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Gradient-based hybrid method for multi-objective optimization problems

EXPERT SYSTEMS WITH APPLICATIONS 2025年 272卷

作者： Yang, Dewei Fan, Qinwei Xian Polytech Univ Sch Sci Xian 710048 Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China

How to strike a tricky balance between convergence and diversity is still an ever-present challenge in the field of multi-objective optimization. In this paper, a hybrid method of gradient-based and improved non-dominated sorting genetic algorithm is proposed to solve this complex problem (HMGB). Initially, we propose a partition clustering method under a new criterion to divide the individuals in the target space, which not only facilitates the construction of Pareto descent directions but also prevents the population from falling into local optima. Subsequently, we improve the finite-difference method to obtain gradient information for multiple objective functions, which are used to construct Pareto descent directions that can accelerate convergence. Finally, we replaced the simulated binary crossover in NSGA-II with a normally distributed crossover, and combined it with polynomial variation to generate offspring, which we used for global exploration to increase the diversity of the population. The HMGB algorithm was compared with several state-of-the-art algorithms on benchmark functions and real-world problems. Experimental results demonstrate that the HMGB algorithm possesses strong competitiveness and effectiveness.

关键词： multi-objective optimization Descent direction Partitional clustering multi-objective evolutionary algorithm

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Varied granularity encoding based evolutionary algorithm for multi-objective intensity-modulated radiation therapy optimization

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Engineering Applications of Artificial Intelligence 2025年 157卷

作者： Langchun Si Xingyi Zhang Ye Tian Ruifen Cao Shangshang Yang Limiao Zhang School of Computer Science and Technology Anhui University Hefei China Information Materials and Intelligent Sensing Laboratory of Anhui Province Anhui University Hefei China Institutes of Physical Science and Information Technology Anhui University Hefei China School of Artificial Intelligence Anhui University Hefei China

Intensity-modulated radiation therapy is an interesting multi-objective optimization problem, which holds a large number of aperture shape-related variables, posing a stiff challenge to existing algorithms. To efficiently solve this problem, we propose a varied granularity encoding method in this paper, where the granularity of encoding of the shape in the multi-leaf collimator is progressively refined during the optimization. Specifically, at the beginning of the search, a coarse encoding is adopted by dividing the aperture shape-related variables into several groups and representing each group by one bit, which achieves effective search space reduction for the aperture shape. During the evolution, the granularity of encoding aperture shape-related variables is gradually varied from coarse to fine by reducing the size of each group until only one variable is contained in the group. With the proposed varied granularity encoding method, an evolutionary algorithm is suggested based on a popular evolutionary multi-objective framework (NSGA-II), where an adaptive switching method is developed to determine whether the granularity level needs to be reduced according to the convergence status of the population. The experiment empirically investigates the performance of the proposed varied granularity encoding method based evolutionary algorithm on eight clinical instances with the number of aperture shape-related variables ranging from 1932 to 3180. Compared with seven representative evolutionary algorithms and one traditional direct aperture optimization algorithm, the proposed algorithm demonstrates statistically significant improvements in hypervolume, inverted generational distance, and dose-volume histogram. The experimental results reveal that the proposed algorithm not only exhibits competitiveness but reduces computational time in radiotherapy optimization.

关键词： evolutionary computation Large-scale multi-objective optimization multi-objective evolutionary algorithm Radiation optimization

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Distributed assembly shop scheduling problem for complex products considering multiskilled worker assignment and transportation time

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年

作者： Gao, Qinglin Hu, Hanlin Liu, Jianhua Zhuang, Cunbo Ding, Hongyan Li, Huiting Beijing Inst Technol Sch Mech Engn Lab Digital Mfg Beijing 100081 Peoples R China Beijing Inst Technol Tangshan Res Inst Tangshan 063015 Peoples R China

The distributed assembly hybrid flow shop scheduling problem (DAHFSP) is a type of distributed shop scheduling problem, and each distributed shop can be regarded as a hybrid flow shop. In distributed assembly processes for complex products such as satellites and missiles, transportation time and worker assignment have important effects on production scheduling. Based on real production situations, this study proposes a novel DAHFSP considering worker assignment and transportation time, aiming to minimise the makespan and the imbalance degree of worker workloads. First, to solve these problems, we construct a mathematical model and design a two-layer chromosome coding scheme including worker assignment and task sequence. Then, in the local search stage, we propose a mutation-based search method and an elite search method. On that basis, we propose a multi-objective evolutionary algorithm with reinforced elite retention strategy (MOEA-RERS). Finally, based on a set of 12 test instances generated by actual enterprise production data, we compare the MOEA-RERS algorithm with five multi-objective evolutionary algorithms. The results show that the MOEA-RERS algorithm is superior to other algorithms in terms of solution quality and distribution.

关键词： Distributed assembly shop scheduling hybrid flow shop scheduling complex products workers assignment multi-objective evolutionary algorithm

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A clustering-based archive handling method and multi-objective optimization of the optimal power flow problem

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APPLIED INTELLIGENCE 2024年第22期54卷 11603-11648页

作者： Akbel, Mustafa Kahraman, Hamdi Tolga Duman, Serhat Temel, Seyithan Pusula Iletisim Bilisim Internet Sanayi Ve Ticaret Istanbul Turkiye Karadeniz Tech Univ Software Engn Technol Fac Trabzon Turkiye Bandirma Onyedi Eylul Univ Elect Engn Engn & Nat Sci Fac Bandirma Turkiye TEKNOPAR Ankara Turkiye

The main challenge in finding the optimal Pareto Front (PF) and Pareto Set (PS) sets for multimodal multi-objective optimization problems (MMOPs) with conflicting objective functions is to exhibit a balanced and sustainable diversity and exploitation capability in both the objective and decision spaces. This paper introduces dynamic reference spaces based clustering (DRSC) as a new archive handling method to overcome this challenge. DRSC incorporates a niche method called dynamically switched reference spaces and adapts the K-means-based method for clustering non-dominant vectors and handling the archive. The performance of the proposed DRSC is tested on twenty-four benchmark problems. According to the results of non-parametric statistical analysis using data from four different performance metrics, DRSC-MOAGDE designed using the proposed archiving mechanism managed to achieve the best Friedman rank among thirty different competitors. According to the stability analysis results, the average success rates and average computation times of the three best performing algorithms DRSC-MOAGDE, MMODE-ICD and SSMOPSO are (88.69%, 3.01 s), (66.87%, 9.47 s) and (64.29%, 1372.49 s), respectively. It is also observed that the proposed DRSC-MOAGDE outperforms the best cost optimization values in the literature with a minimum of 0.1838 $/h and a maximum of 30.9157 $/h for the multi-objective OPF real-world problem.

关键词： Archive handling Dynamic reference spaces based clustering multi-objective evolutionary algorithm multimodal multi- objective optimization Real-world constrained optimal power flow problem

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Design and Investigation of a New Torque-Enhanced Flux Modulated Permanent Magnet Arc Motor With Flux-Concentrated Stator PMs

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 2024年第8期34卷 1页

作者： Chen, Nan Fang, Shuhua Southeast Univ Sch Elect Engn Nanjing 210096 Jiangsu Peoples R China

This article proposes an innovative flux modulated permanent magnet (PM) arc motor enhanced with flux-concentrated stator PMs (FCS-FMPMAM). With the primary goal of increasing the average torque output, the FCS-FMPMAM incorporates a set of flux-focused stator PMs. This article initially introduces the configuration and performance of the FCS-FMPMAM. The combination of the flux-switching PMs, consequent-pole PMs and PMs in the stator yoke is beneficial to generate abundant harmonics and bolster the triple flux-modulation effect. Then, the optimal rotor pole number of the proposed machine is analyzed and selected. The sensitivity analysis is performed on the design parameters of FCS-FMPMAM for the consequent optimization of the torque performance of FCS-FMPMAM. This facilitates the subsequent torque performance optimization of FSC-FMPMAM. Based on the multi-objective evolutionary algorithm, the torque capabilities of FCS-FMPMAM are optimized to obtain the maximized average torque output and the minimized torque ripple. The optimized machine is analyzed under different PM excitation conditions to reveal the superiority of the proposed PM arrangement. Finally, the proposed machine is compared with an existing flux-modulated stator-PM arc motor in electromagnetic performances with finite element analysis method to exhibit the superiority of FCS-FMPMAM.

关键词： Arc motor flux-concentrated stator PMs multi-objective evolutionary algorithm sensitivity analysis triple flux-modulation effect torque

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multi-objective flexible flow-shop rescheduling with rigid-flexible hybrid constraints and preventive maintenance

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COMPUTERS & INDUSTRIAL ENGINEERING 2025年 200卷

作者： Zhao, Ziye Chen, Xiaohui An, Youjun Chongqing Univ Coll Mech & Vehicle Engn Chongqing 400030 Peoples R China China Three Gorges Univ Coll Mech & Power Engn Yichang 443002 Peoples R China

The synergy between production rescheduling and machine maintenance is critical, particularly incases where unforeseen equipment failures, not fully prevented by maintenance, might threaten the viability of the original plan. In this context, this paper explores a novel integrated optimization problem of production rescheduling and preventive maintenance in a capacity-limited flexible flow-shop (CLFFS), in which random equipment failures, hybrid rigid-flexible constraints of buffer capacity and due window are considered. Specifically, (1) an integrated optimization model is established to minimize the makespan, average flow time, earliness/tardiness penalty, machine workload extreme deviation and system instability;(2) an adaptive hybrid rescheduling strategy (AHRS) that amalgamates three classical rescheduling approaches is designed to effectively respond to random equipment failures;and (3) an improved bi-population cooperative evolutionary algorithm with an adaptive environment selection mechanism (AES-IBCEA) is developed to deal with the integrated problem. In the numerical experiments, Taguchi method is first employed to set the parameters of the proposed algorithm. Second, the effectiveness and superiority of designed operators and proposed AES-IBCEA are validated through algorithm comparison. Next, the competitiveness of the proposed AHRS is demonstrated by contrasting it with other rescheduling strategies, and the average improvement rate is up to 22.12%. Finally, a sensitivity analysis on the fault impact threshold (delta 0) and the individual selection threshold (beta) is performed, and the results reveal that beta has a significant impact on the algorithm's performance.

关键词： Flexible flow-shop rescheduling Preventive maintenance Rigid-flexible hybrid constraints Adaptive hybrid rescheduling strategy multi-objective evolutionary algorithm

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Cultural transmission based multi-objective evolution strategy for evolutionary multitasking

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INFORMATION SCIENCES 2022年 582卷 215-242页

作者： Xu, Zhiwei Liu, Xiaoming Zhang, Kai He, Juanjuan Wuhan Univ Sci & Technol Sch Comp Sci & Technol Wuhan 430065 Peoples R China Hubei Prov Key Lab Intelligent Informat Proc & Re Wuhan 430065 Peoples R China

In recent years, many efficient evolutionary multitasking (EMT) algorithms have been pro-posed to solve multi-objective multi-task optimization problems. However, EMT algo-rithms often face negative transfer problems. In this paper, a novel multi-objective evolution strategy, called CT-EMT-MOES, is proposed based on a cultural transmission the-ory for solving multi-objective multitask optimization problems. First, two evolutionary operators inspired by cultural transmission theory are proposed. The elite-guided variation strategy can transfer the information from the current Pareto front to all individuals and guide the population to quickly converge. The horizontal cultural transmission strategy can efficiently transfer information from the source task to the target task. Second, to solve the negative transfer problem, an adaptive information transfer strategy is proposed to adaptively adjust the probability of an information transfer. Third, the proposed algorithm can gain a Pareto front with good convergence and diversity by utilizing a smaller popula-tion size and fewer computing resources. As a result, the proposed algorithm can effec-tively utilize the implicit similarity and complementarity between simultaneous optimized tasks to improve the overall convergence efficiency and reduce a negative trans-fer. Finally, comprehensive experimental results show that the proposed algorithm can achieve a better performance compared with previous state-of-the-art multi-objective EMT algorithms. (c) 2021 Elsevier Inc. All rights reserved.

关键词： multi-objective evolutionary algorithm evolutionary multitasking multi-task optimization Cultural transmission Evolution strategy

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Distributed multi-objective optimization for SNP-SNP interaction detection

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METHODS 2024年 221卷 55-64页

作者： Li, Fangting Zhao, Yuhai Xu, Tongze Zhang, Yuhan Northeastern Univ Sch Comp Sci & Engn Shenyang Peoples R China Northeastern Univ Coll Med & Biol Informat Engn Shenyang Peoples R China

The detection of complex interactions between single nucleotide polymorphisms (SNPs) plays a vital role in genome-wide association analysis (GWAS). The multi-objective evolutionary algorithm is a promising technique for SNP-SNP interaction detection. However, as the scale of SNP data further increases, the exponentially growing search space gradually becomes the dominant factor, causing evolutionary algorithm (EA)-based approaches to fall into local optima. In addition, multi-objective genetic operations consume significant amounts of time and computational resources. To this end, this study proposes a distributed multi-objective evolutionary framework (DM-EF) to identify SNP-SNP interactions on large-scale datasets. DM-EF first partitions the entire search space into several subspaces based on a space-partitioning strategy, which is nondestructive because it guarantees that each feasible solution is assigned to a specific subspace. Thereafter, each subspace is optimized using a multi-objective EA optimizer, and all subspaces are optimized in parallel. A decomposition-based multi-objective firework optimizer (DCFWA) with several problem-guided operators was designed. Finally, the final output is selected from the Pareto-optimal solutions in the historical search of each subspace. DM-EF avoids the preference for a single objective function, handles the heavy computational burden, and enhances the diversity of the population to avoid local optima. Notably, DM-EF is load-balanced and scalable because it can flexibly partition the space according to the number of available computational nodes and problem size. Experiments on both artificial and real-world datasets demonstrate that the proposed method significantly improves the search speed and accuracy.

关键词： Distributed computing SNP-SNP interactions multi-objective evolutionary algorithm Space-partitioning strategy

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Reinforcement learning for distributed hybrid flowshop scheduling problem with variable task splitting towards mass personalized manufacturing

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JOURNAL OF MANUFACTURING SYSTEMS 2024年 76卷 188-206页

作者： Chen, Xin Li, Yibing Wang, Kaipu Wang, Lei Liu, Jie Wang, Jun Wang, Xi Vincent Wuhan Univ Technol Sch Mech & Elect Engn Wuhan 430070 Peoples R China Wuhan Business Univ Sch Mech & Elect Engn Wuhan 430056 Peoples R China Wuhan Univ Technol Hubei Digital Mfg Key Lab Wuhan 430070 Peoples R China KTH Royal Inst Technol Dept Prod Engn S-10044 Stockholm Sweden

Mass personalization manufacturing (MPM), an emerging production pattern, aims to improve enterprise profit in modern industries. However, the processing of heterogeneous orders from the consumers complicates such production scheduling problem. In addition, different scale tasks should adopt different splitting strategies in practical manufacturing, which makes the task splitting method more worthy of investigation. Towards MPM, this paper presents a distributed hybrid flowshop scheduling problem with variable task splitting (DHFSP-VTS) to minimize the makespan and total energy consumption simultaneously. Meanwhile, the VTS allows the tasks to be split into different sublots so they can save setup and transfer time. To solve these problems, we present an order modularization processing method that can categorize multiple types of orders into specific generation tasks, and a highly effective reinforcement learning-multiple objective evolutionary algorithm based on decomposition (RLMOEA/D) is designed. In RL-MOEA/D, there are three features: (1) three initial rules are used for initialization based on the current splitting scheme that can increase the diversity of solutions;(2) the reinforcement learning agent uses the Q-learning mechanism to dynamically select the scheme of task splitting as action;(3) a neighborhood search strategy improves the exploitation ability and expand the solution space. To verify the effectiveness of RL-MOEA/D, the MOEA/Ds based on four splitting schemes and four RL combined meta-heuristics are compared on 18 instances. The results show that RL-MOEA/D can obtain the best optimization and stability of all the other comparison algorithms. Therefore, it's a new technique to solve DHFSP with large-scale tasks, especially for the problem of MPM.

关键词： Reinforcement learning Distributed hybrid flowshop scheduling Mass personalization manufacturing Variable task splitting multi-objective evolutionary algorithm

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multi-objective Synergetic Operation for Cascade Reservoirs in the Upper Yellow River

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WATER 2024年第10期16卷 1416页

作者： Hong, Kunhui Zhang, Wei Ma, Aixing Wei, Yucong Cao, Mingxiong Hohai Univ Coll Harbour Coastal & Offshore Engn Nanjing 210098 Peoples R China Nanjing Hydraul Res Inst Nanjing 210029 Peoples R China Minist Commun Key Lab Port Waterway & Sedimentat Engn Nanjing 210029 Peoples R China

The Yellow River, a critical water resource, faces challenges stemming from increasing water demand, which has led to detrimental effects on hydropower generation and ecological balance. This paper will address the complex task of balancing the interests of hydropower generation, water supply, and ecology within the context of cascade reservoirs, specifically Longyangxia and Liujiaxia reservoirs. Employing a systemic coupling coordination approach, we constructed a multi-objective synergetic model of the upper Yellow River in order to explore synergies and competitions among multiple objectives. The results reveal that there is a weak competitive relationship between hydropower generation and water supply, a strong synergy between hydropower generation and ecology, and a strong competitive relationship between water supply and ecology. The Pareto solution set analysis indicates a considerable percentage (59%, 20%, and 8% in wet, normal, and dry years, respectively) exhibiting excellent coordination. The probability of excellent coordination decreases with diminishing inflow. The optimization scheme with the highest coupling coordination demonstrates significant improvements in power generation, water supply, and ecological benefits in the upper Yellow River without compromising other objectives, fostering the sustainable operation of hydropower generation, water supply, and ecology in the upper Yellow River.

关键词： Yellow River Basin multi-objective evolutionary algorithm cascade reservoirs coupling

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