Dynamic Multi-objective Optimization Problems Research Articles

A decision variable classification strategy based on the degree of environmental change for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) are constantly changing over time, which requires algorithms to keep track of the location of the Pareto optimal front (POF) at different moments in time. In this work, a decision variable classification strategy based on the degree of environmental change (DVCEC) is proposed. To accurately capture the occurrence of environmental changes, DVCEC designs an adaptive change detection method based on multiple regions. Since environmental changes affect each decision variable to different degrees, DVCEC classifies decision variables into several types and applies an appropriate prediction method to each type. In addition, an adjustment strategy is developed to minimize the impact of inaccurate predictions. The proposed DVCEC is evaluated on 22 benchmark problems and compared with four algorithms. Statistical results show that DVCEC can quickly approach POF and uniformly distribute it in most problems.

A two-level parallel decomposition-based artificial bee colony method for dynamic multi-objective optimization problems

Many real-world multiple-objective optimization problems have objectives that change over time. These multiple-objective optimization problems are called dynamic multiple-objective optimization problems (DMOPs) and have received an increased attention. To track the changing Pareto front in DMOPs, the Pareto front at a certain moment needs to be obtained as efficiently as possible, which is challenging for most of existing methods. To this end, we propose a two-level parallel decomposition-based artificial bee colony method for solving DMOPs. To sufficiently accelerate the process of obtaining the Pareto front, a two-level parallel structure is designed in our method. In the first-level parallel structure, the dynamic multi-objective optimization problem at a certain moment is decomposed into a set of single-objective optimization problems that could be solved in parallel. In the second-level parallel structure, a parallel artificial bee colony algorithm is applied to solve each decomposed single-objective optimization problem. Specially, the parallel bee colony algorithm in our method is improved to support the exchange of information among neighbor problems, which is widely accepted to be effective in improving the efficiency of obtaining optimal solutions. To support the implementation of our improved parallel artificial bee colony algorithm, a two-level shared memory structure is designed. Our proposed method is compared with 4 widely used methods on CEC’ 2018 multi-objective optimization benchmarks and two constrained dynamic multi-objective optimization problems. The experimental results show that our method outperforms other compared methods in efficiency while maintaining good scalability and convergence.

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.

Meta-learning-based multi-objective PSO model for dynamic scheduling optimization

The by-product gas is an important secondary energy in the iron and steel industry. It is important to make the by-product gas’s utilization efficient and reasonable,which is the key to improve the economic efficiency and the level of energy conservation and emission reduction. Aiming at the problems of complex dynamic changes, difficult to accurately model and difficult to predict real-time traffic in gas energy system, this paper proposes an optimal scheduling method based on meta-learning multi-objective particle swarm optimization algorithm. The gas energy optimization scheduling problem is modeled as a multi-objective dynamic scheduling optimization problem. The difficulty of this problem is to comprehensively consider multiple indicators, continuously adapt to the change of the objective function over time, and track the changing Pareto optimal solution set. One of the promising solutions is to build prediction models with better performance under dynamic changes. The model we propose makes full use of the optimization results and the experience information of the optimization process in the historical optimization task. We propose a dynamic parameter initialization method based on meta-learning by starting multiple historical optimization tasks at the same time. Thus,the comprehensive parameters of different tasks are obtained, and a general and best base parameter is learned. Experiments show that the proposed model has better convergence and accuracy than the conventional algorithm.

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 deep learning model for intelligent home energy management system using renewable energy

Home automation is seen as a potential pillar of the smart city revolution that combines smart mobility, lifestyle and ecosystem governed by intelligent sensors connected to the internet. Households can save money and be more comfortable with automated appliances. The cost of electricity and user comfort are fundamentally contradictory, so they can be presented as a dynamic multi-objective optimization problem with fluctuating priorities for the customer to use various devices at different times. For this reason, this paper proposes an advanced Intelligent Home Energy Management (IHEM) approach based on reinforcement learning to achieve home demand response (DR) efficiency. The optimal formulation of the one-hour-ahead energy consumption scheduling problem is considered a Markov Decision Process (MDP) with discrete time steps. An efficient Neural Network (NN)-based approach with a Q-learning algorithm is developed to address this problem, enabling the IHEM system to achieve better cost-effective scheduling performance. The accurate data of electricity price and energy supplied by the Photovoltaic (PV) system are analyzed in sliding periods by machine learning for uncertainty prediction. Using the newly developed approach, which has the dual objective of minimizing the electricity bill, it is possible to obtain scheduling decisions for appliances and energy storage. The results show that the proposed optimization method reduces the monthly electricity costs by 20% compared to the Integer Linear Programming (ILP)-based HEMS method.

Machine Learning Assisted Evolutionary Multi-Objective Optimization [Guest Editorial

Optimization and learning are two main paradigms of artificial intelligence in addressing complex real-world problems, with their respective focuses but frequently enhanced by each other. Evolutionary multi-objective optimization (EMO) algorithms are a family of nature-inspired algorithms widely used for solving multi-objective optimization problems (MOPs). Despite the great success achieved by the existing EMO algorithms, most of these algorithms have also encountered many challenges in terms of optimization performance and efficiency for solving complex MOPs such as large-scale MOPs, expensive MOPs, dynamic MOPs, and real-world MOPs. To cope with these challenges, there has been increasing interest in applying machine learning (ML) techniques to enhance the EMO algorithms. Specifically, ML techniques can be adopted to extract useful knowledge hidden in the data generated by EMO algorithms in the search process, which can be leveraged to assist different components in EMO algorithms in different ways, e.g., problem formulation, offspring generation, fitness evaluation, and/or environmental selection. These machine learning assisted components have substantially enhanced the ability of EMO algorithms in handling complex MOPs.

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.

Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization

Dynamic multi-objective optimization problems (DMOPs) have become a research hotspot in engineering optimization, because their objective functions, constraints, or parameters may change over time, while quickly and accurately tracking the changing Pareto optimal set (POS) during the optimization process. Therefore, solving dynamic multi-objective optimization problems presents great challenges. In recent years, transfer learning has been proved to be one of the effective means to solve dynamic multi-objective optimization problems. However, this paper proposes a new transfer learning method based on clustering difference to solve DMOPs (TCD-DMOEA). Different from the existing methods, it uses the clustering difference strategy to optimize the population quality and reduce the data difference between the target domain and the source domain. On this basis, transfer learning technology is used to accelerate the construction of initialization population. The advantage of the TCD-DMOEA method is that it reduces the possibility of negative transfer and improves the performance of the algorithm by improving the similarity between the source domain and the target domain. Experimental results show that compared with several advanced dynamic multi-objective optimization algorithms based on different benchmark problems, the proposed TCD-DMOEA method can significantly improve the quality of the solution and the convergence speed.

An adaptive Gaussian process based manifold transfer learning to expensive dynamic multi-objective optimization

Expensive dynamic multi-objective optimization problems (EDMOPs) is one kind of DMOPs where the objectives change over time and the function evaluations commonly involve computationally intensive simulations or costly physical experiments. Hence, the key to solve EDMOPs is to quickly and accurately track the time-varying Pareto optimal fronts under the limit of small number of function evaluations, in which how to augment enough training data to build informative surrogate models and manage the models during the search process. To overcome the issue, we propose a transfer learning based surrogate assisted evolutionary algorithm (TrSA-DMOEA) to efficiently solve EDMOPs. Specifically, when a change occurs, we propose a knee point-based manifold transfer learning method based on geodesic flow kernel, which exploits the knowledge from previous high-quality knee solutions to augment the training data for building Gaussian process models, thereby improving the computational complexity and the quality of solutions. Moreover, to efficiently find the optima with limited budget of function evaluations, a novel surrogate-assisted mechanism based on an adaptive acquisition function is introduced, which achieves a balance between convergence and diversity by adaptively adjusting the weights of the angle-penalized distance and average uncertainty at different search stages. By comparing with state-of-the-art algorithms on widely used test problems, the experimental results demonstrate that the proposed method outperforms others and is able to efficiently solve EDMOPs.

Elitism-based transfer learning and diversity maintenance for dynamic multi-objective optimization

In handling dynamic multi-objective optimization problems (DMOPs), transfer learning driven methods have received considerable attention for finding a high-quality initial population with good convergence and diversity performance to adapt to the new environment. However, they commonly suffer from loss of population diversity and high computational consumption. Therefore, this study proposes a hybrid method combining elitism-based transfer learning and diversity maintenance to efficiently identify a high-quality initial population in response to environmental changes. An elite selection mechanism is developed to select elite individuals from the memory pool when the environment changes. Subsequently, an elitism-based transfer learning method is proposed to predict individuals by leveraging the knowledge from the selected elite individuals, thereby improving the computational efficiency and quality of the solutions. Subsequently, a random diversity maintenance strategy is developed to generate diverse individuals within the regions where the predicted individuals are located to defy the loss of diversity in the population. Finally, the generated diverse and predicted individuals are merged to form an initial population to adapt to the new environment. The experimental results have demonstrated the competitiveness of the proposed algorithm for most DMOP test instances in terms of convergence, diversity, and computational efficiency.

Handling Dynamic Multiobjective Optimization Environments via Layered Prediction and Subspace-Based Diversity Maintenance.

In this article, we propose an evolutionary algorithm based on layered prediction (LP) and subspace-based diversity maintenance (SDM) for handling dynamic multiobjective optimization (DMO) environments. The LP strategy takes into account different levels of progress by different individuals in evolution and historical information to predict the population in the event of environmental changes for a prompt change response. The SDM strategy identifies gaps in population distribution and employs a gap-filling technique to increase population diversity. SDM further guides rational population reproduction with a subspace-based probability model to maintain the balance between population diversity and convergence in every generation of evolution regardless of environmental changes. The proposed algorithm has been extensively studied through comparison with five state-of-the-art algorithms on a variety of test problems, demonstrating its effectiveness in dealing with DMO problems.

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.

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.

Research Progress and Prospect of Satellite Constellation Optimization Design

Satellite constellation optimization has gradually developed from simple single-objective optimization to complex multi-objective optimization. Among them, the high-dimensional and multi-objective dynamic optimization problem poses a great challenge to the performance of the algorithm. To improve convergence speed and optimization performance, researchers continue to improve modern optimization algorithms. Firstly, the construction process of the optimization model is reviewed. The model takes the coverage performance, network performance, and system cost as objective functions or constraints. Secondly, the general forms of multi-objective constellation optimization design models under various constraints are given, and the applications of modern optimization algorithms such as genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA-2), multi-objective particle swarm optimization algorithm (MOPSO), differential evolution algorithm (DE) in different constellation design tasks, as well as their characteristics and development trends are introduced. Finally, it is pointed out that in the era of vigorous development of Leo mega-constellations, the combination of modern optimization algorithms and machine learning is the future research direction to solve high-dimensional and multi-objective dynamic optimization problems.

Multiobjective Dynamic Optimization of Nonlinear Systems With Path Constraints

In this article, two algorithms are proposed to solve multiobjective path-constrained dynamic optimization problems. In each algorithm, an adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method is employed to solve the multiobjective dynamic optimization problems (MODOPs) with path constraints in two iterative loops. In the outer loop, the adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method adaptively adjusts the choice of the parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> , which transfers MODOP into a sequence of single-objective dynamic optimization problems (SODOPs) with extra inequality constraints. In the inner loop, two different algorithms are used to solve the single-objective optimization problems. The first algorithm guarantees that the path constraints can be satisfied with any finite prescribed tolerance by replacing path constraints with a finite number of point constraints. Furthermore, the second algorithm guarantees that the path constraints are rigorously satisfied by enforcing the path constraints at a limited number of time points and by restricting the right-hand side of the path constraints. The proposed algorithms are proven to converge within finite iterations. The effectiveness of the algorithms is verified via numerical studies, along with a comparison to a state-of-the-art algorithm.

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.

Time-varying multi-objective smart home appliances scheduling using fuzzy adaptive dynamic SPEA2 algorithm

The smart city is an idea of upcoming revolution in cities, which includes smart home, smart mobility, smart living, and smart environment that can be operated using a smartphone connected to the internet. By adequately scheduling appliances, residential consumers can reduce their electricity expenses while increasing their comfort. Electricity cost and user comfort being conflicting in nature, can be formulated as a dynamic multi-objective optimization problem with varying user priority to use different home appliances at different times. Further to solve this problem, a Fuzzy Adaptive Dynamic SPEA2 with Borda Ranking Method (FDSPEA2-BR) is proposed based on the dynamic modification of popular SPEA2 algorithm. The algorithm includes an improved Borda count method along with Mamdani fuzzy rules to select the best solutions. The changes in crossover and mutation rate in the SPEA2 algorithm is now being controlled with fuzzy rules. Proposed FDSPEA2-BR is validated on fourteen benchmark dynamic multi-objective functions taken from the FDA, JY, dMOP, and DF test suites, results have validated the optimization model’s efficacy. Simulation study is performed on the scheduling of 11 smart home appliances varying over 10 time slots. The results in the form of time varying Pareto Fronts is demonstrated and the schedules corresponding to 5 diversified points on each Pareto Front are reported. The end user can make use of the optimized schedules that were thus obtained to modify his or her patterns of demand and energy use.