamic multi-objective evolutionary algorithm based on knowledge transfer

Dynamic multi-objective optimization problems (DMOPs) are mainly reflected in objective changes with changes in the environment. To solve DMOPs, a transfer learning (TL) approach is used, which can continuously adapt to environmental changes and reuse valuable knowledge from the past. However, if all individuals are transferred, they may experience negative transfers. Therefore, this paper proposes a novel knowledge transfer method for the dynamic multi-objective evolutionary algorithm (T-DMOEA) to solve DMOPs, which consists of a multi-time prediction model (MTPM) and a manifold TL algorithm. First, according to the movement trend of historical knee points, the MTPM model uses a weighted method to effectively track knee points after environmental changes. Then, the knowledge of the suboptimal solution is reused in the non-knee point set using the manifold TL technique, which yields more high-quality individuals and speeds up the convergence. In the dynamic evolutionary process, the knee points and high-quality solutions are combined to guide the generation of the initial population in the next environment, ensuring the diversity of the population while reducing the computational cost. The experimental results show that the proposed T-DMOEA algorithm can converge rapidly in solving DMOPs while obtaining better-quality solutions.

Co-evolutionary algorithm based on problem analysis for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) vary over time, requiring an optimization algorithm to track the position of Pareto-optimal front (PF) in a dynamic environment. To achieve that, a novel co-evolutionary algorithm based on problem analysis (CAPA) is proposed in this paper. CAPA is designed to solve DMOPs from decision space and objective space simultaneously, which is achieved by the combination of adjustable prediction (AP) and precise mapping strategy (PM). In decision space, the proposed multi-model prediction can estimate the location of new population based on the historical median points. In objective space, a novel sampling method is developed to search for sample points with better convergence or diversity. Then, mapping these sample points back to decision space based on inverse model. Through the problem analysis mechanism, the proportion of the new solutions produced by each strategy changes adaptively. CAPA is incorporated into the dynamic multiobjective evolutionary algorithm (DMOEA) based on decomposition (MOEA/D) to construct a novel algorithm. The efficacy of CAPA is validated by comparison with five state-of-the-art algorithms on 28 benchmarks. Experimental results show that CAPA has the ability to generate high quality population uniformly along PF.

Dynamic multi-objective evolutionary algorithms in noisy environments

Real-world multi-objective optimization problems encounter different types of uncertainty that may affect the quality of solutions. One common type is the stochastic noise that contaminates the objective functions. Another type of uncertainty is the different forms of dynamism including changes in the objective functions. Although related work in the literature targets only a single type, in this paper, we study Dynamic Multi-objective Optimization problems (DMOPs) contaminated with stochastic noises by dealing with the two types of uncertainty simultaneously. In such problems, handling uncertainty becomes a critical issue since the evolutionary process should be able to distinguish between changes that come from noise and real environmental changes that resulted from different forms of dynamism. To study both noisy and dynamic environments, we propose a flexible mechanism to incorporate noise into the DMOPs. Two novel techniques called Multi-Sensor Detection Mechanism (MSD) and Welford-Based Detection Mechanism (WBD) are proposed to differentiate between real change points and noise points. The proposed techniques are incorporated into a set of Dynamic Multi-objective Evolutionary Algorithms (DMOEAs) to analyze their impact. Our empirical study reveals the effectiveness of the proposed techniques for isolating noise from real dynamic changes and diminishing the noise effect on performance.

Cluster-Based Regression Transfer Learning for Dynamic Multi-Objective Optimization

Many multi-objective optimization problems in the real world have conflicting objectives, and these objectives change over time, known as dynamic multi-objective optimization problems (DMOPs). In recent years, transfer learning has attracted growing attention to solve DMOPs, since it is capable of leveraging historical information to guide the evolutionary search. However, there is still much room for improvement in the transfer effect and the computational efficiency. In this paper, we propose a cluster-based regression transfer learning-based dynamic multi-objective evolutionary algorithm named CRTL-DMOEA. It consists of two components, which are the cluster-based selection and cluster-based regression transfer. In particular, once a change occurs, we employ a cluster-based selection mechanism to partition the previous Pareto optimal solutions and find the clustering centroids, which are then fed into autoregression prediction model. Afterwards, to improve the prediction accuracy, we build a strong regression transfer model based on TrAdaboost.R2 by taking advantage of the clustering centroids. Finally, a high-quality initial population for the new environment is predicted with the regression transfer model. Through a comparison with some chosen state-of-the-art algorithms, the experimental results demonstrate that the proposed CRTL-DMOEA is capable of improving the performance of dynamic optimization on different test problems.

Dynamic Multi-Objective Optimization in Brazier-Type Gasification and Carbonization Furnace.

With the special porous structure and super-long carbon sequestration characteristic, the biochar has shown to have potential in improving soil fertility, reducing carbon emissions and increasing soil carbon sequestration. However, the biochar technology has not been applied on a large scale, due to the complex structure, long transportation distance of raw materials, and high cost. To overcome these issues, the brazier-type gasification and carbonization furnace is designed to carry out dry distillation, anaerobic carbonization and have a high carbonization rate under high-temperature conditions. To improve the operation and maintenance efficiency, we formulate the operation of the brazier-type gasification and carbonization furnace as a dynamic multi-objective optimization problem (DMOP). Firstly, we analyze the dynamic factors in the work process of the brazier-type gasification and carbonization furnace, such as the equipment capacity, the operating conditions, and the biomass treated by the furnace. Afterward, we select the biochar yield and carbon monoxide emission as the dynamic objectives and model the DMOP. Finally, we apply three dynamic multiobjective evolutionary algorithms to solve the optimization problem so as to verify the effectiveness of the dynamic optimization approach in the gasification and carbonization furnace.

A dynamic multiobjective evolutionary algorithm based on fine prediction strategy and nondominated solutions-guided evolution

A dynamic multiobjective evolutionary algorithm based on fine prediction strategy and nondominated solutions-guided evolution

A dynamic multi-objective optimization evolutionary algorithm based on particle swarm prediction strategy and prediction adjustment strategy

Dynamic Multi-objective Optimization Evolutionary Algorithm (DMOEA) is a promising approach for solving Dynamic Multi-objective Optimization Problems (DMOPs), which has attracted extensive attention owing to its wide application value recently. The focus and difficulty of DMOEA research is to design algorithms that can quickly respond to environmental changes. To achieve this goal, a novel DMOEA based on particle swarm prediction strategy and prediction adjustment strategy is proposed in this paper. After detecting environmental changes, the particle swarm prediction strategy is implemented through the population information at the moment before environmental change to form a predicted population that approximates the new Pareto optimal set (PS)/Pareto optimal front (PF) as much as possible. In addition, by comparing the individual information of the predicted population with that of the population at the moment before the environmental change, a prediction adjustment strategy is given to leave the better individuals to form the initial population in the new environment. The performance of the algorithm is evaluated on the DF test cases and compared with the advanced DMOEAs. The results show that the algorithm has competitive performance in most of the test problems.

A data augmentation based Kriging-assisted reference vector guided evolutionary algorithm for expensive dynamic multi-objective optimization

Expensive dynamic multi-objective optimization problems (EXDMOPs) involve multiple objective functions changing over time steps. In this kind of problems, only a small number of function evaluations can be allowed in each time step. The challenge of EXDMOP is how to quickly and accurately track the changing optimal solutions with only a small number of function evaluations. Although EXDMOP can be solved as a series of independent expensive multi-objective optimization problems or as an ordinary dynamic multi-objective optimization problems, these two methods either ignore the connection between different time steps or degrade the performance significantly due to the requirement for a large number of function evaluations. In this paper, we incorporate two proposed strategies named training data augmentation and sampling pool expansion to the Kriging-assisted reference vector guided evolutionary algorithm to construct a novel algorithm for solving EXDMOPs. The training data augmentation strategy tries to look for the previous similar time step, and adds the solutions evaluated by the objective functions at that time step to current time step. The accuracies of the Kriging models are improved in this way. The sampling pool expansion strategy sends the predicted optimal solutions to the competition of the function evaluations assignment at each time step, where the predicted optimal solutions are generated by the improved population prediction strategy. We set the ablation experiment for the proposed algorithm and compare it with four dynamic multi-objective evolutionary algorithms on various of problems. The experiment results validate the effectiveness of the proposed two strategies. It also indicates that the proposed algorithm is promising for solving EXDMOPs.

Optimization design of two-layer Walker constellation for LEO navigation augmentation using a dynamic multi-objective differential evolutionary algorithm based on elite guidance.

The online version contains supplementary material available at 10.1007/s10291-022-01366-5.

A dynamic multi-objective evolutionary algorithm based on prediction

Abstract The dynamic multi-objective optimization problem (DMOP) is a common problem in optimization problems; the main reasons are the objective’s conflict and environment changes. In this paper, we provide a prediction approach based on diversity screening and special point prediction (DSSP) to tackle the dynamic optimization issue. First, we introduce a decision variable clustering and screening strategy that clusters the decision space of the non-dominated solution set to find the cluster centroids and then employs a decision variable screening strategy to filter out solutions that have an impact on the distribution of individuals. This approach can broaden the range of dynamic multi-objective optimization algorithms. Second, an approach for predicting special points is suggested. The algorithm’s convergence is improved following environmental changes by forecasting the special point tracking Pareto front in the object space. Finally, the forward-looking center points are used to predict the non-dominated solution set and eliminate the useless individuals in the population. The prediction strategy can help the solution set converge while maintaining its diversity, which is compared with the four other state-of-the-art strategies. Our experimental results demonstrate that the proposed algorithm, DSSP, can effectively tackle DMOPs.

DPb-MOPSO: A Dynamic Pareto bi-level Multi-objective Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) system based on the distributed architecture over multiple sub-swarms is very efficient for static multi-objective optimization but has not been considered for solving dynamic multi-objective problems (DMOPs). Tracking the most effective solutions over time and ensuring good exploitation and exploration are the main challenges of solving DMOP. This study proposes a Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected in the objective values, the Pareto ranking operator is used to enable multiple sub-swarm’ subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes in the objective function due to time-varying parameters. A response strategy consisting in reevaluating all unimproved solutions and replacing them with newly generated ones is also implemented. The DPb-MOPSO system is tested on DMOPs with different types of time-varying Pareto Optimal Set (POS) and Pareto Optimal Front (POF). Inverted generational distance (IGD), mean inverted generational distance (MIGD), hypervolume difference (HVD), Robust IGD (RIGD), and Robust General Distance (RGD) metrics are used to assess the DPb-MOPSO performance. Quantitative results are analyzed using Friedman’s analysis of variance, and the Wilcoxon sum ranks test, while the stability is analyzed using Lyapunov’s theorem. The DPb-MOPSO is more robust than several dynamic multi-objective evolutionary algorithms in solving 21 complex problems over a range of changes in both the POS and POF. On IGD and HVD, DPb-MOPSO can solve 8/13 and 8/13 of the 13 UDF and ZJZ functions with moderate changes. DPb-MOPSO can resolve 7/8 FDA and DMOP benchmarks with severe changes to the MIGD, and 6/8 with moderate changes. DPb-MOPSO assumes 7/8, 6/8, and 5/8 for solving FDA, and dMOP functions on IGD and 6/8, 5/8, and 5/8 on HVD metrics considering severe, moderate, and slight environmental changes respectively. Also, it is the winner for solving 8 DMOPs based on RIGD, and RGD metrics.

A self-evolving fuzzy system online prediction-based dynamic multi-objective evolutionary algorithm

The changes of dynamic multi-objective optimization problems in decision space are usually nonlinear. However, the previous dynamic multi-objective evolutionary algorithms usually use linear prediction models to generate the initial population in the new environment, and some nonlinear prediction models often have high computational cost. Therefore, it is difficult to quickly and accurately respond to nonlinear environmental changes. This paper presents a dynamic multi-objective evolutionary algorithm based on online prediction of self-evolving fuzzy system (SEFS). In this algorithm, the decomposition based multi-objective evolutionary algorithm (MOEA/D) acts as the static optimizer. When the environment changes, individuals are first put into an associate set of their corresponding weight vectors. Then, the time series of each variable is constructed based on the associate set, and the SEFS online prediction model is established. Finally, an environmental response strategy based on SEFS is designed to quickly generate an initial population with high performance in the new environment. The proposed algorithm is compared with seven state-of-the-art dynamic multi-objective evolutionary algorithms on 20 benchmark functions. Experimental results show that the proposed algorithm can quickly and accurately respond to nonlinear environmental changes, and has competitiveness.

An Online Prediction Approach Based on Incremental Support Vector Machine for Dynamic Multiobjective Optimization

Real-world multiobjective optimization problems usually involve conflicting objectives that change over time, which requires the optimization algorithms to quickly track the Pareto-optimal front (POF) when the environment changes. In recent years, evolutionary algorithms based on prediction models have been considered promising. However, most existing approaches only make predictions based on the linear correlation between a finite number of optimal solutions in two or three previous environments. These incomplete information extraction strategies may lead to low prediction accuracy in some instances. In this article, an incremental support vector machine (ISVM)-based dynamic multiobjective evolutionary algorithm, in short called ISVM-DMOEA, is proposed. We treat the solving of dynamic multiobjective optimization problems (DMOPs) as an online learning process, using the continuously obtained optimal solution to update an ISVM without discarding the solution information at earlier time. ISVM is then used to filter random solutions and generate an initial population for the next moment. To overcome the obstacle of insufficient training samples, a synthetic minority oversampling strategy is implemented before the training of ISVM. The advantage of this approach is that the nonlinear correlation between solutions can be explored online by ISVM, and the information contained in all historical optimal solutions can be exploited to a greater extent. The experimental results and comparison with the chosen state-of-the-art algorithms demonstrate that the proposed algorithm can effectively tackle DMOPs.

Knowledge guided Bayesian classification for dynamic multi-objective optimization

Dynamic multi-objective optimization problems (DMOPs) typically contain multiple conflicting objectives that vary over time, requiring the optimization algorithms to quickly track the changing Pareto-optimal solutions (POS). Recently, prediction-based dynamic multi-objective evolutionary algorithms (DMOEAs) using transfer learning ideas have been considered promising, which could accelerate the search towards the POS by transferring information from previous environments to estimate the location of the POS in the next environment. However, most of the existing methods only transfer the search experiences from one or two previous environments to construct the prediction model for the next moment, which may ignore the effective information in the earlier search process thereby degrading the prediction accuracy in some cases. In this paper, a knowledge-guided Bayesian classification for DMOEA, called KGB-DMOEA, is proposed, which aims to achieve a robust prediction by fully exploiting the information from all historical environments. Particularly, when an environmental change is detected, a knowledge reconstruction–examination strategy is designed to divide all historical optimal solutions into useful and useless ones, which are used as positive and negative samples, respectively, for training the prediction model in subsequent steps. Then, a non-linear probabilistic classifier, i.e., naive Bayesian classifier, is constructed by using the above training samples, which can fully mine the effective knowledge from all historical environments and predict a high-quality initial population for the new environment. Experimental results on multiple DMOPs test suits demonstrate that KGB-DMOEA is superior to several state-of-the-art DMOEAs in solving various DMOPs.

Multiple source transfer learning for dynamic multiobjective optimization

Recently, dynamic multiobjective evolutionary algorithms (DMOEAs) with transfer learning have become popular for solving dynamic multiobjective optimization problems (DMOPs), as the used transfer learning methods in DMOEAs can effectively generate a good initial population for the new environment. However, most of them only transfer non-dominated solutions from the previous one or two environments, which cannot fully exploit all historical information and may easily induce negative transfer as only limited knowledge is available. To address this problem, this paper presents a multiple source transfer learning method for DMOEA, called MSTL-DMOEA, which runs two transfer learning procedures to fully exploit the historical information from all previous environments. First, to select some representative solutions for knowledge transfer, one clustering-based manifold transfer learning is run to cluster non-dominated solutions of the last environment to obtain their centroids, which are then fed into the manifold transfer learning model to predict the corresponding centroids for the new environment. After that, multiple source transfer learning is further run by using multisource TrAdaboost, which can fully exploit information from the above centroids in new environment and old centroids from all previous environments, aiming to construct a more accurate prediction model. This way, MSTL-DMOEA can predict an initial population with better quality for the new environment. The experimental results also validate the superiority of MSTL-DMOEA over several competitive state-of-the-art DMOEAs in solving various kinds of DMOPs.