Suboptimal Solution Research Articles

Topography‐dependent eikonal solver in tilted transverse isotropic media with anelliptical factorization

AbstractIncorporating anisotropy and complex topography is necessary to perform traveltime tomography in complex land environments while being a computational challenge when traveltimes are computed with finite‐difference eikonal solvers. Previous studies have taken this challenge by computing traveltimes in transverse isotropic media involving complex topography with a finite‐difference eikonal equation solver on a curvilinear grid. In this approach, the source singularity, which is a major issue in eikonal solvers, is managed with the elliptical multiplicative factorization method, where the total traveltime field is decomposed into an elliptical base traveltime map, which has a known analytical expression and an unknown perturbation field. However, the group velocity curve can deviate significantly from an ellipse in anellipitically anisotropic media. In this case, the elliptical base traveltime field differs significantly from the anelliptical counterpart, leading to potentially suboptimal traveltime solutions, even though it helps to mitigate the detrimental effects of the source singularity. To overcome this issue, we develop a more accurate topography‐dependent eikonal solver in transverse isotropic media that relies on anelliptical factorization. To achieve this, we first define the coordinate transform from the Cartesian to the curvilinear coordinate system, which provides the necessary framework to implement the topography‐dependent transverse isotropic finite‐difference eikonal solver with arbitrary source and receiver positioning. Then, we develop a semi‐analytical method for the computation of the topography‐dependent anelliptical base traveltime field. Finally, we efficiently solve the resulting quadratic elliptical equation using the fast sweeping method and a quartic anelliptical source term through fixed‐point iteration. We assess the computational efficiency, stability and accuracy of the new eikonal solver against the solver based on elliptical factorization using several transverse isotropic numerical examples. We conclude that this new solver provides a versatile and accurate forward engine for traveltime tomography in complex geological environments such as foothills and thrust belts. It can also be used in marine environments involving complex bathymetry when tomography is applied to redatumed data on the sea bottom.

A novel metaheuristic population algorithm for optimising the connection weights of neural networks

The efficacy of feed-forward multi-layer neural networks relies heavily on their training procedure, where identifying appropriate weights and biases plays a pivotal role. Nonetheless, conventional training algorithms such as backpropagation encounter limitations, including getting trapped in sub-optimal solutions. To rectify these inadequacies, metaheuristic population algorithms are advocated as a dependable alternative. In this paper, we introduce a novel training methodology termed, DDE-OP, which leverages the principles of differential evolution enriched with a division-based scheme and an opposite-direction strategy. Our approach integrates two effective concepts with differential evolution. Initially, the proposed algorithm identifies partitions within the search space through a clustering algorithm and designates the obtained cluster centres to serve as representatives. Subsequently, an updating scheme incorporates these clusters into the current population. Lastly, a quasi-opposite-direction strategy is used to augment search space exploration. Extensive evaluation on diverse classification and approximation tasks demonstrate that DDE-OP surpasses conventional and population-based methodologies.

Decision Making for Communication Anti-Jamming Tasks with Knowledge-Graph-Based Q-Learning

Due to the severe threats posed by smart jammers, anti-jamming decision making has become an essential technology for wireless communications. Most of the existing anti-jamming decision-making approaches have adopted Q-Learning to improve accuracy. However, the performances of these approaches drop dramatically in fast-varying jamming environments. Thus, an advanced Q-Learning approach utilizing domain knowledge graph as prior knowledge is proposed to select the optimal strategies with high flexibility and accuracy in different jamming environments. Specifically, by taking a knowledge graph that contains anti-jamming knowledge to initialize the Q-table, Q-Learning can avoid becoming stuck at local suboptimal solutions and obtain accurate strategies with fewer iterations. The iterations of the proposed approach are one third of those of other approaches based on Q-Learning and the average rewards of the proposed approach have improved by 2 percent. Numerical results demonstrate the optimality and excellent performance of the proposed approach over various existing benchmarks.

A comprehensive multi-objective framework for the estimation of crash frequency models

A common and challenging data and modeling aspect in crash analysis is unobserved heterogeneity, which is often handled using random parameters and special distributions such as Lindley. Random parameters can be estimated with respect to each observation for the entire dataset, and grouped across segments of the dataset, with variable means, or variable variances. The selection of the best approach to handle unobserved heterogeneity depends on the data characteristics and requires the corresponding hypothesis testing. In addition to dealing with unobserved heterogeneity, crash frequency modeling often requires explicit consideration of functional forms, transformations, and identification of likely contributing factors. During model estimation, it is important to consider multiple objectives such as in- and out-of-sample goodness-of-fit to generate reliable and transferable insights. Taking all of these aspects and objectives into account simultaneously represents a very large number of modeling decisions and hypothesis testing. Limited testing and model development may lead to bias and missing relevant specifications with important insights. To address these challenges, this paper proposes a comprehensive optimization framework, underpinned by a mathematical programming formulation, for systematic hypothesis testing considering simultaneously multiple objectives, unobserved heterogeneity, grouped random parameters, functional forms, transformations, heterogeneity in means, and the identification of likely contributing factors. The proposed framework employs a variety of metaheuristic solution algorithms to address the complexity and non-convexity of the estimation and optimization problem. Several metaheuristics were tested including Simulated Annealing, Differential Evolution and Harmony Search. Harmony Search provided convergence with low sensitivity to the choice of hyperparameters. The effectiveness of the framework was evaluated using three real-world data sets, generating sound and consistent results compared to the corresponding published models. These results demonstrate the ability of the proposed framework to efficiently estimate sound and parsimonious crash data count models while reducing costs associated with time and required knowledge, bias, and sub-optimal solutions due to limited testing. To support experimental testing for analysts and modelers, the Python package “MetaCountRegressor,” which includes algorithms and software, is available on PyPi.

Cooperative resource sharing and cost minimization in energy hub systems using an improved grasshopper optimization algorithm approach

This study presents a cooperative paradigm for energy hub systems (EHSs) where a network of interconnected hubs cooperates in exploiting the resources with the purpose of economic saving. In such an architecture, each hub provided with various sources of energy, such as combined heat and power (CHP), hot water tanks, renewable sources, electric chillers, and absorption chillers, will integrate all these sources for more adaptability and efficiency to the system. Moreover, the integration of energy storage systems (ESSs) is considered to enhance the flexibility of the energy hub concerning power, heating, and cooling. Recognizing the complexity associated with incorporating multiple constraints, the improved grasshopper optimization algorithm (IGOA) is introduced to effectively address this challenge. By leveraging this algorithm, the study aims to overcome the intricacies involved in considering various constraints and achieve an optimal outcome. The IGOA improves the efficiency and effectiveness of local and national searches in solving complex energy hub optimization problems. Reducing the likelihood of getting stuck in suboptimal solutions, enhances the algorithm's ability to find optimal solutions considering multiple constraints, thereby enhancing the overall performance and cost-effectiveness of EHSs. The issue is defined as a planning challenge, and by collaborative efforts, the expenses associated with the network energy hubs are reduced, illustrating the efficacy of this concept. The findings indicate the influence of the suggested cooperative technique, with operating cost reductions of 19.09 %, 13.27 %, and 8.75 % for Hub 1, Hub 2, and Hub 3, respectively. Furthermore, the cooperative framework eradicates energy deficits and disruptions, in contrast to 1,198.21 kWh of unfulfilled demand and 22 interruptions in the non-cooperative scenario. These results underscore the significant advantages of the collaborative technique in improving cost-efficiency, reliability, and resource utilization.

An adaptive enhanced human memory algorithm for multi-level image segmentation for pathological lung cancer images

Lung cancer is a critical health issue that demands swift and accurate diagnosis for effective treatment. In medical imaging, segmentation is crucial for identifying and isolating regions of interest, which is essential for precise diagnosis and treatment planning. Traditional metaheuristic-based segmentation methods often struggle with slow convergence speed, poor optimized thresholds results, balancing exploration and exploitation, leading to suboptimal performance in the multi-thresholding segmenting of lung cancer images. This study presents ASG-HMO, an enhanced variant of the Human Memory Optimization (HMO) algorithm, selected for its simplicity, versatility, and minimal parameters. Although HMO has never been applied to multi-thresholding image segmentation, its characteristics make it ideal to improve pathology lung cancer image segmentation.The ASG-HMO incorporating four innovative strategies that address key challenges in the segmentation process. Firstly, the enhanced adaptive mutualism phase is proposed to balance exploration and exploitation to accurately delineate tumor boundaries without getting trapped in suboptimal solutions. Second, the spiral motion strategy is utilized to adaptively refines segmentation solutions by focusing on both the overall lung structure and the intricate tumor details. Third, the gaussian mutation strategy introduces diversity in the search process, enabling the exploration of a broader range of segmentation thresholds to enhance the accuracy of segmented regions. Finally, the adaptive t-distribution disturbance strategy is proposed to help the algorithm avoid local optima and refine segmentation in later stages.The effectiveness of ASG-HMO is validated through rigorous testing on the IEEE CEC'17 and CEC'20 benchmark suites, followed by its application to multilevel thresholding segmentation in nine histopathology lung cancer images. In these experiments, six different segmentation thresholds were tested, and the algorithm was compared to several classical, recent, and advanced segmentation algorithms. In addition, the proposed ASG-HMO leverages 2D Renyi entropy and 2D histograms to enhance the precision of the segmentation process.Quantitative result analysis in pathological lung cancer segmentation showed that ASG-HMO achieved superior maximum Peak Signal-to-Noise Ratio (PSNR) of 31.924, Structural Similarity Index Measure (SSIM) of 0.919, Feature Similarity Index Measure (FSIM) of 0.990, and Probability Rand Index (PRI) of 0.924. These results indicate that ASG-HMO significantly outperforms existing algorithms in both convergence speed and segmentation accuracy. This demonstrates the robustness of ASG-HMO as a framework for precise segmentation of pathological lung cancer images, offering substantial potential for improving clinical diagnostic processes.

High-Fidelity and Efficient Pluralistic Image Completion With Transformers.

Image completion has made tremendous progress with convolutional neural networks (CNNs), because of their powerful texture modeling capacity. However, due to some inherent properties (e.g., local inductive prior, spatial-invariant kernels), CNNs do not perform well in understanding global structures or naturally support pluralistic completion. Recently, transformers demonstrate their power in modeling the long-term relationship and generating diverse results, but their computation complexity is quadratic to input length, thus hampering the application in processing high-resolution images. This paper brings the best of both worlds to pluralistic image completion: appearance prior reconstruction with transformer and texture replenishment with CNN. The former transformer recovers pluralistic coherent structures together with some coarse textures, while the latter CNN enhances the local texture details of coarse priors guided by the high-resolution masked images. To decode diversified outputs from transformers, auto-regressive sampling is the most common method, but with extremely low efficiency. We further overcome this issue by proposing a new decoding strategy, temperature annealing probabilistic sampling (TAPS), which firstly achieves more than 70× speedup of inference at most, meanwhile maintaining the high quality and diversity of the sampled global structures. Moreover, we find the full CNN architecture will lead to suboptimal solutions for guided upsampling. To render more realistic and coherent contents, we design a novel module, named texture-aware guided attention, to concurrently consider the procedures of texture copy and generation, meanwhile raising several important modifications to solve the boundary artifacts. Through dense experiments, we found the proposed method vastly outperforms state-of-the-art methods in terms of four aspects: 1) large performance boost on image fidelity even compared to deterministic completion methods; 2) better diversity and higher fidelity for pluralistic completion; 3) exceptional generalization ability on large masks and generic dataset, like ImageNet. 4) Much higher decoding efficiency over previous auto-regressive based methods.

Integrated model and automatically designed solver for power system restoration

Power system restoration strategies schedule the power plants to re-energize the power network and loads after a blackout. These strategies are of great significance to ensure a resilient power system. Most power system restoration models consider either certain restoration stage(s) or all stages, with each or some of the stages managed independently. They destroy the essential characteristics of the interaction among the restoration stages and lead to sub-optimal solutions. To address this issue, in this paper, we first propose an improved integrated power system restoration (IPSR) model covering the entire restoration process without decoupling and sectionalization. We then develop both mathematical and metaheuristic solvers for the proposed model. In particular, we introduce the automated solver design paradigm to the highly non-linear constrained restoration problem-solving. By the paradigm, we automatically design the metaheuristic solver that gains enhanced performance beyond handcrafted solvers without algorithmic expertise. It is suggested that the automatically designed metaheuristic solver is a promising new option in variable and complicated power system operation scenarios without algorithmic expertise. Finally, a comprehensive case study demonstrates the proposed model’s significance and the proposed solver’s efficiency. Numerical tests show that the proposed IPSR model and solver obtained over 20% lower restoration time than current restoration methods, demonstrating IPSR’s and the proposed solver’s efficiency and effectiveness.

Topology-informed Derivative-Free Metaheuristic Optimization Method

In this study, we propose a novel topology-informed search strategy for derivative-free metaheuristic optimization, enhancing both Simulated Annealing (SA) and Particle Swarm Optimization (PSO) through Topology Data Analysis (TDA). The proposed methods utilize persistence diagram and Gaussian kernel density estimation to guide search processes effectively. For SA, TDA evaluates neighboring points to generate persistence diagrams, guiding the search towards regions with significant topological features. This approach balances exploration and exploitation, reducing the risk of converging to suboptimal solutions. In PSO, dynamic adjustment of social and cognitive coefficients based on feature density in persistence diagrams ensures robust convergence. This strategy guides particles toward the best positions, promoting early exploration and later convergence. Lastly, nine continuous non-linear numerical problems and a cost optimization problem in pharmaceutical manufacturing illustrate the feasibility of the proposed methods. The study highlights the potential of TDA-informed metaheuristic strategies to improve derivative-free optimization methods, offering an advancement in navigating complex optimization landscapes.

Optimal Design of Rectangular Tank Walls With Ribs Using Numerical Models and Global Optimization

This paper addresses the optimization of the cross-section in rectangular above-ground tank walls, incorporating vertical ribs and an optional top ring. The objective is to minimize the volume of concrete used, while maintaining key performance criteria such as keeping the maximum tensile stress below the material’s allowable limit and minimizing deflections. The analysis is performed using the finite element method (FEM), with the optimization handled through a local gradient-based algorithm (trust region method), supported by a multistart technique to navigate the complexity of the design space and avoid suboptimal solutions. The results demonstrate that this approach effectively reduces concrete consumption without exceeding the tensile stress limits or causing excessive deflection, offering more efficient and cost-effective designs for rectangular tanks used in water storage applications. This method provides valuable insights into the balance between material usage and performance constraints, contributing to sustainable engineering practices.

Machine fault detection model based on MWOA-BiLSTM algorithm.

This paper proposes the Modulated Whale Optimization Algorithm(MWOA), an innovative metaheuristic algorithm derived from the classic WOA and tailored for bionics-inspired optimization. MWOA tackles common optimization problems like local optima and premature convergence using two key methods: shrinking encircling and spiral position updates. In essence, it prevents algorithms from settling for suboptimal solutions too soon, encouraging exploration of a broader solution space before converging, by incorporating cauchy variation and a perturbation term, MWOA achieve optimization over a wide search space. After that, comparisons were conducted between MWOA and seven recently proposed metaheuristics, utilizing the CEC2005 benchmark functions to assess MWOA's optimization performance. Moreover, the Wilcoxon rank sum test is used to verify the effectiveness of the proposed algorithm. Eventually, MWOA was juxtaposed with the BiLSTM classifier and six other meta-heuristics combined with the BiLSTM classifier. The aim was to affirm that MWOA-BiLSTM outperforms its counterparts, showcasing superior performance across crucial metrics such as accuracy, precision, recall, and F1-Score. The study results unequivocally demonstrate that MWOA showcases exceptional optimization capabilities, adeptly striking a harmonious balance between exploration and exploitation.

Automating TODO-missed Methods Detection and Patching

TODO comments are widely used by developers to remind themselves or others about incomplete tasks. In other words, TODO comments are usually associated with temporary or suboptimal solutions. In practice, all the equivalent suboptimal implementations should be updated (e.g., adding TODOs) simultaneously. However, due to various reasons (e.g., time constraints or carelessness), developers may forget or even are unaware of adding TODO comments to all necessary places, which results in the TODO-missed methods . These “hidden” suboptimal implementations in TODO-missed methods may hurt the software quality and maintainability in the long-term. Therefore, in this paper, we propose the novel task of TODO-missed methods detection and patching, and develop a novel model, namely TDPatcher ( T O D O-comment Patcher ), to automatically patch TODO comments to the TODO-missed methods in software projects. Our model has two main stages: offline learning and online inference. During the offline learning stage, TDPatcher employs the GraphCodeBERT and contrastive learning for encoding the TODO comment (natural language) and its suboptimal implementation (code fragment) into vector representations. For the online inference stage, we can identify the TODO-missed methods and further determine their patching position by leveraging the offline trained model. We built our dataset by collecting TODO-introduced methods from the top-10,000 Python GitHub repositories and evaluated TDPatcher on them. Extensive experimental results show the promising performance of our model over a set of benchmarks. We further conduct an in-the-wild evaluation which successfully detects 26 TODO-missed methods from 50 GitHub repositories.

Research on online optimization scheme and deployment of PMSM control parameters based on honey badger algorithm

Permanent magnet synchronous motor (PMSM) drive systems are receiving increasing attention due to their superior control quality and efficiency. Optimizing the control parameters are key to achieve the high-performance operation of PMSMs. Although heuristic algorithms demonstrate excellent optimization outcomes in simulations, there are still challenges in deploying optimization schemes in practical drives. In this study, a real-time online deployable control parameter optimization scheme is proposed. The optimization effect is evaluated through the system step response performance, and a framework for deploying optimization algorithms within the driver is developed. A fault suppression mechanism is also designed to mitigate overshoot and vibration issues caused by suboptimal solutions. The proposed scheme is validated on a rapid prototyping control platform. Experimental results confirm that the scheme exhibits good optimization performances across various operating conditions. The honey badger algorithm employed in this paper shows faster convergence and more stable optimization effects than other optimization algorithms. The optimization effect is improved by 2.2% and its performance in terms of consistency across multiple optimization results has increased by 40%.

Decoherence time control by interconnection for finite-level quantum memory systems

This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson-Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems.

Differential evolution with multi-strategies for UAV trajectory planning and point cloud registration

The present study introduces a novel adaptive algorithm, MELSHADE-cnEpSin, which aims to enhance the performance of LSHADE-cnEpSin, which is not only stands out as one of the most competitive versions of differential evolution but also holds the distinction of being one of the CEC winner algorithms. Compared to the original methodology, four main distinctions are presented. To begin with, we adopt an adaptive selection mechanism (ASM) of crossover rate Cr value based on the external archive to rechoose a suitable value. In the next place, a nonlinear population reduction strategy using Sigmoid function is employed to improve population distribution. Additionally, a restart strategy is implemented to mitigate the risk of algorithmic convergence towards suboptimal solutions. Furthermore, the performance of MELSHADE-cnEpSin was evaluated using standard CEC2017 and CEC2022 test suites in conjunction with nine CEC-winning algorithms (L-SHADE, EBOwithCMAR, AGSK, LSHADE-SPACMA, LSHADE-cnEpSin, ELSHADE-SPACMA, EA4eig, MadDE and APGSK-IMODE) as well as two novel algorithms (ACD-DE and MIDE). Furthermore, MELSHADE-cnEpSin was effectively employed to address the challenge of UAV trajectory planning in intricate mountainous terrain and underwent simulation with point cloud registration cases utilizing a rapid global registration dataset, thereby showcasing the potential of MELSHADE-cnEpSin in tackling real-world optimization problems.

Effect of microbial interactions on performance of community metabolic modeling algorithms: flux balance analysis (FBA), community FBA (cFBA) and SteadyCom.

To explore the impact of microbial interactions on outcomes from three prevalent algorithms (Flux Balance Analysis (FBA), community FBA (cFBA), and SteadyCom) analyzing microbial community metabolic networks, five toy community models representing common microbial interactions were designed. These include commensalism, mutualism, competition, mutualism-competition, and commensalism-competition. Various scenarios, considering different biomass yields and substrate constraints, were examined for each type. In commensal communities, all algorithms consistently produced similar results. However, changes in biomass yields and substrate constraints led to variable abundances (0.33-0.8) and community growth rates (2-5 1/h) within a broad range. For competitive communities, all algorithms predicted growth of fastest-growing member. To comply with the natural coexistence of members, suboptimal solutions over optimal point are recommended. FBA faced challenges in modeling mutualism, consistently predicting growth of only one member. Although cFBA and SteadyCom resulted in a lower community growth rate, coexistence of both members were satisfied. In toy models with dual interactions, more realistic outcomes were achieved contrary to purely competitive model as the dependency fosters the coexistence which was missing in the competitive only scenarios. These findings emphasize the importance of algorithm choice based on specific microbial interaction types for reliable community behavior predictions.​.

A joint resource allocation strategy in a radar-communication coexistence network for target tracking and user serving

With the rapid development of commercial communications, the research on Radar-Communication Coexistence (RCC) systems is becoming a hot spot. The resource allocation techniques play a crucial role in the RCC systems. A performance-driven Joint Radar-target and Communication-user Assignment, along with Power and Subchannel Allocation (JRCAPSA) strategy, is proposed for an RCC network. The optimization model aims to minimize the sum of weighted Bayesian Cramér-Rao Lower Bounds (BCRLBs) of target state estimates for radar purpose. This is subject to constraints such as the Communication Data Rate (CDR) for communication purpose, the total power budget in each RCC system, assignment relationships, and the number of available subchannels. Considering that such a problem falls into the realm of Mixed Integer Programming (MIP), a Three-stage Iteratively Augment-based Optimization Method (TIAOM) is developed. The Communication-User Assignment (CUA), Communication Subchannel Allocation (SCA), and Radar-Target Assignment (RTA) feasible solution domains are iteratively expanded based on their importance, leading to the efficient acquisition of a suboptimal solution. Simulation results show the outperformance of the proposed JRCAPSA strategy, compared to the other benchmarks and the OPTI toolbox. The results also imply that the Bayesian Cramér-Rao Lower Bound (BCRLB) is a more stringent optimization metric for the achieved Mean Square Error (MSE), compared to Mutual Information (MI) and Signal-to-Interference-Noise Ratio (SINR).

Joint jammer selection and power optimization in covert communications against a warden with uncertain locations

In covert communications, joint jammer selection and power optimization are important to improve performance. However, existing schemes usually assume a warden with a known location and perfect channel state information (CSI), which is difficult to achieve in practice. To be more practical, it is important to investigate covert communications against a warden with uncertain locations and imperfect CSI, which makes it difficult for legitimate transceivers to estimate the detection probability of the warden. First, the uncertainty caused by the unknown warden location must be removed, and the optimal detection position (OPTDP) of the warden is derived which can provide the best detection performance (i.e., the worst case for a covert communication). Then, to further avoid the impractical assumption of perfect CSI, the covert throughput is maximized using only the channel distribution information. Given this OPTDP based worst case for covert communications, the jammer selection, the jamming power, the transmission power, and the transmission rate are jointly optimized to maximize the covert throughput (OPTDP-JP). To solve this coupling problem, a heuristic algorithm based on maximum distance ratio (H-MAXDR) is proposed to provide a sub-optimal solution. First, according to the analysis of the covert throughput, the node with the maximum distance ratio (i.e., the ratio of the distances from the jammer to the receiver and that to the warden) is selected as the friendly jammer (MAXDR). Then, the optimal transmission and jamming power can be derived, followed by the optimal transmission rate obtained via the bisection method. In numerical and simulation results, it is shown that although the location of the warden is unknown, by assuming the OPTDP of the warden, the proposed OPTDP-JP can always satisfy the covertness constraint. In addition, with an uncertain warden and imperfect CSI, the covert throughput provided by OPTDP-JP is 80% higher than the existing schemes when the covertness constraint is 0.9, showing the effectiveness of OPTDP-JP.

Phylogenetic tree instability after taxon addition: empirical frequency, predictability, and consequences for online inference.

Online phylogenetic inference methods add sequentially arriving sequences to an inferred phylogeny without the need to recompute the entire tree from scratch. Some online method implementations exist already, but there remains concern that additional sequences may change the topological relationship among the original set of taxa. We call such a change in tree topology a lack of stability for the inferred tree. In this paper, we analyze the stability of single taxon addition in a Maximum Likelihood framework across 1, 000 empirical datasets. We find that instability occurs in almost 90% of our examples, although observed topological differences do not always reach significance under the AU-test. Changes in tree topology after addition of a taxon rarely occur close to its attachment location, and are more frequently observed in more distant tree locations carrying low bootstrap support. To investigate whether instability is predictable, we hypothesize sources of instability and design summary statistics addressing these hypotheses. Using these summary statistics as input features for machine learning under random forests, we are able to predict instability and can identify the most influential features. In summary, it does not appear that a strict insertion-only online inference method will deliver globally optimal trees, although relaxing insertion strictness by allowing for a small number of final tree rearrangements or accepting slightly suboptimal solutions appears feasible.

Optimal scheduling strategy of household electrical equipment based on scenario dynamic modeling

Household electricity is highly unpredictable, necessitating a deep understanding of its impact on energy scheduling for optimal resource allocation and economic gains. This issue’s complexity can lead traditional optimization methods to converge on suboptimal solutions. In this study, the dynamic Copula (DC) model is used to construct the dynamic correlation between power consumption characteristics, and the Monte Carlo (MC) method is used to generate multiple power consumption scenarios to cope with the uncertainty of user behavior. Then, the optimal scenario set is selected through the average distribution error (ADE) to participate in the subsequent scheduling. In addition, based on the established equipment operation characteristic model, the electricity cost and load peak-to-average ratio (PAR) are comprehensively considered. The Improved Dynamic search multi-objective particle swarm optimization (IDSMOPSO) is introduced to optimize the running time of the equipment. Taking the electricity consumption of a family in Xi’an as an example, the results show that the algorithm is significantly better than the other two improved algorithms in performance. Meanwhile, the electricity cost of the family was significantly reduced by 17.09 %, and the PAR value was also reduced by 31.59 %, which realized the economic operation of household electricity.