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Constrained multi-objective state transition algorithm via adaptive bidirectional coevolution

EXPERT SYSTEMS WITH APPLICATIONS 2025年 266卷

作者： Sun, Yan Zhou, Xiaojun Yang, Chunhua Huang, Tingwen Cent South Univ Sch Automat Changsha 410083 Peoples R China Texas A&M Univ Qatar Doha Qatar

Constrained multi-objective optimization problems (CMOPs) involve optimizing multiple conflicting objectives subject to at least one constraint. These constraints often divide the search space into various infeasible regions and narrow or disconnected feasible regions. Most existing constrained multi-objective evolutionary algorithms struggle with imbalanced exploration between feasible and infeasible regions and exhibit poor search capabilities, resulting in populations becoming trapped in locally optimal feasible or infeasible areas. To overcome this limitation, we propose a novel constrained multi-objective state transition algorithm via adaptive bidirectional coevolution (CMOSTA). This algorithm comprises amain population (MP) and a cooperative population (CP), facilitating balanced exploration of both feasible and infeasible regions. CMOSTA adapts environmental selection strategies based on the proportion and distribution of feasible solutions within the MP , promoting efficient information sharing and avoiding unnecessary searches. Additionally, a dynamic Econstraint relaxation strategy is put forward for the MP to prevent stagnation in locally feasible areas. A mating selection approach combining binary tournament and dynamic E-constrained dominance is developed, followed by state transformation operators to generate candidate solutions with both global and local search capabilities. The effectiveness of CMOSTA is verified through 62 benchmark tests and an industrial case study on optimal copper removal, showing superior performance compared to ten well-established constrained multi-objective evolutionary algorithms.

关键词： Constrained multi-objective optimization state transition algorithm Adaptive bidirectional coevolution Dynamic E-constraint boundary

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A fast optimization approach for seeking Nash equilibrium based on Nikaido-Isoda function, state transition algorithm and Gauss-Seidel technique

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NEUROCOMPUTING 2025年 616卷

作者： Zhou, Xiaojun Wang, Zheng Huang, Tingwen Cent South Univ Sch Automat Changsha 410083 Peoples R China NARI Relays Elect Co Ltd Nanjing 211100 Peoples R China Texas A&M Univ Qatar Doha 23874 Qatar

This paper proposes a fast optimization approach for non-cooperative games with complicated payoff functions (non-smooth, non-concave, etc.). The Nikaido-Isoda function is employed to convert knotty Nash equilibrium problems (NEPs) into large-scale optimization problems with complex objective functions. To efficiently seek Nash equilibrium, the resulting optimization problems are decomposed into many subproblems where each player tries to maximize its payoff when observing others' current strategies. All players' strategies are updated iteratively until reaching Nash equilibrium. Specifically, a dynamic state transition algorithm (STA) is proposed to seek global optima of subproblems at each iteration, and the sequential quadratic programming (SQP) is embedded into dynamic STA for convergence acceleration. A Gauss-Seidel technique is utilized for players' strategy updates to improve computational efficiency further. Numerical examples drawn from multidisciplinary contexts validate that the proposed approach could effectively seek out Nash equilibrium for simultaneously decreasing the time-consuming remarkably.

关键词： Nash equilibrium Non-cooperative game state transition algorithm Gauss-Seidel technique

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state transition algorithm for traveling salesman problem

State transition algorithm for traveling salesman problem

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31st Chinese Control Conference

作者： Yang Chunhua Tang Xiaolin Zhou Xiaojun Gui Weihua Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China Univ Ballarat Sch Sci Informat Technol & Engn Ballarat Vic 3353 Australia

ISBN: (纸本)9789881563811

Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence analysis and time complexity of the algorithm are also considered. To make the algorithm simple and efficient, no parameter adjusting is suggested in current version. Experiments are carried out to test the performance of the strategy, and comparisons with simulated annealing and ant colony optimization have demonstrated the effectiveness of the proposed algorithm. The results also show that the discrete state transition algorithm consumes much less time and has better search ability than its counterparts, which indicates that state transition algorithm is with strong adaptability.

关键词： state transition algorithm Traveling Salesman Problem Swap Shift Symmetry

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Parameter Estimation of Fractional-Order Chaotic Power System Based on Lens Imaging Learning Strategy state transition algorithm

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IEEE ACCESS 2023年 11卷 13724-13737页

作者： Ai, Chunyu He, Shan Fan, Xiaochao Xinjiang Univ Sch Elect Engn Urumqi 830047 Peoples R China Xinjiang Univ Engn Res Ctr Minist Educ Renewable Energy Generat & Grid Connec Urumqi 830047 Peoples R China Xinjiang Inst Engn Urumqi 830047 Peoples R China

Parameter identification of fractional-order chaotic power systems is a multidimensional optimization problem that plays a decisive role in the synchronization and control of fractional-order chaotic power systems. In this paper, a state transition algorithm based on the lens imaging learning strategy is proposed for parameter identification of fractional-order chaotic power systems. Taking a fractional-order six-dimensional chaotic power system mathematical model as an example, the mathematical model and chaotic state are analyzed. First, the Tent chaotic mapping is used to initialize the population, thus increasing population diversity. The randomness and ergodicity of the Tent chaotic sequence are used to enhance the global searching ability of the algorithm. Second, a maturity index is employed to determine population maturity. The lens imaging learning strategy is used to suppress the premature convergence of the state transition algorithm effectively and help the population jump out of local optima. Finally, the improved state transition algorithm is used to identify the parameters of the fractional-order six-dimensional chaotic power system model. The proposed improved state transition algorithm shows high estimation accuracy and convergence speed, and is superior to the traditional state transition and particle swarm optimization algorithms. The simulation results show that the parameters of the fractional-order chaotic power system are identified accurately even in the presence of white noise, demonstrating the strong robustness and versatility of the proposed algorithm.

关键词： Parameter estimation Power systems Power system stability Optimization Estimation Statistics Chaos Image processing Fractional-order chaotic power system parameter estimation state transition algorithm lens imaging learning strategy

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A Novel Cognitively Inspired state transition algorithm for Solving the Linear Bi-Level Programming Problem

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COGNITIVE COMPUTATION 2018年第5期10卷 816-826页

作者： Huang, Zhaoke Yang, Chunhua Zhou, Xiaojun Gui, Weihua Cent South Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

Linear bi-level programming (LBLP) is a useful tool for modeling decentralized decision-making problems. It has two-level (upper-level and lower-level) objectives. Many studies have shown that the LBLP problem is NP-hard, meaning it is difficult to find a global solution in polynomial time. In this paper, we present a novel cognitively inspired computing method based on the state transition algorithm (STA) to obtain an approximate optimal solution for the LBLP problem in polynomial time. The proposed method is applied to a supply chain model that fits the definition of an LBLP problem. The experimental results indicate that the proposed method is more efficient in terms of solution accuracy through a comparison to other metaheuristic-based methods using four problems from the literature in addition to the supply chain distribution model. In this study, a cognitively inspired STA-based method was proposed for the LBLP problem. In the future, we expect to extent the proposed method for linear multi-level programming problems.

关键词： Linear bi-level programming state transition algorithm Cognitively inspired computing Global optimization

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Discrete state transition algorithm for unconstrained integer optimization problems

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NEUROCOMPUTING 2016年第Part3期173卷 864-874页

作者： Zhou, Xiaojun Gao, David Yang Yang, Chunhua Gui, Weihua Cent S Univ Sch Informat Sci & Engn Changsha 410083 Peoples R China Federat Univ Australia Sch Sci Informat Technol & Engn Ballarat Vic 3353 Australia

A recently new intelligent optimization algorithm called discrete state transition algorithm is considered in this study, for solving unconstrained integer optimization problems. Firstly, some key elements for discrete state transition algorithm are summarized to guide its well development. Several intelligent operators are designed for local exploitation and global exploration. Then, a dynamic adjustment strategy "risk and restoration in probability" is proposed to capture global solutions with high probability. Finally, numerical experiments are carried out to test the performance of the proposed algorithm compared with other heuristics, and they show that the similar intelligent operators can be applied to ranging from traveling salesman problem, boolean integer programming, to discrete value selection problem, which indicates the adaptability and flexibility of the proposed intelligent elements. (C) 2015 Elsevier B.V. All rights reserved.

关键词： state transition algorithm Integer optimization Traveling salesman problem Maximum cut problem Discrete value selection

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Kernel intuitionistic fuzzy c-means and state transition algorithm for clustering problem

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SOFT COMPUTING 2020年第20期24卷 15507-15518页

作者： Zhou, Xiaojun Zhang, Rundong Wang, Xiangyue Huang, Tingwen Yang, Chunhua Cent South Univ Sch Automat Changsha 410083 Peoples R China Peng Cheng Lab Changsha 51800 Peoples R China Texas A&M Univ Qatar POB 23874 Doha Qatar

Clustering problems widely exist in machine learning, pattern recognition, image analysis and information sciences, etc. Although many clustering algorithms have been proposed, it is unpractical to find a clustering algorithm suitable for all types of datasets. Fuzzy c-means (FCM) is one of the most frequently-used fuzzy clustering algorithm for the reason that it is efficient, straightforward, and easy to implement. However, the traditional FCM taking Euclidean distance as similarity measurement can not distinguish the intersection between two clusters. Therefore, kernel function has been taken as similarity measurement to solve this issue. As a comprehensive partition criterion, intuitionistic fuzzy set which consider both membership degree and non-membership degree has been used to replace traditional fuzzy set to describe the natural attributes of objective phenomena more delicately. Thus, Kernel intuitionistic fuzzy c-means (KIFCM) has been proposed in this paper to settle clustering problem. Considering FCM is easily getting trapped in local optima due to its high sensitivity to initial centroid. state transition algorithm (STA) has been adopted in this study to obtain the initial centroid to enhance its stability. The proposed STA-KIFCM compared with some other clustering algorithms are implemented using five benchmark datasets. Experimental results not only show that the proposed method is efficient and can reveal encouraging results, but also indicate that the proposed method can achieve high accuracy.

关键词： Clustering problem state transition algorithm Kernel function Intuitionistic fuzzy set Fuzzy c-means

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Fractional-order PID controller tuning using continuous state transition algorithm

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NEURAL COMPUTING & APPLICATIONS 2018年第10期29卷 795-804页

作者： Zhang, Fengxue Yang, Chunhua Zhou, Xiaojun Gui, Weihua Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

Theoretical and applied studies of fractional-order PID (FOPID) controller in many scientific and engineering fields have shown many advantages compared to the classical PID control. However, the adjustment of FOPID controller becomes more complicated due to two additional parameters. In this study, the FOPID controller adjustment problem is transformed into a nonconvex optimization problem, and then a new metaheuristic method, named state transition algorithm (STA), is introduced to select the optimal FOPID controller parameters. In the meanwhile, the influence of objective criterion and sample size on the performance of FOPID controller design is analyzed. The dominance of the proposed method, especially for tuning FOPID controller parameters, is attested by several simulation cases and the comparisons of STA with other stochastic global optimization algorithms over the same problems.

关键词： Fractional-order control (PID mu)-D-lambda state transition algorithm Objective criterion Sample size

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Using hybrid normalization technique and state transition algorithm to VIKOR method for influence maximization problem

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NEUROCOMPUTING 2020年 410卷 41-50页

作者： Zhou, Xiaojun Zhang, Rundong Yang, Ke Yang, Chunhua Huang, Tingwen Cent South Univ Sch Automat Changsha 410083 Peoples R China Peng Cheng Lab Shenzhen 518000 Peoples R China Texas A&M Univ Qatar POB 23874 Doha Qatar

Influence maximization problem is the procedure of attempting to identify a group of K nodes in a social network in order to maximize the dissemination of influence under certain influence models. Based on state transition algorithm (STA) and a multiple criteria decision making (MCDM) method called Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), a novel hybrid approach has been proposed to cope with the influence maximization problem in this paper. Firstly, an intelligent optimization paradigm called STA is introduced to obtain the most appropriate weights that are used to integrate the criteria of each alternative in the VIKOR method. Then, a hybrid normalization technique has been presented to allow the process of aggregating criterion with numerical and comparable data properly in this method. Several typical networks have been used to testify the effectiveness of proposed method and technique. Compared with other approaches, experimental results show that our approach can solve the influence maximization problem more effectively. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Influence maximization Normalization technique Multiple criteria decision making state transition algorithm

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A dynamic state transition algorithm with application to sensor network localization

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NEUROCOMPUTING 2018年 273卷 237-250页

作者： Zhou, Xiaojun Shi, Peng Lim, Cheng-Chew Yang, Chunhua Gui, Weihua Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China Univ Adelaide Sch Elect & Elect Engn Adelaide SA 5005 Australia

The sensor network localization (SNL) problem aims to reconstruct the positions of all the sensors in a network with given distance between pairs of sensors and within the radio range between them. It is proved that the computational complexity of the SNL problem is NP-hard, and semi-definite programming or second-order cone programming relaxation methods can only solve some special problems of this kind. In this study, a stochastic intelligent optimization method based on the state transition algorithm is introduced to solve the SNL problem without additional assumptions and conditions on the problem structure. To transcend local optimality, a novel dynamic adjustment strategy called " risk and restoration in probability" is incorporated into the state transition algorithm. An empirical study is investigated to appropriately choose the risk probability and restoration probability, yielding the dynamic state transition algorithm, which is further improved with gradient-based refinement. The refined dynamic state transition algorithm is applied to the SNL problem, and satisfactory simulation results show the effectiveness of the proposed approach. (C) 2017 Elsevier B.V. All rights reserved.

关键词： state transition algorithm Dynamic adjustment Sensor network localization Global optimization

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