Stochastic Optimization Research Articles

Distributed Broadcast Control of Multi-Agent Systems Using Hierarchical Coordination.

Broadcast control (BC) is a bio-inspired coordination technique for a swarm of agents in which a single coordinator broadcasts an identical scalar signal to all performing agents without discrimination, and the agents make appropriate moves towards the agents' collective optimal state without communicating with one another. The BC technique aims to accomplish a globally assigned task for which BC utilizes a stochastic optimization algorithm to coordinate a group of agents. However, the challenge intensifies as the system becomes larger: it requires a larger number of agents, which protracts the converging time for a single coordinator-based BC model. This paper proposes a revamped version of BC model, which assimilates distributed multiple coordinators to control a larger multi-agent system efficiently in a pragmatic manner. Precisely, in this hierarchical BC scheme, the distributed multiple sub-coordinators broadcast the identical feedback signal to the agents, which they receive from the global coordinator to accomplish the coverage control task of the ordinary agents. The dual role of sub-coordinators is manipulated by introducing weighted averaging of the gradient estimation under the stochastic optimization mechanism. The potency of the proposed model is analyzed with numerical simulation for a coverage control task, and various performance aspects are compared with the typical BC schemes to demonstrate its practicability and performance improvement. Particularly, the proposed scheme shows the same convergence with about 30% less traveling costs, and the near convergence is reached by only about one-third of iteration steps compared to the typical BC.

Optimal methods for convex nested stochastic composite optimization

Optimal methods for convex nested stochastic composite optimization

Stochastic Optimization of Distribution Networks: Application of Probabilistic Graphical Models in Electrical Grid Management

In electricity grid management, optimizing distribution networks is a must for making sure that the grid is reliable, efficient, and resilient. Stochastic optimization methods have become very useful for dealing with the unknowns that come up in grid operations because of things like adding green energy, changing demand, and broken equipment. We present a new way to improve distribution networks when there is doubt in this study. It uses probabilistic graphical models (PGMs). Using PGMs lets us describe the complicated connections between loads, producers, and grid infrastructure, as well as the relationships between these parts of the distribution network. By recording these relationships, we can accurately show how unclear the grid is and make smart choices to make it work better. In particular, we use Bayesian networks (BNs) and Markov random fields (MRFs) to describe how the different factors in the network are likely to be related to each other. We show how well our method works by using it on a real-life delivery network problem. We look at a case study of a distribution network that has a lot of green energy sources and changing load levels. We use PGMs to build a statistical model of the distribution network by combining past data, weather forecasts, and real-time measures. Then, we create a stochastic optimization problem to find the best way to reduce the predicted operational cost while still meeting different operational restrictions, like voltage limits, power balance, and equipment limitations. We use advanced optimization algorithms, like stochastic gradient descent and genetic algorithms, to quickly solve the optimization problem that was given. We show that our method works and can be scaled up for handling distribution networks when there is doubt by doing a lot of computer tests and risk analyses. The suggested method can make delivery networks much more reliable, cost-effective, and resilient than traditional linear optimization methods, as shown by our results. Overall, this study shows that probabilistic graphical models can be a very useful tool for managing the electricity grid and finding the best ways to use distribution networks in the face of randomness. Including unknowns in the modeling process helps we make stronger and more dependable choices that will help current distribution systems work well.

Precision Mars Entry Navigation with Atmospheric Density Adaptation via Neural Networks

Spacecraft entering Mars require precise navigation algorithms capable of accurately estimating the vehicle’s position and velocity in dynamic and uncertain atmospheric environments. Discrepancies between the true Martian atmospheric density and the onboard density model can significantly impair the navigation performance. This work introduces a new approach to online filtering for Martian entry using a neural network to estimate atmospheric density and employing a “consider” analysis to account for the uncertainty in the estimate. The network is trained on an exponential atmospheric density model, and its parameters are dynamically adapted in real time to account for any mismatch between the true and estimated densities. The adaptation of the network is formulated as a maximum likelihood problem by leveraging the measurement innovations of the filter to identify optimal network parameters. Within the context of the maximum likelihood approach, incorporating a neural network enables the use of stochastic optimizers known for their efficiency in the machine learning domain. Performance comparisons are conducted against two online adaptive approaches, covariance matching and state augmentation and correction, in various realistic Martian entry navigation scenarios. The results show superior estimation accuracy compared to other approaches and precise alignment of the estimated density with a broad selection of realistic Martian atmospheres sampled from perturbed Mars Global Reference Atmospheric Model data.

Estimation of P(X < Y) Stress–Strength Reliability Measures for a Class of Asymmetric Distributions: The Case of Three-Parameter p-Max Stable Laws

Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, we derive stress–strength reliability formulas of the type P(X<Y) when both X and Y follow p-max stable laws with three parameters, which are inherently asymmetric. The new relations are given in terms of extreme-value H-functions and have been obtained under fewer parameter restrictions when compared to similar results in the literature. We estimate the parameters of the p-max stable laws by a stochastic optimization method and the stress–strength probability by a maximum likelihood procedure. The performance of the analytical models is evaluated through simulations and real-life dataset modeling.

Algorithm-Dependent Generalization of AUPRC Optimization: Theory and Algorithm.

Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Despite extensive studies on AUPRC optimization, generalization is still an open problem. In this work, we present the first trial in the algorithm-dependent generalization of stochastic AUPRC optimization. The obstacles to our destination are three-fold. First, according to the consistency analysis, the majority of existing stochastic estimators are biased with biased sampling strategies. To address this issue, we propose a stochastic estimator with sampling-rate-invariant consistency and reduce the consistency error by estimating the full-batch scores with score memory. Second, standard techniques for algorithm-dependent generalization analysis cannot be directly applied to listwise losses. To fill this gap, we extend the model stability from instance-wise losses to listwise losses. Third, AUPRC optimization involves a compositional optimization problem, which brings complicated computations. In this work, we propose to reduce the computational complexity by matrix spectral decomposition. Based on these techniques, we derive the first algorithm-dependent generalization bound for AUPRC optimization. Motivated by theoretical results, we propose a generalization-induced learning framework, which improves the AUPRC generalization by equivalently increasing the batch size and the number of valid training examples. Practically, experiments on image retrieval and long-tailed classification speak to the effectiveness and soundness of our framework.

Deep Tensor Spectral Clustering Network via Ensemble of Multiple Affinity Tensors.

Tensor spectral clustering (TSC) is an emerging approach that explores multi-wise similarities to boost learning. However, two key challenges have yet to be well addressed in the existing TSC methods: (1) The construction and storage of high-order affinity tensors to encode the multi-wise similarities are memory-intensive and hampers their applicability, and (2) they mostly employ a two-stage approach that integrates multiple affinity tensors of different orders to learn a consensus tensor spectral embedding, thus often leading to a suboptimal clustering result. To this end, this paper proposes a tensor spectral clustering network (TSC-Net) to achieve one-stage learning of a consensus tensor spectral embedding, while reducing the memory cost. TSC-Net employs a deep neural network that learns to map the input samples to the consensus tensor spectral embedding, guided by a TSC objective with multiple affinity tensors. It uses stochastic optimization to calculate a small part of the affinity tensors, thereby avoiding loading the whole affinity tensors for computation, thus significantly reducing the memory cost. Through using an ensemble of multiple affinity tensors, the TSC can dramatically improve clustering performance. Empirical studies on benchmark datasets demonstrate that TSC-Net outperforms the recent baseline methods.

Combining Conjugate Gradient and Momentum for Unconstrained Stochastic Optimization With Applications to Machine Learning

Combining Conjugate Gradient and Momentum for Unconstrained Stochastic Optimization With Applications to Machine Learning

Focus and Shake Algorithm: A New Stochastic Optimization Employing Strict and Randomized Dimension Mappings

Focus and Shake Algorithm: A New Stochastic Optimization Employing Strict and Randomized Dimension Mappings

A forecast-driven stochastic optimization method for proactive activation of manual reserves

Reducing operating balancing costs is paramount for an affordable transition towards renewable-dominated power systems. In European balancing markets, operating balancing costs are driven by the activation of automatic and manual frequency restoration reserves, respectively aFRR and mFRR. An inadequate combination of both products for resolving grid imbalances may result in economic inefficiencies where, e.g., saturated aFRR can lead to balancing price spikes. To avoid such situation, we propose a proactive activation policy of manual reserves, aiming at an optimal trade-off between aFRR and mFRR products via a stochastic optimization method. The tool is fed with 1-min time trajectories of system imbalances covering the next quarter hour. The one minute temporal granularity allows modeling the ramping phenomena of mFRR products, while keeping track of the faster activation of aFRR products. The proposed balancing energy activation methodology is tested on Belgian market data, which currently adopts a reactive balancing strategy. Ex-post comparisons of the proposed balancing strategy with a reactive one show that our methodology allows a decrease of the balancing activation costs. This is expected as early activation of mFRR, when appropriately provided, allows avoiding the activation of extremely high aFRR bids.

Advanced OCTA imaging segmentation: Unsupervised, non-linear retinal vessel detection using modified self-organizing maps and joint MGRF modeling

Background and Objective:This paper proposes a fully automated and unsupervised stochastic segmentation approach using two-level joint Markov-Gibbs Random Field (MGRF) to detect the vascular system from retinal Optical Coherence Tomography Angiography (OCTA) images, which is a critical step in developing Computer-Aided Diagnosis (CAD) systems for detecting retinal diseases. Methods:Using a new probabilistic model based on a Linear Combination of Discrete Gaussian (LCDG), the first level models the appearance of OCTA images and their spatially smoothed images. The parameters of the LCDG model are estimated using a modified Expectation Maximization (EM) algorithm. The second level models the maps of OCTA images, including the vascular system and other retina tissues, using MGRF with analytically estimated parameters from the input images. The proposed segmentation approach employs modified self-organizing maps as a MAP-based optimizer maximizing the joint likelihood and handles the Joint MGRF model in a new, unsupervised way. This approach deviates from traditional stochastic optimization approaches and leverages non-linear optimization to achieve more accurate segmentation results. Results:The proposed segmentation framework is evaluated quantitatively on a dataset of 204 subjects. Achieving 0.92 ± 0.03 Dice similarity coefficient, 0.69 ± 0.25 95-percentile bidirectional Hausdorff distance, and 0.93 ± 0.03 accuracy, confirms the superior performance of the proposed approach. Conclusions:The conclusions drawn from the study highlight the superior performance of the proposed unsupervised and fully automated segmentation approach in detecting the vascular system from OCTA images. This approach not only deviates from traditional methods but also achieves more accurate segmentation results, demonstrating its potential in aiding the development of CAD systems for detecting retinal diseases.

Solving the Online On-Demand Warehousing Problem

In On-Demand Warehousing, an online platform acts as a central mechanism to match unused storage space and related services offered by suppliers to customers. Storage requests can be for small capacities and very short commitment periods if compared to traditional leasing models. The objective of the On-Demand Warehousing Problem (ODWP) is to maximize the number of successful transactions among the collected offers and requests, considering the satisfaction of both the supply and demand side to preserve future participation to the platform. The Online ODWP can be modeled as a stochastic reservation and assignment problem, where dynamically arriving requests of customers must be rapidly assigned to suppliers. Firstly, an online stochastic combinatorial optimization framework is adapted to the Online ODWP. The key idea of this approach is to generate samples of future requests by evaluating possible allocations for the current request against these samples. In addition, expectation, consensus, and regret, and two greedy algorithms are implemented. All solution methods are compared on a dataset of realistic instances of different sizes and features, demonstrating their effectiveness compared to the oracle solutions, which are based on the assumption of perfect information about future request arrivals. A newly proposed approach of risk approximation is shown to outperform alternative algorithms on large instances. Managerial insights regarding acceptance and rejection strategies for the platform are derived. It is shown how requests with large demand, long time frame, not very long spanning time, and average compatibility degree, are very likely to be rejected in the optimal solution.

Stochastic Optimization for Long-Term Planning of a Mining Complex with In-Pit Crushing and Conveying Systems

Semi-mobile in-pit crushing and conveying (IPCC) systems can help reduce truck haulage in open-pit mines by bringing the crusher closer to the excavation areas. Optimizing a production schedule with semi-mobile IPCC requires integrating extraction sequence, destination policy, crusher relocation, conveyor layout, and truck fleet investment decisions. A mining complex with multiple mines and IPCC systems should be optimized simultaneously to find an optimal schedule for the entire value chain. An integrated stochastic optimization framework is proposed to produce long-term production schedules for mining complexes using multiple semi-mobile IPCC systems. The optimization model has flexibility to select the crusher locations and conveyor routes from anywhere inside the pits. The framework uses simulated orebody realizations to consider multi-element grade uncertainty and manage associated risk. A hybrid metaheuristic solution approach based on simulated annealing and evolutionary algorithms is implemented. The method is demonstrated using an iron ore mining complex.

Short-term stochastic multi-objective optimization scheduling of wind-solar-hydro hybrid system considering source-load uncertainties

Uncertainties in energy outputs (source side) and load side are simultaneously present and cannot be ignored in the actual operation of multi-energy systems. Adopting a reasonable uncertainty modeling method and understanding the impact of source-load uncertainties on optimization scheduling are key to formulating accurate and effective multi-energy scheduling plans. To address the uncertainties on both the source side and the load side in wind-solar-hydro hybrid systems, this paper proposes a multi-objective optimization scheduling model based on stochastic programming theory. The model aims to maximize the net profit of the system's power generation and minimize the fluctuation of the remaining load. It employs Vine-Copula coupled with Monte Carlo simulation and the deep learning method TimeGAN to generate joint wind and solar power output and load scenario sets. The generated source-load uncertainty scenarios are then reduced to representative scenarios using the K-Means clustering method, which are used as inputs for the scheduling model. The proposed model is applied to a wind-solar-hydro energy base in China, and the results show that: 1) The Vine-Copula-based source-side scenario generation method can quantitatively consider the correlations among meteorological factors. The relative errors of the generated scenarios' statistics compared to the original data are all less than 5%, and the relative errors of the correlation coefficients are less than 10%. 2) The TimeGAN-based load-side scenario generation method avoids the presupposition of the load probability distribution. Compared to the original data, the generated scenarios have R2 and Pearson correlation coefficients of 0.77 and 0.87, respectively. Additionally, TimeGAN shows significant advantages over traditional random sampling methods in simulating extreme scenarios. 3) Both source-side and load-side uncertainties significantly impact the optimization scheduling results of multi-energy systems, leading to increased fluctuation of the remaining load and decreased net profit. 4) The combined source-load uncertainties have a synergistic negative impact on the multi-objective optimization scheduling results. 5) The Pareto front of the optimization results is a concave function with low marginal benefits. Decision-makers should adopt a compromise solution as a guide for the operation of multi-energy systems.

Flexibility modeling for parking lots with multiple EV charging stations

The paper proposes an aggregated model that represents the flexibility potential of car parks equipped with multiple electric vehicle (EV) charging stations. The model is used in a stochastic optimization procedure to estimate in advance the maximum flexibility margins of the parking lot. The EV aggregator responsible for the charging stations offers intra-day ancillary services to the grid by specifying the possible margins within which the absorbed power can be varied, either up or down. These adjustments are made at the request of the distribution system operator, ensuring an appropriate level of EV charging. The effectiveness of the model is evaluated for parking lots with different numbers of charging stations and different daily profile forecasts of the number of EV arrivals and departures.

Optimal day-ahead offering strategy for large producers based on market price response learning

In day-ahead electricity markets based on uniform marginal pricing, small variations in the offering and bidding curves may substantially modify the resulting market outcomes. In this work, we deal with the problem of finding the optimal offering curve for a risk-averse profit-maximizing generating company (GENCO) in a data-driven context. In particular, a large GENCO’s market share may imply that its offering strategy can alter the marginal price formation, which can be used to increase profit. We tackle this problem from a novel perspective. First, we propose an optimization-based methodology to summarize each GENCO’s step-wise supply curves into a subset of representative price-energy blocks. Then, the relationship between the resulting market price and the energy block offering prices is modeled through a probabilistic forecasting tool: a Distributional Neural Network, which also allows us to generate stochastic scenarios for the sensibility of the market towards the GENCO strategy via a set of linear constraints. Finally, this predictive model is embedded in the stochastic optimization model employing a constraint learning approach. Results show how allowing the GENCO to deviate from its true marginal costs renders significant changes in its profits and the marginal price of the market. Additionally, these results have also been tested in an out-of-sample validation setting, showing how this optimal offering strategy can effective in a real-world market context.

Deterministic Multi-Objective Optimization of Analog Circuits

Stochastic optimization approaches benefit from random variance to produce a solution in a reasonable time frame that is good enough for solving the problem. Compared with them, deterministic optimization methods feature faster convergence rates and better reproducibility but may get stuck at a local optimum that is insufficient to solve the problem. In this paper, we propose a group-based deterministic optimization method, which can efficiently achieve comparable performance to heuristic optimization algorithms, such as particle swarm optimization. Moreover, the weighted sum method (WSM) is employed to further improve our deterministic optimization method to be multi-objective optimization, making it able to seek a balance among multiple conflicting circuit performance metrics. With a case study of three common analog circuits tested for our optimization methodology, the experimental results demonstrate that our proposed method can more efficiently reach a better estimation of the Pareto front compared to NSGA-II, a well-known multi-objective optimization approach.

Distributed optimal scheduling for virtual power plant with high penetration of renewable energy

The virtual power plants are aggregations of distributed generators, grid-connected devices in user side. The operation of virtual power plants affects the economic benefits and environmental benefits. However, due to the stochastic and fluctuating nature of power generation from renewable energy sources, the optimal scheduling problem for the virtual power plant containing high-dimensional random variables is difficult to solve. The conic power flow constraints are considered in the virtual power plant day-ahead optimal scheduling models to maximize the revenue by virtue of optimizing the flexible resources such as energy storage system and interruptible load. To quantify the uncertainties in the optimization problem, this paper proposes a network state-based power scenario reduction strategy for renewable energy generation, where typical scenarios are selected by the state of the grid voltage. The proposed day-ahead scheduling model is a mixed-integer, nonlinear, large-scale, stochastic optimization problem with high dimensional random variables, which is difficult to be solved directly by traditional centralized method. By temporally decoupling the charging and discharging model of energy storage systems, a distributed optimization algorithm is proposed based on multi-temporal power flow decoupling optimization model. The simulation results show that the proposed distributed optimization algorithm has high accuracy and good convergence, the virtual power plant can achieve day-ahead optimal scheduling and effectively promote renewable energy accommodation under the security and reliability of the grid.

Prescriptive analytics for low and high water management in German waterways

Abstract The real-time management of multi-purpose storage reservoirs aims at an efficient operation of existing hydraulic infrastructure. This management process can be structured as a prescriptive analytics setup that considers both current and predicted system states to recommend actions and outline potential implications. In application to a reservoir and river system, it combines hydrological modelling components for the system schematization, observations and data assimilation for the identification of the current system state, meteorological and hydrological predictions as well as optimization-based techniques to support decision-making regarding reservoir operations. In this paper, we present the application of such a framework to the short-term management of the Eder and Diemel storage reservoirs. These reservoirs are operated by the German Federal Waterways and Shipping Administration (WSV) with the primary goal to support navigation in the River Weser during low flow periods. In addition, partially conflicting objectives such as flood protection, energy generation and recreation are considered. The implementation includes an explicit consideration of forecast uncertainty and its impact on the decision-making by using probabilistic forecasts in combination with a multi-stage stochastic optimization approach. We demonstrate the applicability of the approach based on low and high water use cases. Special attention is paid on the benefits of the probabilistic forecast in combination with the multi-stage stochastic optimization versus a deterministic setup. It provides an explicit translation of the forecast uncertainty in the decision variables, in this case the reservoir releases helping the operators to better anticipate the range of future release decisions. Furthermore, the stochastic approach is expected to provide more stable decisions in an operational setting, based on more stable forecasts by considering various possible realizations of the future instead of picking a single one, which gets random after 4–5 days.

Non-orthogonal multiple access-based MEC for energy-efficient task offloading in e-commerce systems

Mobile edge computing (MEC) reduces the latency for end users to access applications deployed at the edge by offloading tasks to the edge. With the popularity of e-commerce and the expansion of business scale, server load continues to increase, and energy efficiency issues gradually become more prominent. Computation offloading has received widespread attention as a technology that effectively reduces server load. However, how to improve energy efficiency while ensuring computing requirements is an important challenge facing computation offloading. To solve this problem, using non-orthogonal multiple access (NOMA) to increase the efficiency of multi-access wireless transmission, MEC supporting NOMA is investigated in the research. Computing resources will be divided into separate sub-computing that will be handled via e-commerce terminals or transferred to edge sides by reutilizing radio resources, we put forward a Group Switching Matching Algorithm Based on Resource Unit Allocation (GSM-RUA) algorithm that is multi-dimensional. To this end, we first formulate this task allocation problem as a long-term stochastic optimization problem, which we then convert to three short-term deterministic sub-programming problems using Lyapunov optimization, namely, radio resource allocation in a large timescale, computation resource allocating and splitting in a small-time frame. Of the 3 short-term deterministic sub-programming problems, the first sub-programming problem can be remodeled into a 1 to n matching problem, which can be solved using the block-shift-matching-based radio resource allocation method. The latter two sub-programming problems are then transformed into two continuous convex problems by relaxation and then solved easily. We then use simulations to prove that our GSM-RUA algorithm is superior to the state-of-the-art resource management algorithms in terms of energy consumption, efficiency and complexity for e-commerce scenarios.