Dynamic Multi-objective Optimization Problems Research Articles

Evolutionary Dynamic Multiobjective Optimization via Learning From Historical Search Process.

Dynamic multiobjective optimization problems are challenging due to their fast convergence and diversity maintenance requirements. Prediction-based evolutionary algorithms currently gain much attention for meeting these requirements. However, it is not always the case that an elaborate predictor is suitable for different problems and the quality of historical solutions is sufficient to support prediction, which limits the availability of prediction-based methods over various problems. Faced with these issues, this article proposes a knowledge learning strategy for change response in the dynamic multiobjective optimization. Unlike prediction approaches that estimate the future optima from previously obtained solutions, in the proposed strategy, we react to changes via learning from the historical search process. We introduce a method to extract the knowledge within the previous search experience. The extracted knowledge can accelerate convergence as well as introduce diversity for the optimization of the future environment. We conduct a comprehensive experiment on comparing the proposed strategy with the state-of-the-art algorithms. Results demonstrate the better performance of the proposed strategy in terms of solution quality and computational efficiency.

Combining Key-Points-Based Transfer Learning and Hybrid Prediction Strategies for Dynamic Multi-Objective Optimization

Dynamic multi-objective optimization problems (DMOPs) have been of interest to many researchers. These are problems in which the environment changes during the evolutionary process, such as the Pareto-optimal set (POS) or the Pareto-optimal front (POF). This kind of problem imposes more challenges and difficulties for evolutionary algorithms, mainly because it demands population to track the changing POF efficiently and accurately. In this paper, we propose a new approach combining key-points-based transfer learning and hybrid prediction strategies (KPTHP). In particular, the transfer process combines predictive strategy with obtaining anticipated key points depending on the previous moments to acquire the optimal individuals at the new instance during the evolution. Additionally, center-point-based prediction is used to complement transfer learning to comprehensively generate initial populations. KPTHP and six state-of-the-art algorithms are tested on various test functions for MIGD, DMIGD, MMS, and HVD metrics. KPTHP obtains superior results on most of the tested functions, which shows that our algorithm performs excellently in both convergence and diversity, with more competitiveness in addressing dynamic problems.

Artificial Intelligence for Sustainable Complex Socio-Technical-Economic Ecosystems

The strong and functional couplings among ecological, economic, social, and technological processes explain the complexification of human-made systems, and phenomena such as globalization, climate change, the increased urbanization and inequality of human societies, the power of information, and the COVID-19 syndemic. Among complexification’s features are non-decomposability, asynchronous behavior, components with many degrees of freedom, increased likelihood of catastrophic events, irreversibility, nonlinear phase spaces with immense combinatorial sizes, and the impossibility of long-term, detailed prediction. Sustainability for complex systems implies enough efficiency to explore and exploit their dynamic phase spaces and enough flexibility to coevolve with their environments. This, in turn, means solving intractable nonlinear semi-structured dynamic multi-objective optimization problems, with conflicting, incommensurable, non-cooperative objectives and purposes, under dynamic uncertainty, restricted access to materials, energy, and information, and a given time horizon. Given the high-stakes; the need for effective, efficient, diverse solutions; their local and global, and present and future effects; and their unforeseen short-, medium-, and long-term impacts; achieving sustainable complex systems implies the need for Sustainability-designed Universal Intelligent Agents (SUIAs). The proposed philosophical and technological SUIAs will be heuristic devices for harnessing the strong functional coupling between human, artificial, and nonhuman biological intelligence in a non-zero-sum game to achieve sustainability.

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.

A dynamic multi-objective evolutionary algorithm based on polynomial regression and adaptive clustering

• This paper proposes A Dynamic Multi-objective Evolutionary Algorithm based on Polynomial Regression and Adaptive Clustering. • A predictor based on polynomial regression is designed for generating initial population according to the change of Pareto-optimal set in the decision space. • An adaptive reference vector regulator based on K-means clustering is suggested to track the complex changes of Pareto-optimal front in the objective space. • The proposed algorithm shows the superiority over other dynamic multi-objective evolutionary algorithms. In this paper, a dynamic multi-objective evolutionary algorithm is proposed based on polynomial regression and adaptive clustering, called DMOEA-PRAC. As the Pareto-optimal solutions and fronts of dynamic multi-objective optimization problems (DMOPs) may dynamically change in the optimization process, two corresponding change response strategies are presented for the decision space and objective space, respectively. In the decision space, the potentially useful information contained in all historical populations is obtained by the proposed predictor based on polynomial regression, which extracts the linear or nonlinear relationship in the historical change. This predictor can generate good initial population for the new environment. In the objective space, in order to quickly adapt to the new environment, an adaptive reference vector regulator is designed in this paper based on K-means clustering for the complex changes of Pareto-optimal fronts, in which the adjusted reference vectors can effectively guide the evolution. Finally, DMOEA-PRAC is compared with some recently proposed dynamic multi-objective evolutionary algorithms and the experimental results verify the effectiveness of DMOEA-PRAC in dealing with a variety of DMOPs.

A domain adaptation learning strategy for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) require the robust tracking of Pareto-optima varying over time. Previous transfer learning-based problem solvers consume the most time on complex training of transfer model or applying a plenty of evaluations to find transferred individuals, decreasing computational efficiency. To address this issue, a domain adaptation learning strategy based dynamic multiobjective evolutionary algorithm is proposed in this paper. The mapping matrix learned by subspace distribution alignment (SDA) is utilized to transform the search space between last and current environments for promoting efficient knowledge transfer. Especially, the process of constructing mapping is derived from the simpler calculation, saving computational cost. Based on this model, transferred individuals are generated from a part of historical optima at last time. Additionally, an increment information is defined as the difference between center points of POSs in past two environments, and employed to produce a noise obeying uniform distribution. After adding it on a temporary population consisting of transferred individuals and the rest historical optima, an initial population with good diversity under new environment is formed. Experimental results on 12 benchmark functions indicate that the proposed method outperforms the other six state-of-the-art comparative ones, achieving the promising performance in solving DMOPs.

Deep multi-layer perceptron-based evolutionary algorithm for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) challenge multiobjective evolutionary algorithms (MOEAs) because of the varying Pareto-optimal sets (POS) over time. Research on DMOPs has attracted a great interest from academic, due to widespread applications of DMOPs. Recently, a few learning-based approaches have been proposed to predict new solutions in the following environments as an initial population for a multiobjective evolutionary algorithm. In this paper, we propose an alternative learning-based method for DMOPs, a deep multi-layer perceptron-based predictor to generate an initial population for the MOEA in the new environment. The historical optimal solutions are used to train a deep multi-layer perceptron which then predicts a new set of solutions as the initial population in the new environment. The deep multi-layer perceptron is incorporated with the multiobjective evolutionary algorithm based on decomposition to solve DMOPs. Empirical results demonstrate that our proposed algorithm is effective in tracking varying solutions over time and shows great superiority comparing with state-of-the-art methods.

A Quick Search Dynamic Vector-Evaluated Particle Swarm Optimization Algorithm Based on Fitness Distance

A quick search dynamic vector-evaluated particle swarm optimization algorithm based on fitness distance (DVEPSO/FD) is proposed according to the fact that some dynamic multi-objective optimization methods, such as the DVEPSO, cannot achieve a very accurate Pareto optimal front (POF) tracked after each objective changes, although they exhibit advantages in multi-objective optimization. Featuring a repository update mechanism using the fitness distance together with a quick search mechanism, the DVEPSO/FD is capable of obtaining the optimal values that are closer to the real POF. The fitness distance is used to streamline the repository to improve the distribution of nondominant solutions, and the flight parameters of the particles are adjusted dynamically to improve the search speed. Groups of the standard benchmark experiments are conducted and the results show that, compared with the DVEPSO method, from the figures generated by the test functions, DVEPSO/FD achieves a higher accuracy and clearness with the POF dynamically changing; from the values of performance indexes, the DVEPSO/FD effectively improves the accuracy of the tracked POF without destroying the stability. The proposed DVEPSO/FD method shows a good dynamic change adaptability and solving set ability of the dynamic multi-objective optimization problem.

An efficient spread-based evolutionary algorithm for solving dynamic multi-objective optimization problems

An efficient spread-based evolutionary algorithm for solving dynamic multi-objective optimization problems

Dynamic multiobjective evolutionary algorithm with adaptive response mechanism selection strategy

In this paper, a dynamic multiobjective evolutionary algorithm (DMOEA) with an adaptive response mechanism selection strategy is proposed to address the shortcoming that a single response mechanism is suitable only for solving a certain type of dynamic multiobjective optimization problem. The proposed algorithm combines an adaptive response mechanism selection (ARMS) strategy and a multiobjective evolutionary algorithm based on decomposition (MOEA/D), and it is denoted as the MOEA/D-ARMS. Unlike the existing approaches, the ARMS strategy can adaptively select effective response mechanisms from the response mechanism pool based on the recent performance of each response mechanism. Four representative response mechanisms are selected to form the response mechanism pool. An overall evaluation strategy that assigns rewards to the response mechanism is adopted, and a probability-based method that is used to decide which response mechanism can be used to generate a new solution is employed. The proposed MOEA/D-ARMS algorithm is tested on two groups of test instances and compared with the decomposition-based and dominance-based DMOEAs. The results of the proposed MOEA/D-ARMS algorithm are superior to the compared algorithms, demonstrating its effectiveness.

Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization

The environments of the dynamic multiobjective optimization problems (DMOPs), such as Pareto optimal front (POF) or Pareto optimal set (POS), usually frequently change with the evolution process. This kind of problem poses a higher challenge for evolutionary algorithms because it requires the population to quickly track (i.e., converge) to the position of a new environment and be widely distributed in the search space. The prediction-based response mechanism is a commonly used method to deal with environmental changes, but it’s only suitable for predictable changes. Moreover, the imbalance of population diversity and convergence in the process of tracking the dynamically changing POF has aggravated. In this paper, we proposed a new change response mechanism that combines a hybrid prediction strategy and a precision controllable mutation strategy (HPPCM) to solve the DMOPs. Specifically, the hybrid prediction strategy coordinates the center point-based prediction and the guiding individual-based prediction to make accurate predictions. Thus, the population can quickly adapt to the predictable environmental changes. Additionally, the precision controllable mutation strategy handles unpredictable environmental changes. It improves the diversity exploration of the population by controlling the variation degree of solutions. In this way, our change response mechanism can adapt to various environmental changes of DMOPs, such as predictable and unpredictable changes. This paper integrates the HPPCM mechanism into a prevalent regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) to optimize DMOPs. The results of comparative experiments with some state-of-the-art algorithms on various test instances have demonstrated the effectiveness and competitiveness of the change response mechanism proposed in this paper.

A prediction method based on fractional order displacement for dynamic multiobjective optimization

Prediction-based methods have become more popular for solving dynamic multiobjective optimization problems. However, most of these proposed methods only use the optimal solutions in the previous two or three environments to predict the new optimal solutions after a change. Doing so neglects information from earlier in the history, which may reduce the accuracy of the prediction method. Conversely, if all history information is utilized for prediction, it will incur exorbitant computing costs, and it is not necessary because it is not all old optimal solutions correlate strongly with predicted solutions. Therefore, a novel prediction method based on fractional displacement (FDPM) is proposed. In this method, the previous optimal solutions that have a certain degree of correlation with the new solutions after a change are identified using the proposed prediction model, the parameters of which are obtained by training a certain length of previous optimal solution series. Then, these identified solutions are used to predict the optimal solutions in the new environment. This can balance the accuracy and computation cost of the prediction method. The performance of the proposed method is compared with five chosen state-of-the-art algorithms over fourteen benchmark problems covering diverse properties, and the results demonstrate that the proposed method is superior to the other selected algorithms.

A survey of artificial immune algorithms for multi-objective optimization

Multi-objective immune algorithm (MOIA) is a heuristic algorithm based on artificial immune system model. Due to its characteristics of antibody clonal selection, automatic antigen recognition and immune memory in the immune system, artificial immune algorithm has become a research hotspot in the field of multi-objective optimization after the evolutionary algorithms. In this paper, most MOIAs can be classified into three main categories according to the type of problem solving, i.e., they are mostly designed to solve multi-objective optimization problems (MOPs), dynamic MOPs, and constrained MOPs. In this paper, a comprehensive survey is presented to summarize most existing MOIAs, in which their corresponding characteristics, principles and theoretical analyses are discussed in details. Moreover, the performance of MOIAs on solving various kinds of MOPs and many-objective optimization problems is also studied in our experimental comparisons. Finally, a brief conclusion is given to summarize the current drawbacks, challenges, and some future directions for MOIAs.

Utopia constrained multi objective optimisation evolutionary algorithm

ABSTRACT A new multiobjective evolutionary optimisation algorithm (MOEA) to solve multimodal, multidimensional, nonconvex, nonlinear, dynamic multiobjective optimisation problems (MOPs) is the need of the hour. The quality of an MOEA lies in a good balance between the exploration and exploitation stages of the MOEA. Utopia constrained MOEA (U-MOEA) is proposed in this paper that improves the exploitation in the replacement step to achieve a perfect balance between exploration and exploitation. The proposed U-MOEA is tested on benchmark MOPs and a multivariable controller design problem. The performance of the proposed algorithm is also compared with other MOEAs such as NSGA-II and ICMDRA concerning hyper volume, nondomination count, combined Pareto set metric, and Cmetric . The performance metrics show better hyper volume and spread metric values for the proposed algorithm, indicating the ability in attaining trade-off region closeness along with diversified Pareto front for U-MOEA when compared to the other two algorithms. Results clearly show that the proposed U-MOEA produces good convergence, diversity characteristics with many numbers of trade-off solutions in a Pareto front.

A special point-based transfer component analysis for dynamic multi-objective optimization

To solve dynamic multi-objective optimization problems better, the key is to adapt quickly to environmental changes and track the possible changing optimal solutions in time. In this paper, we propose a special point-based transfer component analysis for dynamic multi-objective optimization algorithm (SPTr-RM-MEDA). To be specific, when a change occurs, the neighbors of some special points are selected from the optimal set at previous time, and the transfer component analysis makes the use of minimizing the distance between the mapped previous optima and the mapped current optima. Accordingly, the purpose is to predict a part of next initial population from the neighborhoods of special points by transfer component analysis. To adapt to the change well, SPTr-RM-MEDA also reevaluates the previous optimal set. In addition, an adaptive diversity introduction strategy is adopted to maintain the population size. SPTr-RM-MEDA is performed on 12 test problems under 8 kinds of environmental changes, and experimental results show that it is superior to other five state-of-the-art algorithms on most of test problems.

The comparison of efficiency of the population formation approaches in the dynamic multi-objective optimization problems

The comparison of efficiency of the population formation approaches in the dynamic multi-objective optimization problems

Modeling Human Resource Experience Evolution for Multiobjective Project Scheduling in Large Scale Software Projects

The software project scheduling (SPS) is a project-scheduling problem where limited human resources are assigned to the tasks in multi-team project settings. Besides other dynamic events, employees experience evolution has direct influence in completing large-scale projects within budget and time. In this paper, a new SPS model is developed as a dynamic multi-objective optimization problem, which incorporates employees experience evolution with their learning ability over time. The experimental results on 24 problem instances (including six real-world instances) show that the developed SPS model reduces project duration by 40% while being within budget. The results provide evidence that consideration of experience evolution while tasks reallocation under dynamic events significantly optimizes project schedules. Moreover, the developed SPS model is evaluated with six state-of-the-art algorithms as bi-criterion evolution (BCE), NSGA-II, NSGA-III, Two_Arch2, OMOPSO, speed-constrained multi-objective particle swarm optimization (SMPSO) where BCE demonstrated distinct superiority for 63% data instances.

Improved NSGA-III using transfer learning and centroid distance for dynamic multi-objective optimization

Multi-objective problems in real world are often contradictory and even change over time. As we know, how to find the changing Pareto front quickly and accurately is challenging during the process of solving dynamic multi-objective optimization problems (DMOPs). In addition, most solutions obey different distributions in decision space and the performance of NSGA-III when dealing with DMOPs should be further improved. In this paper, centroid distance is proposed and combined into NSGA-III with transfer learning together for DMOPs, called TC_NSGAIII. Centroid distance-based strategy is regarded as a prediction method to prevent some inappropriate individuals through measuring the distance of the population centroid and reference points. After the distance strategy, transfer learning is used for generating an initial population using the past experience. To verify the effectiveness of our proposed algorithm, NSGAIII, Tr_NSGAIII (NSGA-III combining with transfer learning only), Ce_NSGAIII (NSGA-III combining with centroid distance only), and TC_NSGAIII are compared. Seven state-of-the-art algorithms have been used for comparison on CEC 2015 benchmarks. Besides, transfer learning and centroid distance are regarded as a dynamic strategy, which is incorporated into three static algorithms, and the performance improvement is measured. What’s more, twelve benchmark functions from CEC 2015 and eight sets of parameters in each function are used in our experiments. The experimental results show that the performance of algorithms can be greatly improved through the proposed approach.

A multipopulation evolutionary framework with Steffensen\u2019s method for dynamic multiobjective optimization problems

Dynamic multiobjective optimization problems (DMOPs) require the evolutionary algorithms that can track the moving Pareto-optimal fronts efficiently. This paper presents a dynamic multiobjective evolutionary framework (DMOEF-MS), which adopts a novel multipopulation structure and Steffensen’s method to solve DMOPs. In DMOEF-MS, only one population deals with the original DMOP, while the others focus on single-objective problems that are generated by the weighted summation of the original DMOP. Then, Steffensen’s method is used to control the evolving process in two ways: prediction and diversity-maintenance. Particularly, the prediction strategy is devised to predict the next promising positions for the individuals that handle single-objective problems, and the diversity-maintenance strategy is used to increase population diversity before the environment changes and reinitialize the multiple populations after the environment changes. This paper gives a comprehensive comparison of DMOEF-MS with some state-of-the-art DMOEAs on 14 DMOPs and the experimental results demonstrate the effectiveness of the proposed algorithm.