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Feature information prediction algorithm for dynamic multi-objective optimization problems

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第3期295卷 965-981页

作者： Ma, Xuemin Yang, Jingming Sun, Hao Hu, Ziyu Wei, Lixin Yanshan Univ Sch Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Key Lab Ind Comp Control Engn Hebei Prov Qinhuangdao 066004 Hebei Peoples R China

dynamic multi-objective optimization problems (DMOPs) contain multiple conflicting goals while track -ing the changing Pareto-optimal front (PF) or Pareto-optimal set (PS). Most algorithms treat the solutions of DMOPs as if they were dealing with static multi-objective optimization problems. However, solutions under different environments may obey different distributions. To solve some of the existing limitations of currently available methods, a dynamic multi-objective optimization algorithm based on feature in-formation prediction (FIP) is proposed. To identify the distribution of solutions after an environmental change, joint distribution adaptation (JDA) is used to construct a mapping function. The feature informa-tion, which is extracted from the objective space at the current time step, is mapped to a higher dimen-sional space. Then the feature information of decision space at the next time step is obtained using the interior point method. Based on this information, the initial population at the next time step is gener-ated when a change is detected. The performance of FIP is validated by comparing it with respect to four state-of-the-art evolutionary algorithms on eight benchmark functions. Experimental results demonstrate that FIP can quickly cover the front with rapidly changing environments. (c) 2021 Published by Elsevier B.V.

关键词： Evolutionary computations dynamic multi-objective optimization Different distributions Feature information prediction Joint distribution adaptation

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A new hybrid prediction model with entropy-like kernel function for dynamic multi-objective optimization

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APPLIED INTELLIGENCE 2023年第9期53卷 10500-10519页

作者： Cao, Siyu Zou, Feng Chen, Debao Liu, Hui Ji, Xuying Zhang, Yan Huaibei Normal Univ Sch Phys & Elect Informat Huaibei 235000 Peoples R China Huaibei Normal Univ Sch Comp Sci & Technol Huaibei 235000 Peoples R China

dynamic multi-objective problems (DMOPs) permeate all aspects of daily life and practical applications. As the variables of the search space or target space alter in pace with time, savants are also deepening the research on DMOPs, among which methods based on prediction mechanisms have been extensively developed. The historical optimal solutions can effectively predict the trend and location of the optimal solutions in the future. In this paper, a new hybrid prediction model (HPM) integrating the fuzzy linear prediction model with entropy-like kernel function and the one-step prediction model is developed to sort out DMOPs. In the method, the predicted center by the HPM prediction model is combined with the approximate manifold of PS to generate a trail population, and the linear one-step prediction model is utilized to generate another trail population. When the environment changes, the initial PS at the next moment is obtained by randomly crossing these two trail populations. To assess the proposed HPM model, it is compared with the reinitialization strategy, feedforward prediction strategy, population prediction strategy, T-S nonlinear regression strategy with multistep prediction and individual-based transfer learning under different MOEA optimizers for 22 benchmark problems. The results indicate that HPM has great advantages in solving these dynamic optimization problems.

关键词： dynamic multi-objective optimization Fuzzy linear prediction Entropy-like kernel function multiple subgroups One-step prediction

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multi-spatial information joint guidance evolutionary algorithm for dynamic multi-objective optimization with a changing number of objectives

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NEURAL COMPUTING & APPLICATIONS 2023年第20期35卷 15167-15199页

作者： Ma, Xuemin Sun, Hao Hu, Ziyu Wei, Lixin Yang, Jingming Yanshan Univ Engn Res Ctr Minist Educ Intelligent Control Syst & Intelligent Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Key Lab Ind Comp Control Engn Hebei Prov Qinhuangdao 066004 Hebei Peoples R China

Existing research on dynamic multi-objective optimization problems involving changes in the number of objectives has received little attention, but it is widespread in practical applications. This problem would cause the expansion or contraction of the manifold in the objective space. If it is accompanied by changes in Pareto set/front (PS/PF), the problem becomes more complex. However, several dynamic response techniques have been developed to handling this kind of dynamics. Faced with these issues, a multi-spatial information joint guidance evolutionary algorithm is proposed. To more accurately identify the optimal solutions after the change, a space adaptive transfer strategy is introduced, which adopts the geodesic flow kernel method to extract spatial information at different times. Afterwards it adaptively transfers the space via different changes to generate new individuals. In order to improve the diversity after the change, a dual space multi-dimensional joint sampling strategy is proposed. It fully combines the individual information in the objective and the decision space. Then the promising solutions are sampled in multiple dimensions near the representative individuals. Comprehensive experiments are conducted on 15 benchmark functions with a varying number of objectives and PS/PF. Simulation results verify the capability of the proposed algorithm.

关键词： dynamic multi-objective optimization multi-objective optimization Changing objectives Evolutionary algorithm

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A reinforcement learning approach for dynamic multi-objective optimization

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INFORMATION SCIENCES 2021年 546卷 815-834页

作者： Zou, Fei Yen, Gary G. Tang, Lixin Wang, Chunfeng Northeastern Univ Key Lab Data Analyt & Optimizat Smart Ind Liaoning Engn Lab Operat Analyt & Optimizat Smart Minist Educ Shenyang 110819 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA Northeastern Univ Liaoning Key Lab Mfg Syst & Logist Inst Ind & Syst Engn Shenyang 110819 Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Henan Peoples R China

dynamic multi-objective optimization Problem (DMOP) is emerging in recent years as a major real-world optimization problem receiving considerable attention. Tracking the movement of Pareto front efficiently and effectively over time has been a central issue in solving DMOPs. In this paper, a reinforcement learning-based dynamic multi-objective evolutionary algorithm, called RL-DMOEA, which seamlessly integrates reinforcement learning framework and three change response mechanisms, is proposed for solving DMOPs. The proposed algorithm relocates the individuals based on the severity degree of environmental changes, which is estimated through the corresponding changes in the objective space of their decision variables. When identifying different severity degree of environmental changes, the proposed RL-DMOEA approach can learn better evolutionary behaviors from environment information, based on which apply the appropriate response mechanisms. Specifically, these change response mechanisms including the knee-based prediction, center-based prediction and indicator-based local search, are devised to promote both convergence and diversity of the algorithm under different severity of environmental changes. To verify this idea, the proposed RL-DMOEA is evaluated on CEC 2015 test problems involving various problem characteristics. Empirical studies on chosen state-ofthe-art designs validate that the proposed RL-DMOEA is effective in addressing the DMOPs. (c) 2020 Elsevier Inc. All rights reserved.

关键词： dynamic multi-objective optimization Severity degree Reinforcement learning Prediction

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Cluster-Based Regression Transfer Learning for dynamic multi-objective optimization

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PROCESSES 2023年第2期11卷 613页

作者： Zhang, Xi Qian, Feng Zhang, Liping East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China Shanxi Agr Univ Inst Cotton Res Yuncheng 044000 Peoples R China

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.

关键词： dynamic multi-objective optimization evolutionary algorithm regression transfer transfer learning

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Performance metrics analysis of dynamic multi-objective optimization for energy consumption and productivity improvement in batch electrodialysis

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CHEMICAL ENGINEERING COMMUNICATIONS 2021年第4期208卷 517-529页

作者： Rohman, Fakhrony Sholahudin Aziz, Norashid Univ Sains Malaysia Sch Chem Engn Engn Campus Seri Ampangan Penang Malaysia

Empty fruit bunch (EFB) can be utilized to produce sugar via hydrochloric acid (HCl) hydrolysis where the HCl must be concentrated to retain the pure sugar. Electrodialysis (ED) is an effective method for acid-sugar separation and has to be optimized to ensure that the most economical operation can be achieved. However, ED batch optimization consists of conflicting multiple objectives that are required to be solved as a dynamic multi-objective optimization (MOO) problem. In the past, the dynamic optimization of acid-sugar ED separation was carried out by solving a single objective optimization problem in sequence but this approach could not be accomplished with different objective functions simultaneously. In this work, the results of the MOO which consist of a number of optimal solutions are configured as a Pareto Front (PF). The weighted sum, the ?-constraint, and the elitist non-dominated sorting genetic algorithm or NSGA-II approaches are applied to solve the conflicting objectives functions i.e. minimization of energy consumption and maximization of acid concentration These result in a set of several Pareto optimal solutions with two objectives: maximizing concentrated acid ranging from 1.89?M to 2.1?M is accompanied by minimizing energy consumption ranging from 630?Wh to 848?Wh. Each point of the Pareto solutions contains a different combination of optimal current density and flowrate trajectories which promotes a different amount of energy consumption and acid concentration. This set of solutions provides choices in assessing the tradeoffs and determining the most appropriate operating policy.

关键词： Electrodialysis Energy consumption dynamic multi-objective optimization Optimal control trajectory

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A new prediction strategy combining T-S fuzzy nonlinear regression prediction and multi-step prediction for dynamic multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2020年 59卷

作者： Zou, Feng Chen, Debao Xu, Qingzhen Lu, Renquan Huaibei Normal Univ Sch Phys & Elect Informat Huaibei 235000 Peoples R China Natl Univ Def Technol Coll Informat & Commun Xian 710106 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China

Many dynamic multi-objective optimization problems have been widely developed to track the changing optima quickly and effectively in dynamic environments. Prediction-based methods can be used to predict future changes by learning past experience. This paper employed a new prediction strategy combining Takagi-Sugeno fuzzy nonlinear regression prediction and multi-step prediction named TSMP to estimate the new initial Pareto solutions whenever the environment changes. In TSMP, when environmental changes occur, the next initial center of Pareto solutions (PS) is predicted by a Takagi-Sugeno fuzzy nonlinear regression prediction model and then one trail population is generated by combining the predicted center and an approximate manifold of PS. More over, the other trail population is generated by a linear multi-step prediction model. Furthermore, the next initial PS is reinitialized by a random hybridization of these two trail populations. The proposed TSMP strategy is systematically compared with re-initialization strategy (RIS), feed-forward prediction strategy (FPS) and population prediction strategy (FPS) under different multi-objective optimizers on benchmark test problems with different features. Experimental results and performance comparisons with other state-of-the-art algorithms indicate that TSMP is effective and promising for solving dynamic multi-objective optimization problems.

关键词： dynamic multi-objective optimization Prediction Nonlinear regression T-S fuzzy multi-step

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Approaching the cell switch-off problem in 5G ultra-dense networks with dynamic multi-objective optimization

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2020年 110卷 876-891页

作者： Luna, Francisco Zapata-Cano, Pablo H. Gonzalez-Macias, Juan C. Valenzuela-Valdes, Juan F. Univ Malaga Dept Languages & Comp Sci Malaga Spain Univ Extremadura Dept Comp Syst & Telemat Engn Ctr Univ Merida Badajoz Spain Univ Granada Dept Signal Theory Telemat & Commun Granada Spain

Energy efficiency is a major issue in the fifth generation (5G) of cellular networks as they require an ultra-dense deployment of small base stations (SBSs) to meet the forecasted traffic demands. Switching off cells is a widely recognized strategy to reduce the power consumption of these networks during off-peak conditions but, as times goes by, these demands change, thus requiring the activation or deactivation of a different set of cells that provide the users with a minimum QoS. In this context, the optimization problem of selecting which cells have to be switched on/off in each period of time has been approached from the dynamic multi-objective evolutionary (MOEA) domain, by proposing a novel restart method that enables the algorithms to react to changes in the traffic demands. The newly devised operator, named Adjacent Cell Restart (ACR), is based on exploiting the spatial continuity of the mobile users in the network. The experiments over a set of 9 ultra-dense networks with increasing densities of both users and base station has shown the enhanced capabilities of the ACR-enabled dynamic MOEAs to better approximate the newly induced the Pareto fronts in consecutive periods of time. (C) 2019 Elsevier B.V. All rights reserved.

关键词： dynamic multi-objective optimization Problem-specific restart operator Cell switch-off problem Energy efficiency 5G networks

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Tracking Variable Fitness Landscape in dynamic multi-objective optimization Using Adaptive Mutation and Crossover Operators

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IEEE ACCESS 2020年 8卷 188927-188937页

作者： Essiet, Ima Okon Sun, Yanxia Univ Johannesburg Dept Elect & Elect Engn Sci ZA-2006 Johannesburg South Africa

Many real-world problems are modeled as multi-objective optimization problems whose optimal solutions change with time. These problems are commonly termed dynamic multi-objective optimization problems (DMOPs). One challenge associated with solving such problems is the fact that the Pareto front or Pareto set often changes too quickly. This means that the optimal solution set at period t may likely vary from that at (tC1), and this makes the process of optimizing such problems computationally expensive to implement. This article proposes the use of adaptive mutation and crossover operators for the non-dominated sorting genetic algorithm III (NSGA-III). The aim is to and solutions that can adapt to fitness changes in the objective function space over time. The proposed approach improves the capability of NSGA-III to solve multi-objective optimization problems with solutions that change quickly in both space and time. Results obtained show that this method of population reinitialization can effectively optimize selected benchmark dynamic problems. In addition, we test the capability of the proposed algorithm to select robust solutions over time. We recognize that DMOPs are characterized by rapidly changing optimal solutions. Therefore, we also test the ability of our proposed algorithm to handle these changes. This is achieved by evaluating its performance on selected robust optimization over time (ROOT) and robust Pareto-optimality over time (RPOOT) benchmark problems.

关键词： Heuristic algorithms optimization Sociology Statistics Genetic algorithms Prediction algorithms Convergence Convergence diversity dynamic multi-objective optimization inverted generational distance reference points

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The effect of diversity maintenance on prediction in dynamic multi-objective optimization

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APPLIED SOFT COMPUTING 2017年 58卷 631-647页

作者： Ruan, Gan Yu, Guo Zheng, Jinhua Zou, Juan Yang, Shengxiang Xiangtan Univ Informat Engn Coll Minist Educ Key Lab Intelligent Comp & Informat Proc Xiangtan Hunan Peoples R China Hengyang Normal Univ Minist Educ Hengyang Hunan Peoples R China Hengyang Normal Univ Sch Comp Sci & Technol Hengyang Hunan Peoples R China Univ Surrey Comp Sci Guildford GU2 7XH Surrey England De Montfort Univ Sch Comp Sci & Informat Leicester LE1 9BH Leics England

There are many dynamic multi-objective optimization problems (DMOPs) in real-life engineering applications whose objectives change over time. After an environmental change occurs, prediction strategies are commonly used in dynamic multi-objective optimization algorithms to find the new Pareto optimal set (POS). Being able to make more accurate prediction means the algorithm requires fewer computational resources to make the population approximate to the Pareto optimal front (POF). This paper proposes a hybrid diversity maintenance method to improve prediction accuracy. The method consists of three steps, which are implemented after an environmental change. The first step, based on the moving direction of the center points, uses the prediction to relocate a number of solutions close to the new Pareto front. On the basis of self-defined minimum and maximum points of the POS in this paper, the second step applies the gradual search to produce some well-distributed solutions in the decision space so as to compensate for the inaccuracy of the first step, simultaneously and further enhancing the convergence and diversity of the population. In the third step, some diverse individuals are randomly generated within the region of next probable POS, which prompts the diversity of the population. Eventually the prediction becomes more accurate as the solutions with good convergence and diversity are selected after the non-dominated sort [1] on the combined solutions generated by the three steps. Compared with three other prediction methods on a series of test instances, our method is very competitive in convergence and diversity as well as the speed at which it responds to environmental changes. (C) 2017 Elsevier B.V. All rights reserved.

关键词： dynamic multi-objective optimization Evolutionary algorithms Diversity maintenance Prediction

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