Three-dimensional facility layout optimization using large language model-driven A-star and non-dominated sorting genetic Algorithm-II

For a high-speed and high-acceleration planar parallel mechanism, a design for control (DFC) approach is proposed for the optimization of the mechanism structure. Several evaluation indexes of kinematics and dynamics performance are established for the object functions and constraints, and then a standard multi-objective optimization problem can be formed. The dimension synthesis is carried out by solving the multi-objective optimization with NSGA-II (non-dominated sorting genetic algorithm-II) algorithm. The final result shows that the mechanism with the optimized parameters can eliminate the systematic coupling and enhance the dynamic performance greatly, which provides a solid mechanism hardware platform for designing the high-speed control system.

Mathematical runtime analysis for the non-dominated sorting genetic algorithm II (NSGA-II)

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.

With the deteriorating environment and excessive consumption of primary energy, solar energy has become used in buildings worldwide for renewable energy. Due to the fluctuations of solar radiation, a solar photovoltaic (PV) power system is often combined with a storage battery to improve the stability of a building’s energy supply. In addition, the real-time energy consumption pattern of the residual houses fluctuates; a larger size for a PV and battery integrated system can offer more solar energy but also bring a higher equipment cost, and a smaller size for the integrated system may achieve an energy-saving effect. The traditional methods to size a PV and battery integrated system for a detached house are based on the experience method or the traversal algorithm. However, the experience method cannot consider the real-time fluctuating energy demand of a detached house, and the traversal algorithm costs too much computation time. Therefore, this study applies Nondominated Sorting Genetic Algorithm-II (NSGA-II) to size a PV and battery integrated system by optimizing total electricity cost and usage of the grid electricity simultaneously. By setting these two indicators as objectives separately, single-objective genetic algorithms (GAs) are also deployed to find the optimal size specifications of the PV and battery integrated system. The optimal solutions from NSGA-II and single-objective GAs are mutually verified, showing the high accuracy of NSGA-II, and the rapid convergence process demonstrates the time-saving effect of all these deployed genetic algorithms. The robustness of the deployed NSGA-II to various grid electricity prices is also tested, and similar optimal solutions are obtained. Compared with the experience method, the final optimal solution from NSGA-II saves 68.3% of total electricity cost with slightly more grid electricity used. Compared with the traversal algorithm, NSGA-II saves 94% of the computation time and provides more accurate size specifications for the PV and battery integrated system. This study suggests that NSGA-II is suitable for sizing a PV and battery integrated system for a detached house.

This paper presents an application of non-dominated sorting genetic algorithm-II (NSGA-II) technique for solving shortest path routing problems in computer networks. The problem is formulated as a non-linear constrained multi-objective optimisation problem. NSGA-II is applied to handle shortest path routing problem as a true multi-objective optimisation problem (MOOP) with competing and non-commensurable objectives. A priority-based encoding scheme is employed for population initialisation. Priorities are assigned to all the edges and NSGA-II is implemented to find the optimal solution. It is noted that this approach can find a diverse set of solutions and is converging near the true Pareto-optimal set. Results for a sample test network have been presented to demonstrate the capabilities of the NSGA-II algorithm to generate well-distributed Pareto-optimal solutions of shortest path routing problem in one single run. The results obtained by NSGA-II are compared with single objective weighting factor method for which genetic algorithm (GA) is applied.

Determining the contribution of an agent to a system-level objective function (credit assignment) is a key area of research in cooperative multiagent systems. Multi-objective optimization is a growing area of research, though mostly focused on single agent settings. Many real-world problems are multiagent and multi-objective, (e.g., air traffic management, scheduling observations across multiple exploration robots) yet there is little work on their intersection. In this work, we leverage recent advances in single-objective multiagent learning to address multi-objective domains. We focus on the impact of difference evaluation functions (which extracts an agent's contribution to the team objective) on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), a state-of-the-art multi-objective evolutionary algorithm. We derive multiple methods for incorporating difference evaluations into the NSGA-II framework, and test each in a multiagent rover exploration domain, which is a good surrogate for a wide variety of distributed scheduling and resource gathering problems. We show that how and where difference evaluations are incorporated in the NSGA-II algorithm is critical, and can either provide significant benefits or destroy system performance, depending on how it is used. Median performance of the correctly used difference evaluations dominates best-case performance of NSGA-II in a multiagent multi-objective problem.

In order to obtain higher quality silicon single crystal, a hybrid strategy for modeling of Czochralski silicon crystal growth and optimizing of process parameters is presented in the paper. The hybrid strategy includes the computational fluid dynamics (CFD) method, neural network of group method of data handing (GMDH), and improved nondominated sorting genetic algorithm II (NSGA‐II). The shape variable of solid‐liquid interface h and the defect evaluation criteria V/G are set to objective functions according to engineering experience and process requirement. The polynomial of the objective functions is produced by GMDH and CFD. Ultimately, an improved elitist strategy and crowding distance NSGA‐II is proposed in the paper to obtain the Pareto optimum solution by the objective functions identified by the GMDH. Compared with other optimization algorithms, the improved NSGA‐II can increase the lateral diversity and the uniform distribution of the nondominated solutions. Engineering validation proved that the proposed hybrid strategy can effectively solve the complex uncertain multiobjective optimization problem of system and provides a new method for obtaining high‐quality crystal growth process parameters.

Degradation state identification for hydraulic pumps is crucial to ensure system performance. As an important step, feature extraction has always been challenging. The non-stationary and non-Gaussian characteristics of the vibration signal are likely to weaken the performance of traditional features. In this paper, an efficient feature extraction algorithm named multi-scale ternary dynamic analysis (MTDA) is proposed. MTDA reconstructs the phase space based on the given signal and converts each embedding vector into a ternary pattern independently, which enhances its capacity of describing the details of non-stationary signals. State entropy (SE) and state transition entropy (STE) are calculated to estimate the dynamical changes and complexity of each signal sample. The excellent performance of SE and STE in detecting frequency changes, amplitude changes, and the development process of fault is verified with the use of four simulated signals. The proposed multi-scale analysis enables them to provide a more precise estimation of entropy. Furthermore, support vector machine (SVM) and nondominated sorting genetic algorithm II (NSGA-II) are introduced to conduct feature selection and state identification. NSGA-II and SVM can conduct the joint optimization of these two goals. The details of the method proposed in this paper are tested using simulated signals and experimental data, and some studies related to the fault diagnosis of rotating machinery are compared with our method. All the results show that our proposed method has better performance, which obtains higher recognition accuracy and lower feature set dimension.

The non-dominated sorting genetic algorithm II (NSGA-II) is applied to the concurrent generation scheduling and load management of the isolated microgrid: the joint generation — voyage scheduling of an all-electric ship (AES). The AES uses integrated power generators and an energy storage system (ESS) to match its propulsion and service loads, thus forming an isolated microgrid. The propulsion load is the variable load that determines th ship voyage; hence, the schedulings of the generator, the propulsion load and the ESS have to be processed concurrently, for the optimal operation of the AES. NSGA-II outperforms the existing methods for the AES scheduling problem by modelling the schedulings in a one-stage optimisation. Another advantage of NSGA-II applied here is its multi-objective optimisation. Existing work on ship scheduling has hitherto set the minimisation of the AES operational cost as the single optimisation objective, with the reduction of the greenhouse gas (GHG) emission merely treated as a constraint of the optimisation. The proposed work emphasises the environmental concerns and makes GHG mitigation a separate objective, thus expanding the optimisation into multi-objective. The simulation demonstrate that optimising the ship voyage jointly with the generation scheduling results in the reduction of both operational cost and GHG emission, compared to the fixed-voyage generation scheduling. Integrating the ESS dispatch into the generation scheduling further enhances the benefits.

Machine configuration is a crucial strategic decision in designing a flow shop system (FSS) and directly affects its performance. This involves selecting device suppliers and determining the number of machines to be configured. This study addresses a bi-objective optimization problem for an FSS that considers repair actions and aims to determine the most suitable machine configuration that balances the production reliability and purchase cost. A nondominated sorting genetic algorithm II (NSGA-II) is used to determine all the Pareto solutions. The technique for order preference by similarity to an ideal solution is then used to identify a compromise alternative. It is necessary to assess the production reliability of any machine configuration identified by the NSGA-II. The FSS under the machine configuration is modeled as a multistate flow shop network, and Absorbing Markov Chain and Recursive Sum of Disjoint Products are integrated into the NSGA-II for reliability evaluation. The experimental results of solar cell manufacturing demonstrate the applicability of the proposed hybrid method and validate the efficiency of the NSGA-II compared with an improved strength Pareto evolutionary algorithm.

The aim of this paper is to present an intelligent method for fault diagnosis of induction motors which doesn't need any expert to analyze the signals. A new intelligent fault diagnosis scheme based on multi-objective feature selection using non-dominated sorting genetic algorithm II (NSGA-II) is proposed. Firstly, to improve the signal-to-noise ratio, wavelet packet decomposition is performed. Multiple statistical features are then extracted from the decomposed signals. Some of these features contain unhelpful information, so the most superior features are selected using NSGA-II. Finally, the classification of type and severity of faults is performed using a multilayer perceptron (MLP) neural network. The proposed scheme is tested on a bearing fault dataset, and the results show that it, unlike signal processing techniques, is able to detect the faults of induction motor without any expert. It also achieves a better classification rate comparing with the methods based on conventional feature selection algorithms.

Optimization of some properties of hydraulic asphalt concrete mix using RSM and NSGA-II

Improving voltage stability, reducing real power loss (PL) and voltage deviation (VD) are the most important tasks in the operation of electrical power systems. Voltage instability and voltage collapse are the severe problems which may take place because of deficit reactive power at load buses due to increased loading or contingencies. In this paper, the problem of obtaining optimal location and size of SVC is formulated as true multi-objective optimization problem for simultaneous minimization of the two objectives namely real power losses and load bus voltage deviation. The two algorithms real coded genetic algorithm (RCGA) and non-dominated sorting genetic algorithm-II (NSGA-II) with a feature of adoptive crowding distance have been used for solving nonlinear constrained multi-objective optimization problem. Both the algorithms have been used for obtaining optimal location and sizing of SVC. Voltage security of the power system has also been analyzed separately for all placement of SVC to ensure secure operation of the system. The proposed approaches have been implemented on IEEE 30-bus test system. The simulation results of the two algorithms have been compared for solution quality, computational complexity and computational time. It has been found that NSGA-II presents better performance in solving multi-objective optimization problem and also in obtaining a diverse set of solutions which converge near the true Pareto-optimal front. The simulation results of NSGA-II have also been presented to exhibit the capabilities of the algorithm to generate well-distributed Pareto-optimal front.

A new approach for assessing the assembled vulnerability of coastal aquifers based on optimization models

The Pareto optimal solutions to a multi-objective optimization problem often distribute very regularly in both the decision space and the objective space. Most existing evolutionary algorithms do not explicitly take advantage of such a regularity. This paper proposed a model-based evolutionary algorithm (M-MOEA) for bi-objective optimization problems. Inspired by the ideas from estimation of distribution algorithms, M-MOEA uses a probability model to capture the regularity of the distribution of the Pareto optimal solutions. The local principal component analysis (local PCA) and the least-squares method are employed for building the model. New solutions are sampled from the model thus built. At alternate generations, M-MOEA uses crossover and mutation to produce new solutions. The selection in M-MOEA is the same as in non-dominated sorting genetic algorithm-II (NSGA-II). Therefore, MOEA can be regarded as a combination of EDA and NSGA-II. The preliminary experimental results show that M-MOEA performs better than NSGA-II.