Escape Local Minima Research Articles

Nonmonotone Spectral Analysis for Variational Inclusions

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.

Mitigating local minima in extracting optimal parameters for photovoltaic models: An optimizer leveraging multiple initial populations (OLMIP)

The accurate identification of parameters in photovoltaic models is of paramount importance to accurately predict the electrical behavior of photovoltaic systems and improve their performance. Nowadays, this task poses a multimodal optimization problem, aiming to find the best combination of parameters that fit the model to real data. This article presents a proposal for an Optimizer Leveraging Multiple Initial Populations (OLMIP) that aims to achieve optimal solutions while effectively avoiding undesirable local optima. By utilizing a separate evolution strategy involving four distinct initial populations, followed by the construction of an elite population, the algorithm can explore multiple regions of the search space and escape local minima. Experiments were conducted with four models: the single diode, double diode, triple diode from RTC France cell, and Photowatt-PWP201 module. The mean squared errors obtained are 9.860219E-04, 9.824849E-04, 9.824849E-04, and 2.425075 E−03, respectively. These results indicate that the algorithm achieves superior or comparable accuracy to that of six competitors. Furthermore, the statistical analysis of the results, including the Wilcoxon and Friedman tests, confirms the robustness and effectiveness of the approach used for parameter estimation in photovoltaic systems. These findings open up new prospects for the improvement and optimization of photovoltaic systems.

Safe Exploration and Escape Local Minima With Model Predictive Control Under Partially Unknown Constraints

Safe Exploration and Escape Local Minima With Model Predictive Control Under Partially Unknown Constraints

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

The Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

A Novel Adaptive Multi-Objective Particle Swarm Optimization Based on Decomposition and Dominance for Long-term Generation Scheduling of Cascade Hydropower System

Multi-objective long-term generation scheduling (MLGS) considering ecological flow demands is important for comprehensive utilization of water resources in cascade hydropower system (CHS). A novel adaptive multi-objective particle swarm optimization based on decomposition and dominance (D2AMOPSO) is developed in this paper to solve the MLGS problem. In D2AMOPSO, a constraint handling method based on repair strategy and individualconstraints and group constraints (ICGC) technique is embedded to address various constraints. An improved logistic map is adopted to initialize the population. During the evolutionary process, an improved Tchebycheff decomposition is introduced to select personal best and global best for each particle, and the non-dominated solutions found so far are stored in an external archive where crowding distance and elitist learning strategy are performed to improve its diversity. Meanwhile, an adaptive flight parameter adjustment mechanism based on Pareto entropy is adopted to balance the global exploration and local exploitation abilities of the population. A normal cloud mutation operator is used to keep the population diversity and escape local minima. In the case study of the Three Gorges Cascade hydropower system (TGC) under three typical years, the results of the proposed method and other four competitors show that D2AMOPSO can obtain better diversity and faster convergence solutions for the MLGS problem in less time.

Efficient discriminative clustering via QR decomposition-based Linear Discriminant Analysis

Discriminative Clustering (DC) can effectively cluster high dimension data sets. It performs in the iterative Linear Discriminant Analysis (LDA) dimensionality reduction and clustering process. However, most existing algorithms for DC have high computational complexity and are not feasible to apply in practical problems. In order to improve the efficiency of DC, we first present a variant of QR decomposition based LDA (LDA/QR) algorithm by making a minor modification to it. The proposed algorithm inherits the high efficiency of the initial LDA/QR, and has a better adaptability to data due to its ability of making full use of the discriminative information in data. We also present an objective function for the proposed variant of LDA/QR, and the proposed variant of LDA/QR can solve this objective function approximately. We then combine the proposed variant of LDA/QR and K-means (KM) into a single clustering algorithm, and obtain an efficient algorithm for DC: LDA/QR guided KM (LDA/QR-KM). Finally, in order to make LDA/QR-KM escape local minima, we adopt anomalous cluster based intelligent KM (IKM) to initialize it. Extensive experiments on a collection of benchmark data sets are presented to show the effectiveness and efficiency of the proposed LDA/QR-KM algorithm.

Optimization of cluster resource indexing of Internet of Things based on improved ant colony algorithm

In Internet of Things, the resource distribution is random in space, which leads to the poor precision ratio of the cluster resource indexing of Internet of Things, so in order to improve the information fusion and dispatching ability of Internet of Things, it is necessary to optimize the resource indexing of Internet of Things. Therefore, an algorithm for cluster resource indexing of Internet of Things based on improved ant colony algorithm is proposed in this paper. Directed graph models are used to construct a distribution structure model of cluster resource indexing nodes of Internet of Things, carry out semantic association feature extraction in the cluster resource storage information flow of Internet of Things. And the improved ant colony algorithm is used to crawl and capture cluster information in Internet of Things. According to the ant colony trajectory information, the velocity and position of the cluster resource indexing of Internet of Things are updated, and the balanced ant colony algorithm is used to carry out the global search and local search to resources and initialize the clustering center, and the target function of the cluster resource indexing of Internet of Things is constructed and the optimization parameter is solved with the constraint condition of the minimum variance of the whole fitness. The strong ability of global optimization of the ant colony algorithm is used to realize resource indexing optimization. Simulation results show that the improved algorithm can quickly realize resource index convergence, effectively escape local minimum points, and has strong global search ability and relatively high resource indexing precision ratio.

Complete Local Search: Boosting Hill-Climbing through Online Relaxation Refinement

Several known heuristic functions can capture the input at different levels of precision, and support relaxation-refinement operations guaranteeing to converge to exact information in a finite number of steps. A natural idea is to use such refinement online, during search, yet this has barely been addressed. We do so here for local search, where relaxation refinement is particularly appealing: escape local minima not by search, but by removing them from the search surface. Thanks to convergence, such an escape is always possible. We design a family of hill-climbing algorithms along these lines. We show that these are complete, even when using helpful actions pruning. Using them with the partial delete relaxation heuristic hCFF, the best-performing variant outclasses FF's enforced hill-climbing, outperforms FF, outperforms dual-queue greedy best-first search with hFF, and in 6 IPC domains outperforms both LAMA and Mercury.

A hybrid evaluation model for flight performance based on bacterial foraging and Elman network

The evaluation of the flight performance via multiple physiological signals is an important problem in the field of flight safety. A hybrid prediction model is proposed to dispose multiple physiological signals with high dimension in this paper. Main contribution of our model is that of a novel bacterial foraging algorithm (BF) to optimize Elman neural network, which can perform parallel search and escape local minimum easily, and provide better prediction accuracy of the flight performance. Other bio-inspired algorithms such as genetic algorithm (GA), particle swarm optimization (PSO) and chaotic GA are also used to optimize the unknown parameters of the Elman network. Experimental results indicate that the proposed hybrid model based on BF algorithm and Elman network is well suited for the evaluation and prediction of the flight performance. Compared with the other public algorithms, the BF can easily identify the unknown parameters of the established models and has better optimization capability.

Legendre polynomial modeling of time-varying delay applied to surface EMG signals—Derivation of the appropriate time-dependent CRBs

In surface electromyography (sEMG), the assessment of the muscle fiber conduction velocity (CV) can be performed by estimating the time delay between sEMG signals recorded by means of electrodes. During the dynamic contractions that often occur in daily life, the sEMG signals are not stationary which, induces time-varying delays (TVD). In the present study, the problem of TVD estimation is considered using a new parametric method. First, we propose a polynomial modeling of the TVD. The model is expressed on an orthonormal polynomial basis. Then, the TVD model parameters are estimated by using a maximum likelihood (ML) strategy solved by a stochastic optimization technique, called simulated annealing (SA).The orthogonality property allows parameter decoupling, which helps enhance the estimation accuracy. The SA algorithm helps escape local minima, thereby keeping the optimality property benefit of the ML estimator. We also derive two appropriate Cramer–Rao lower bounds (CRB) for the estimated TVD model parameters and for the TVD waveforms. Simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the mean square error (MSE) obtained is close to the derived CRBs. A comparison with nonparametric approaches of TVD estimation is also presented and shows the superiority of the method proposed.

UNIT COMMITMENT WITH SECURITY ASSESSMENT USING CHAOTIC PSO ALGORITHM

This paper proposes solving short-term unit commitment (UC) problems with security constraints by hybrid chaotic particle swarm optimization (CPSO). The objective of security-constrained UC (SC-UC) is to minimize the total generation cost, which is the sum of both transition cost and production cost of the scheduled combination units. The proposed CPSO method, which involves the chaotic map and the chaotic turbulence, can avoid premature convergence of PSO and escape local minima. Moreover, the proposed hybrid CPSO method has the ability of solving both the continuous and the discrete optimal programming problems. Two power systems are demonstrated for verifying the feasibility and effectiveness of the proposed method in solving SC-UC problems with constraints of a nonlinear generator and operation security assessment taken into consideration. The simulation results show that the proposed CPSO-based SC-UC method is indeed capable of obtaining efficiently high-quality UC solutions and enhancing the system security of UC operation.

Research on the Application of the Prediction of the Expressway Traffic Flow Based on the Neural Network with Genetic Algorithm

In order to improve the efficiency and accuracy of the prediction of expressway traffic flow, this paper, based on the characteristics of the data of the expressway traffic flow, focuses on an optimized method of prediction with the application of the neural network with genetic algorithm. Applying genetic algorithm, optimizing BP neural network structure and establishing a new mixed model, this algorithm speed up the slow convergence velocity of traditional BP neural network prediction and increases the possibility to escape local minima. This algorithm based on the optimized genetic neural network predicts the actual data of the expressway traffic flow, the result of which shows that the application of the optimized method of prediction with the genetic neural network algorithm is effective and that it improves the rate and the accuracy of the prediction of the expressway traffic flow.

Contingency‐Constrained Optimal Power Flow Using Simplex‐Based Chaotic‐PSO Algorithm

This paper proposes solving contingency‐constrained optimal power flow (CC‐OPF) by a simplex‐based chaotic particle swarm optimization (SCPSO). The associated objective of CC‐OPF with the considered valve‐point loading effects of generators is to minimize the total generation cost, to reduce transmission loss, and to improve the bus‐voltage profile under normal or postcontingent states. The proposed SCPSO method, which involves the chaotic map and the downhill simplex search, can avoid the premature convergence of PSO and escape local minima. The effectiveness of the proposed method is demonstrated in two power systems with contingency constraints and compared with other stochastic techniques in terms of solution quality and convergence rate. The experimental results show that the SCPSO‐based CC‐OPF method has suitable mutation schemes, thus showing robustness and effectiveness in solving contingency‐constrained OPF problems.

An efficient variable neighborhood search heuristic for very large scale vehicle routing problems

In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.

Neural network based on adaptive chaotic gradient descending optimization algorithm and its application in matte converting process

An adaptive chaotic gradient descending optimization algorithm for single objective optimization was presented. A local minimum judged by two rules was obtained by an improved mutative-step gradient descending method. A new optimal minimum was obtained to replace the local minimum by mutative-scale chaotic search algorithm whose scales are magnified gradually from a small scale in order to escape local minima. The global optimal value was attained by repeatedly iterating. At last, a BP (back-propagation) neural network model for forecasting slag output in matte converting was established. The algorithm was used to train the weights of the BP neural network model. The simulation results with a training data set of 400 samples show that the training process can be finished within 300 steps to obtain the global optimal value, and escape local minima effectively. An optimization system for operation parameters, which includes the forecasting model, is achieved, in which the output of converter increases by 6.0%, and the amount of the treated cool materials rises by 7.8% in the matte converting process.

Optimal System Frequency Control Using Pre-Defined System Parameters Selected Using Neural Network Techniques

The frequency of a power system provides an easy and direct method of precisely monitoring the balance between consumer load and generated demand. The control of the power generation throughout the network is a hierarchical process which requires the interaction between many layers of the command control with different amounts of interaction depending on the time scales. In many applications the speed and the accuracy of automatic digital control has replaced the much slower and less accurate manual control schemes. With the recent advent of small powerful computers, it has become possible to implement many layers of control automatically, with lime scales from several hours to a second. The automatic control activities start with a prediction of the consumer load at the central control centre and ends with closed loop controllers on the turbine generators themselves, this regulates the amount of energy supplied to the generators in response to variations in the desired and the actual values of frequency and output power. Such system frequency control is used by many utilities around the world. Many of these systems use fixed parameter control schemes which do not enable optimum control action to be undertaken under all system conditions, however, adaptive control techniques may be used to track the simevarying system and monitor the system operating point. This information may be used to provide optimum control for the turbine generators. An adaptive system frequency control scheme will use an updated system model to reduce the frequency and tie-line error to zero and such a controller may be used to minimise the variance of the system error at the future time interval. The minimum variance control scheme may be linked together with model estimation schemes to form a self-tuning regulator. However, instability problems with such controllers require extensive use of monitoring or jacketing software. The main disadvantages of such control schemes occurs when there is little information to be gained from the system under observation and the controller parameters may blow up if the system is not sufficiently exciting. To reduce the inherent problems of adaptive control schemes but to enable optimum control commands to be issued, this paper reviews the idea of matching well defined system parameters to differing system conditions. A neural network technique is used to categorize the particular system operating point and match this to the optimum control parameters. System frequency error profiles will be categorized into a number of typical profiles against which will be matched optimum system parameters. Following the recent resurgence of the non-algorithmic supervised learning, investigations were undertaken into possible applications of such techniques applied to optimal control techniques as described above. In this contribution wc will describe a learning scheme suited to the problem and implemented using a data base consisting of a set input patterns together with the corresponding targets. The objective of learning will be to extract relevant information from the data base for parameter tuning. We will also discuss the conceptual outline of a cross validation scheme by majority polling. This scheme will utilise an embedded expert system and a set of child networks generated fror.i a parent network by using genetic optimisation techniques, and trained on different subsets of the same data base. In such a scheme it will be possible to avoid noise generalisation and escape local minima. The proposed scheme will enable adaptive control techniques to function in real-time environment without the characteristic problems of an under-excited system, and/or corruption of the telemetered data, when standard optimum control systems must revert to predefined fixed parameters.