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Multiple Objective Optimization with Vector Evaluated Genetic Algorithms.
... Then we consider the Schaffer function in two-dimension [50], defined as ...
... The hyperparameters for networks and optimizers are the same as in previous experiments. To explore the relationship between the accuracy of FedDeepONet and various communication frequencies, E is set to be [1,2,5,10,20,50,100,200,500,1000] with the total number of iterations fixed to be 50000. By doing so, local iterations can cover almost identical scenarios to centralized training (E = 1) and huge cases (E = 1000) and demonstrate the property of FedDeepONet more comprehensively. ...
By leveraging neural networks, the emerging field of scientific machine learning (SciML) offers novel approaches to address complex problems governed by partial differential equations (PDEs). In practical applications, challenges arise due to the distributed essence of data, concerns about data privacy, or the impracticality of transferring large volumes of data. Federated learning (FL), a decentralized framework that enables the collaborative training of a global model while preserving data privacy, offers a solution to the challenges posed by isolated data pools and sensitive data issues. Here, this paper explores the integration of FL and SciML to approximate complex functions and solve differential equations. We propose two novel models: federated physics-informed neural networks (FedPINN) and federated deep operator networks (FedDeepONet). We further introduce various data generation methods to control the degree of non-independent and identically distributed (non-iid) data and utilize the 1-Wasserstein distance to quantify data heterogeneity in function approximation and PDE learning. We systematically investigate the relationship between data heterogeneity and federated model performance. Additionally, we propose a measure of weight divergence and develop a theoretical framework to establish growth bounds for weight divergence in federated learning compared to traditional centralized learning. To demonstrate the effectiveness of our methods, we conducted 10 experiments, including 2 on function approximation, 5 PDE problems on FedPINN, and 3 PDE problems on FedDeepONet. These experiments demonstrate that proposed federated methods surpass the models trained only using local data and achieve competitive accuracy of centralized models trained using all data.
... Algoritmos genéticos multi-objectivo (MOGAs) foram sugeridos por Schaffer [16] e desde então diversos algoritmos têm sido propostos com base em processos evolucionários que procuram soluções óptimas de Pareto [17][18][19]. Uma estratégia MOGA consiste em transferir multi-objectivos para um único objectivo usando uma média pesada, sendo os pesos seleccionados aleatoriamente. ...
Próteses artificiais são utilizadas na cirurgia de bypass para restabelecer o fluxo sanguíneo em artérias ocluídas ou severamente estenosadas. A configuração do bypass, incluindo a geometria da prótese e da anastomose, tem uma forte influência na dinâmica do fluxo sanguíneo, verificando-se por vezes a ocorrência de fenómenos de recirculação e criação de zonas de estagnação, positivamente relacionadas com a reestenose póscirúrgica. A optimização, utilizando técnicas de simulação numérica, pode e deve ser utilizada para encontrar soluções que garantam uma minimização dos riscos pós-cirúrgicos. A procura de geometrias de próteses optimizadas tem sido apresentada na literatura quase sempre restringida apenas a uma única função objectivo. Investigação recente para desenvolver uma nova metodologia para optimização multi-objectivo de próteses é aqui apresentada. Ao contrário das metodologias de optimização de uma única função objectivo, a solução deste problema não é um único ponto, mas sim uma família dos pontos permitindo uma selecção de acordo com a experiência do investigador em cirugia vascular. O esquema deste trabalho de optimização multi-objectivo considera um algoritmo genético que procura geometrias sinusoidais óptimas de próteses artificiais iterando sobre resultados de um programa de elementos finitos desenvolvido para a simulação do fluxo sanguíneo. Relativamente à escolha de funções objectivo considera-se a optimização da eficiência do fluxo, minimizando a variação de pressão e ainda a minimização de zonas de ocorrência de recirculação e de estagnação. Os resultados numéricos evidenciam os benefícios da optimização da geometria da prótese antes da cirurgia do bypass arterial, minimizando zonas da recirculação e de estagnação do fluxo e diminuindo a probabilidade de restenose arterial pós-cirúrgica. Este trabalho representa o uso formal de algoritmos de optimização multiobjectivo no projecto de cirurgia hospitalar.
... The concept of genetic algorithms was initially introduced by Holland 49 in the 1960s and 1970s, inspired by the evolutionary theory's survival of the fittest principle. Schaffer 50 introduced the first genetic algorithm, Vector Evaluator, in 1985. In 1992, Hajela 51 integrated weights into genetic algorithms, leading to the proposal of weight-based genetic algorithms. ...
Accurate and timely pest and disease monitoring during the cultivation process of traditional Chinese medicinal materials is crucial for ensuring optimal growth, increased yield, and enhanced content of effective components. This paper focuses on the essential requirements for pest and disease monitoring in a planting base of Cinnamomum Camphora var. Borneol (CCB) and presents a solution using unmanned aerial vehicle (UAV) images to address the limitations of real-time and on-site inspections. In contrast to existing solutions that rely on advanced sensors like multispectral or hyperspectral sensors mounted on UAVs, this paper utilizes visible light sensors directly. It introduces an ensemble learning approach for pest and disease monitoring of CCB trees based on RGB-derived vegetation indices and a combination of various machine learning algorithms. By leveraging the feature extraction capabilities of multiple algorithms such as RF, SVM, KNN, GBDT, XGBoost, GNB, and ELM, and incorporating morphological filtering post-processing and genetic algorithms to assign weights to each classifier for optimal weight combination, a novel ensemble learning strategy is proposed to significantly enhance the accuracy of pest and disease monitoring of CCB trees. Experimental results validate that the proposed method can achieve precise pest and disease monitoring with reduced training samples, exhibiting high generalization ability. It enables large-scale pest and disease monitoring at a low cost and high precision, thereby contributing to improved precision in the cultivation management of traditional Chinese medicinal materials.
... To assess the performance of the three algorithms studied, five well-known problems are selected from the MOP1 (Van Veldhuizen & Lamont, 1999), ZDT (Zitzler et al., 2000), SCH (Schaffer, 1984), and TNK (Tanaka et al., 1995) test suites developed for testing evolutionary MOO algorithms. The test problems are chosen to vary in complexity in terms of problem size and numerical difficulty with convex, nonconvex and disconnected Pareto fronts. ...
any practical multiobjective optimization (MOO) problems include discrete decision variables and/or nonlinear model equations and exhibit disconnected or smooth but nonconvex Pareto surfaces. Scalarization methods, such as the weighted-sum and sandwich (SD) algorithms, are common approaches to solving MOO problems but may fail on nonconvex or discontinuous Pareto fronts. In the current work, motivated by the well-known normal boundary intersection (NBI) method and the SD algorithm, we present SDNBI, a new algorithm for bi-objective optimization (BOO) designed to address the theoretical and numerical challenges associated with the reliable solution of general nonconvex and discrete BOO problems. The main improvements in the algorithm are the effective exploration of the nonconvex regions of the Pareto front and, uniquely, the early identification of regions where no additional Pareto solutions exist. The performance of the SDNBI algorithm is assessed based on the accuracy of the approximation of the Pareto front constructed over the disconnected nonconvex objective domains. The new algorithm is compared with two MOO approaches, the modified NBI method and the SD algorithm, using published benchmark problems. The results indicate that the SDNBI algorithm outperforms the modified NBI and SD algorithms in solving convex, nonconvex-continuous, and combinatorial problems, both in terms of computational cost and of the overall quality of the Pareto-optimal set, suggesting that the SDNBI algorithm is a promising alternative for solving BOO problems.
... Due to the requirement to integrate vectorial performance metrics with the fundamentally scalar method in which EAs compensate individual achievement, i.e., the number of offspring, the majority of research in this field has focused on the selection stage of EAs. In the mid-1980s, the first pioneering research on evolutionary multi-objective optimisation appeared (Fourman, 1985;Schaffer, 1984;Schaffer, 1985). In the years 1991-to-1994, a few alternative MOEA implementations were suggested (Fonseca, 1993;Hajela, 1992;Horn, Nafpliotis and Goldberg, 1994;Srinivas, 1994;Kursawe, 1991). ...
This review will investigate and analyse the application of multi-criteria decision-making (MCDM) techniques in the Chemical Engineering (CE) sector.
... Son yıllarda, çok amaçlı optimizasyon problemlerini (ÇAOP) çözmek için çeşitli evrimsel algoritmalar geliştirilmiştir (Ma ve ark., 2021). İlk çok amaçlı optimizasyon algoritması Vektör Değerlendirilen Genetik Algoritmasıdır (VEGA) (Schaffer, 1985). Daha sonra, Niched Pareto Genetic Algorithm (NPGA) (rey Horn ve ark., 1994), Multi Objective Genetic Algorithm (MOGA) (Murata ve Ishibuchi, 1995), Nondominated Sorting Genetic Algorithm II (NSGA-II) (Deb ve ark., 2000), Pareto Archived Evolution Strategy (PAES) (Knowles ve Corne, 2000) , ...
Dağınık arama algoritması, tek amaçlı optimizasyon problemlerinin çözümünde sıkça kullanılan bir yöntemdir. Ancak, çok amaçlı problemlerle başa çıkmak oldukça zorlu bir süreçtir. Bu makale, çok amaçlı optimizasyon problemleriyle başa çıkabilmek için "Dağınık Arama Algoritması" (DA) olarak adlandırılan yöntemin genişletilmesine yönelik bir öneri sunmaktadır. Önerilen yaklaşım, DA algoritmasına çok amaçlı optimizasyon algoritması olan Baskın Olmayan Sıralama Genetik Algoritması II (NSGA-II) yöntemindeki Yoğunluk Mesafesi (CD) ve Hızlı Bastırılmamış Sıralama kavramlarını ekleyerek hibrit çok amaçlı optimizasyon algoritması önermektedir. Bu önerilen algoritma, ZDT ve DTLZ test problemleri kullanılarak değerlendirilmiştir. Yapılan deneysel sonuçlar, önerilen Çok Amaçlı Dağınık Arama(ÇADA) algoritmasının 19 farklı çok amaçlı optimizasyon yöntemi ile karşılaştırıldığında, ZDT problemi için 2.40 IGD ortalama ile birinci sırada, DTLZ probleminde ise 0.0035 IGD ortalama değeri ile altıncı sırada yer aldığını göstermektedir. Bu sonuçlar, önerilen algoritmanın karşılaştırılabilir düzeyde başarılı bir performansa sahip olduğunu ortaya koymaktadır.
... According to Ref. [36], approximately 90% of approaches for solving multiobjective optimization aim to approximate the true Pareto front, with a significant portion relying on meta-heuristic approaches, 70% of which are evolutionary. The vector evaluation GA (VEGA) was introduced by Ref. [37], and subsequently, numerous multiobjective evolutionary algorithms have been developed, including the niched Pareto genetic algorithm (NPGA) [38], multiobjective genetic algorithm (MOGA) [39], improved strength Pareto evolutionary algorithm (SPEA2) [40], random weighted genetic algorithm (RWGA) [41], weight-based genetic algorithm (WBGA) [42], strength Pareto evolutionary algorithm (SPEA) [43], Pareto-archived evolution strategy (PAES) [44], region-based selection in evolutionary multiobjective optimization (PESA-II) [45], Pareto envelope-based selection algorithm (PESA) [44], multiobjective evolutionary algorithm (MEA) [46], fast non-dominated sorting genetic algorithm (NSGA-II) [47], dynamic multiobjective evolutionary algorithm (DMOEA) [48], micro-GA [49], and rank-density-based genetic algorithm (RDGA) [50]. While there are numerous types of multiobjective GAs, the aforementioned algorithms are widely recognized and have been extensively studied across different applications through comparative studies. ...
Minimizing job waiting time for completing related operations is a critical objective in industries such as chemical and food production, where efficient planning and production scheduling are paramount. Addressing the complex nature of flow shop scheduling problems, which pose significant challenges in the manufacturing process due to the vast solution space, this research employs a novel multiobjective genetic algorithm called distance from ideal point in genetic algorithm (DIPGA) to identify Pareto-optimal solutions. The effectiveness of the proposed algorithm is benchmarked against other powerful methods, namely, NSGA, MOGA, NSGA-II, WBGA, PAES, GWO, PSO, and ACO, using analysis of variance (ANOVA). The results demonstrate that the new approach significantly improves decision-making by evaluating a broader range of solutions, offering faster convergence and higher efficiency for large-scale scheduling problems with numerous jobs. This innovative method provides a comprehensive listing of Pareto-optimal solutions for minimizing makespan and total waiting time, showcasing its superiority in addressing highly complex problems.
As the core component of water-jet propulsion system, water-jet pump, directly affects the ship’s propulsion performance. Three-dimensional (3D) inverse design can obtain higher hydraulic performance of pump impeller and diffuser. It is an efficient and feasible way to coupling optimization based on multi-parameter, multi-objective, and optimization algorithms, and parameterizing the impellers and diffuser geometry based on the 3D model designed by 3D inverse design method. In this paper, the water-jet propulsion pump is selected as the research object. Based on the design methodology of the hydraulic model for the water-jet pump, traditional axial flow blade design methods, modern three-dimensional blade design theory, and parametric 3D inverse design methods are employed to develop an optimization strategy for the water-jet pump impeller using a multi-parameter, multi-objective genetic algorithm. The impeller is optimized using this strategy, and the performance of the model before and after optimization is compared through simulation and experimental results. Under the design conditions, the optimized pump efficiency reaches 89.28%, which is 1.24% higher than the original hydraulic model. The optimized pump head is 13.51 m, which is 0.39 m more than the original hydraulic model. The numerical calculation result is 1.88% higher than the test result, the test measured efficiency is 87.1%, and the numerical calculation result is 2.5% higher than the test result. The experimentally measured critical cavitation margin was 7.58 m, and the numerically calculated critical cavitation margin was 7.36 m, both of which indicate a high critical cavitation margin and strong cavitation resistance.
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