Probabilistic Optimization Research Articles

Corona virus optimization (CVO): a novel optimization algorithm inspired from the Corona virus pandemic

This research introduces a new probabilistic and meta-heuristic optimization approach inspired by the Corona virus pandemic. Corona is an infection that originates from an unknown animal virus, which is of three known types and COVID-19 has been rapidly spreading since late 2019. Based on the SIR model, the virus can easily transmit from one person to several, causing an epidemic over time. Considering the characteristics and behavior of this virus, the current paper presents an optimization algorithm called Corona virus optimization (CVO) which is feasible, effective, and applicable. A set of benchmark functions evaluates the performance of this algorithm for discrete and continuous problems by comparing the results with those of other well-known optimization algorithms. The CVO algorithm aims to find suitable solutions to application problems by solving several continuous mathematical functions as well as three continuous and discrete applications. Experimental results denote that the proposed optimization method has a credible, reasonable, and acceptable performance.

Dynamic Demand Prediction and Allocation in Cloud Service Brokerage

To maximize its own profit, cloud service brokerage (CSB) aims to distribute tenant demands to reserved servers such that the total reservation cost is minimized with the tenants’ service level agreement (SLA) being satisfied. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">demand allocation</i> problem for CSB is non-trivial to solve due to uncertainty of tenants’ behavior. To avoid possible violations among demands, existing schemes allocate additional padding resources on the predicted demands, which leads to under-utilization of reserved resources. Accordingly, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Probabilistic Demand Allocation</i> (PDA) system to address the demand allocation problem for CSB. In PDA, we not only predict tenants’ demands based on their historical records, but also estimate the probability distribution of prediction errors. As over- and under-estimation are equally likely to happen with our prediction method, when allocating demands to a single server, their errors are possibly offset. Hence, it is unnecessary to allocate additional resource to each demand for violation prevention. Given the predication results, we formulate the demand allocation problem by probabilistic optimization, of which the objective is to minimize the overall cost from reserved servers while satisfying tenants’ SLA with high probability. Both simulation and real-world experimental results demonstrate the superiority of PDA in reducing servers’ reservation cost.

Model Learning and Real-Time Tracking Using Multi-Resolution Surfel Maps

For interaction with its environment, a robot is required to learn models of objects and to perceive these models in the livestreams from its sensors. In this paper, we propose a novel approach to model learning and real-time tracking. We extract multi-resolution 3D shape and texture representations from RGB-D images at high frame-rates. An efficient variant of the iterative closest points algorithm allows for registering maps in real-time on a CPU. Our approach learns full-view models of objects in a probabilistic optimization framework in which we find the best alignment between multiple views. Finally, we track the pose of the camera with respect to the learned model by registering the current sensor view to the model. We evaluate our approach on RGB-D benchmarks and demonstrate its accuracy, efficiency, and robustness in model learning and tracking. We also report on the successful public demonstration of our approach in a mobile manipulation task.

An Optimized Positioning Algorithm Based on Improved Gaussian Filtering

WiFi offers simple, convenient, ubiquitous, and economic solutions for indoor positioning services, by matching a pre-established WiFi’s RSSI fingerprint database to a mobile terminal’s received RSSI values. A setback of this fingerprint matching method is its low precision, only miserably on order of meters, due to signal impairment by indoor complicated environment. To circumvent this, we revise the traditional weighted K-neighborhood algorithm by incorporating a Bayesian probability optimization. The proposed combination of Bayesian with weighted K-neighborhood algorithm improves the accuracy and reduces the average running time. Computer simulation shows that proposed Bayesian probabilistic optimization algorithm improves the positioning accuracy from 34% to 46%, with an average of about 14.86%, and the computation stability is also enhanced.

Prolonging Network Lifetime by Optimizing Actuators Deployment with Probabilistic Mutation Multi-layer Particle Swarm Optimization

Prolonging Network Lifetime by Optimizing Actuators Deployment with Probabilistic Mutation Multi-layer Particle Swarm Optimization

Comparison of Feature Selection Techniques for Power Amplifier Behavioral Modeling and Digital Predistortion Linearization.

The power amplifier (PA) is the most critical subsystem in terms of linearity and power efficiency. Digital predistortion (DPD) is commonly used to mitigate nonlinearities while the PA operates at levels close to saturation, where the device presents its highest power efficiency. Since the DPD is generally based on Volterra series models, its number of coefficients is high, producing ill-conditioned and over-fitted estimations. Recently, a plethora of techniques have been independently proposed for reducing their dimensionality. This paper is devoted to presenting a fair benchmark of the most relevant order reduction techniques present in the literature categorized by the following: (i) greedy pursuits, including Orthogonal Matching Pursuit (OMP), Doubly Orthogonal Matching Pursuit (DOMP), Subspace Pursuit (SP) and Random Forest (RF); (ii) regularization techniques, including ridge regression and least absolute shrinkage and selection operator (LASSO); (iii) heuristic local search methods, including hill climbing (HC) and dynamic model sizing (DMS); and (iv) global probabilistic optimization algorithms, including simulated annealing (SA), genetic algorithms (GA) and adaptive Lipschitz optimization (adaLIPO). The comparison is carried out with modeling and linearization performance and in terms of runtime. The results show that greedy pursuits, particularly the DOMP, provide the best trade-off between execution time and linearization robustness against dimensionality reduction.

Multi-fidelity probabilistic optimisation of composite structures under thermomechanical loading using Gaussian processes

A multi-fidelity probabilistic optimisation method for the design of composite structures subjected to thermomechanical loading is introduced in this work for the first time. The proposed multi-fidelity approach offers considerable computation efficiency as well as sufficient accuracy, enabling probabilistic optimisation to include more design variables in the early design phase. This approach incorporates both nonlinear information fusion algorithms and multi-level optimisation to achieve increased accuracy and computation time savings. In this optimisation process, a High-Fidelity Model (HFM) covers only a part of the entire design space with information collected uniformly while providing high-fidelity information of other design spaces sparsely without causing extra computational cost. Simultaneously, a Low-Fidelity Model (LFM) explores the whole design space to compensate lack of high-fidelity information. In this manner, the number of high-fidelity information to construct a multi-fidelity model is dramatically reduced. The Reliability-Based Design Optimisation (RBDO) demonstrated the proposed multi-fidelity method of a mono-stringer stiffened composite panel under thermomechanical loading using Gaussian Processes (GPs).

Cost- and Risk-Based Seismic Design Optimization of Nuclear Power Plant Safety Systems

Seismic analysis, design, and qualification of systems, structures, and components (SSCs) is a significant contributor to the capital cost of a nuclear power plant. To reduce capital costs of advanced nuclear power plants and make commercial nuclear energy more competitive, innovations are needed in their structural design and construction, and not just in the reactor core and associated systems. Seismic isolation has been identified as an important cost-cutting technology that enables standardization of equipment across various sites. This paper develops and demonstrates a cost- and risk-based seismic design optimization of a representative safety system in a nuclear power plant with the dual goals of minimizing overnight capital cost and meeting safety goals. The design optimization can also include component seismic isolation, in which case, the optimized design includes a set of equipment that needs to be seismically isolated to minimize capital cost. The open-source codes MASTODON and Dakota are used for seismic probabilistic risk assessment and design optimization, respectively. A generic nuclear facility with a safety system comprising SSCs that are common to nuclear power plants is considered for the demonstration of the design optimization and is assumed to be located at the Idaho National Laboratory site. Generic costs and seismic design cost functions are assumed for the SSCs of the safety system. The sum of the costs of the SSCs is minimized in the optimization process, while the risk of failure of the safety system is provided as a constraint. Results show that the optimization process reduces capital costs significantly while automatically prioritizing the safety of SSCs that contribute most to the risk of the safety system.

Probabilistic shaping and neural network-based optimization for a nonlinear frequency division multiplexing system.

A joint scheme introducing probabilistic shaping (PS) at the transmitter and utilizing a neural network (NN) equalizer at the receiver is proposed to improve the performance of the b-modulated nonlinear frequency division multiplexing (NFDM) system. Through a numerical simulation, we demonstrate that PS plays a leading role for low launch power case, which improves the performance of the system effectively, while the NN equalizer's superiority appears in a high launch power region, whose main role is to weaken the correlation among subcarriers for improving system performance. The proposed scheme would enlighten the optimum modulation and detection schemes of the NFDM system.

Introducing a probabilistic definition of the target in a robust treatment planning framework

The ‘clinical target distribution’ (CTD) has recently been introduced as a promising alternative to the binary clinical target volume (CTV). However, a comprehensive study that considers the CTD, together with geometric treatment uncertainties, was lacking. Because the CTD is inherently a probabilistic concept, this study proposes a fully probabilistic approach that integrates the CTD directly in a robust treatment planning framework. First, the CTD is derived from a reported microscopic tumor infiltration model such that it explicitly features the probability of tumor cell presence in its target definition. Second, two probabilistic robust optimization methods are proposed that evaluate CTD coverage under uncertainty. The first method minimizes the expected-value (EV) over the uncertainty scenarios and the second method minimizes the sum of the expected value and standard deviation (EV-SD), thereby penalizing the spread of the objectives from the mean. Both EV and EV-SD methods introduce the CTD in the objective function by using weighting factors that represent the probability of tumor presence. The probabilistic methods are compared to a conventional worst-case approach that uses the CTV in a worst-case optimization algorithm. To evaluate the treatment plans, a scenario-based evaluation strategy is implemented that combines the effects of microscopic tumor infiltrations with the other geometric uncertainties. The methods are tested for five lung tumor patients, treated with intensity-modulated proton therapy. The results indicate that for the studied patient cases, the probabilistic methods favor the reduction of the esophagus dose but compensate by increasing the high-dose region in a low conflicting organ such as the lung. These results show that a fully probabilistic approach has the potential to obtain clinical benefits when tumor infiltration uncertainties are taken into account directly in the treatment planning process.

Adaptive Probabilistic Optimization Approach for Vibration-Based Structural Health Monitoring

This paper presents a novel adaptive probabilistic algorithm to identify damage characteristics by integrating the use of the frequency response function with an optimization approach. The proposed algorithm evaluates the probability of damage existence and determines salient details such as damage location and damage severity in a probabilistic manner. A multistage sequence is used to determine the probability of damage parameters including crack depth and crack location while minimizing uncertainties. A simply supported beam with an open edge crack was used to demonstrate the application of the algorithm for damage detection. The robustness of the algorithm was tested by incorporating varying levels of noise into the frequency response. All simulation results show successful detection of damage with a relatively high probability even in the presence of noise. Results indicate that the probabilistic algorithm could have significant advantages over conventional deterministic methods since it has the ability to avoid yielding false negatives that are quite common among deterministic damage detection techniques.

Probabilistic Design and Optimization for Tunnels considering Measuring Uncertainties

Uncertainty is an essential property of rock mechanics and engineering, which is of great significance to excavation, design, and control of rock engineering. In this study, an innovative framework of the reliability-based design was developed for the rock tunnel under uncertainty. The convergence-confinement method is used to characterize the interaction mechanism between the support structure and surrounding rock mass. Artificial bee colony (ABC) was adopted to solve the optimization problem in the reliability-based design. The probabilistic properties of rock strength and failure envelope were obtained based on the triaxial compression test data using the Bayesian method. The reliability of the tunnel and support structure was evaluated based on the abovementioned probabilistic properties of rock strength using the reliability analysis method. A circular tunnel was used to illustrate the developed framework, and the procedure was presented in detail. The time of rockbolt installed, the thickness of the shotcrete, length of rockbolt, circumferential space, and longitudinal space of rockbolt were determined and met the constraints of reliability index. Results show that the developed framework can consider the uncertainty for support design in the tunnel. It provides a good and promising way to support design considering the uncertainty of test data using the reliability-based design.

DETERMINING THE OPTIMAL VALUES OF TARGET RELIABILITY INDEX OF BUILDING STRUCTURES FOR FLAT FLOORS OF FRAME BUILDINGS

Target reliability levels recommended in various national and international documents are inconsistent.&nbsp; In various sources, they are determined depending on the relative costs of safety measures, the consequences of failure, the risk to life, discount rate, etc. It is obvious that the optimal values of reliability index for various designs are very different. In the present paper, a method for determining the target reliability index for flat floor slabs of frame buildings is proposed. This problem is solved based on probabilistic optimization and the societal risk acceptance criterion, which enters the decision as a boundary condition. As a result of the research, the values of the reliability index for flat slabs, with different span sizes and applied loads, were determined. &nbsp; &nbsp; &nbsp

Driving and steering collision avoidance system of autonomous vehicle with model predictive control based on non-convex optimization

A planar motion control system is proposed for autonomous vehicles not only to follow the lanes, but also to avoid collisions by braking, accelerating, and steering. The supervisor is designed first to determine the desired speed and the risk of the maneuvering due to road boundaries and obstacles. In order to allow lane changes on multi-lane roads, the model predictive controller is formulated based on the probabilistic non-convex optimization. The micro-genetic algorithm is applied to calculate the target speed and target steering angle in real time. A software-in-the-loop unit is constructed with the Rapid Control Prototyping device in the vehicle communication environment. The performance of the proposed system is verified for various collision avoidance scenarios and the simulation results demonstrate the safe and effective driving performance of autonomous vehicles with no collision on multi-lane road.

Probabilistic Optimization of Networked Multi-Carrier Microgrids to Enhance Resilience Leveraging Demand Response Programs

Microgrids have emerged as a practical solution to improve the power system resilience against unpredicted failures and power outages. Microgrids offer substantial benefits for customers through the local supply of domestic demands as well as reducing curtailment during possible disruptions. Furthermore, the interdependency of natural gas and power networks is a key factor in energy systems’ resilience during critical hours. This paper suggests a probabilistic optimization of networked multi-carrier microgrids (NMCMG), addressing the uncertainties associated with thermal and electrical demands, renewable power generation, and the electricity market. The approach aims to minimize the NMCMG costs associated with the operation, maintenance, CO2e emission, startup and shutdown cost of units, incentive and penalty payments, as well as load curtailment during unpredicted failures. Moreover, two types of demand response programs (DRPs), including time-based and incentive-based DRPs, are addressed. The DRPs unlock the flexibility potentials of domestic demands to compensate for the power shortage during critical hours. The heat-power dual dependency characteristic of combined heat and power systems as a substantial technology in microgrids is considered in the model. The simulation results confirm that the suggested NMCMG not only integrates the flexibility potentials into the microgrids but also enhances the resilience of the energy systems.

Multi-objective Adaptive Evolutionary Algorithm to Enhance Voltage Stability in Power Systems

Problems with two or more conflicting objectives have been handled as needing a multi-objective approach in recent years. The solution for these types of problems is normally to satisfy the conflicting objectives simultaneously in order to find tradeoffs between different criteria. Optimization in power systems is an important example of how to tackle multi-objective problems since these systems have conflicting performance indicators and normally operate close to their constraints due to the continuous increase in demand. In this paper, a multi-objective approach is applied to the voltage stability problem in power systems by using an adaptive evolutionary algorithm. The proposed method regards examining the following stability indicators of power systems: the voltage profile, the total reactive power loss, and the voltage collapse margin as requiring a multi-objective approach. Several experiments were conducted in IEEE 14, 57, and 118 busbar systems by using the proposed method and other probabilistic and heuristic optimization methods. The results showed that the proposed adaptive evolutionary algorithm enhanced the voltage stability and outperformed the other methods, especially when the size of the power system increases.

Bounds optimization of model response moments: a twin-engine Bayesian active learning method

The efficient propagation of imprecise probabilities through expensive simulators has emerged to be one of the great challenges for mixed uncertainty quantification in computational mechanics. An active learning method, named Collaborative and Adaptive Bayesian Optimization (CABO), is developed for tackling this challenge by combining Bayesian Probabilistic Optimization and Bayesian Probabilistic Integration. Two learning functions are introduced as engines for CABO, where one is introduced for realizing the adaptive optimization search in the epistemic uncertainty space, and the other one is developed for adaptive integration in the aleatory uncertainty space. These two engines work in a collaborative way to create optimal design points adaptively in the joint uncertainty space, by which a Gaussian process regression model is trained and updated to approach the bounds of model response moments with pre-specified error tolerances. The effectiveness of CABO is demonstrated using a numerical example and two engineering benchmarks.

Extension of the single-nonlinear-mode theory by linear attachments and application to exciter-structure interaction

Under certain conditions, the dynamics of a nonlinear mechanical system can be represented by a single nonlinear modal oscillator. This holds, in particular, under external excitation near primary resonance or under self-excitation by negative damping of the respective mode. The properties of the modal oscillator can be determined by computational or experimental nonlinear modal analysis. The simplification to a single-nonlinear-mode model facilitates qualitative and global analysis, and substantially reduces the computational effort required for probabilistic methods and design optimization. Important limitations of this theory are that only purely mechanical systems can be analyzed and that the respective nonlinear mode has to be recomputed when the system’s structural properties are varied. With the theoretical extension proposed in this work, it becomes feasible to attach linear subsystems to the primary mechanical system, and to approximate the dynamics of this coupled system using only the nonlinear mode of the primary mechanical system. The attachments must be described by linear ordinary or differential-algebraic equations with time-invariant coefficient matrices. The attachments do not need to be of purely mechanical nature, but may contain, for instance, electric, magnetic, acoustic, thermal or aerodynamic models. This considerably extends the range of utility of nonlinear modes to applications as diverse as model updating or vibration energy harvesting. As long as the attachments do not significantly deteriorate the host system’s modal deflection shape, it is shown that their effect can be reduced to a complex-valued modal impedance and an imposed modal forcing term. In the present work, the proposed approach is computationally assessed for the analysis of exciter-structure interaction. More specifically, the force drop typically encountered in frequency response testing is revisited. A cantilevered beam with cubic spring and an attached electro-dynamical shaker serves as benchmark. The proposed approach shows excellent accuracy. Mainly the already known limitations of single-nonlinear-mode theory reappear. In particular, higher harmonics should not be too pronounced. In the transient case, the time scales of vibration and amplitude-phase modulation should be well separated, and the attachment dynamics should be in quasi-steady state.

Probabilistic truthlikeness, content elements, and meta-inductive probability optimization

The paper starts with the distinction between conjunction-of-parts accounts and disjunction-of-possibilities accounts to truthlikeness (Sects. 1, 2). In Sect. 3, three distinctions between kinds of truthlikeness measures (t-measures) are introduced: (i) comparative versus numeric t-measures, (ii) t-measures for qualitative versus quantitative theories, and (iii) t-measures for deterministic versus probabilistic truth. These three kinds of truthlikeness are explicated and developed within a version of conjunctive part accounts based on content elements (Sects. 4, 5). The focus lies on measures of probabilistic truthlikeness, that are divided into t-measures for statistical probabilities and single case probabilities (Sect. 4). The logical notion of probabilistic truthlikeness (evaluated relative to true probabilistic laws) can be treated as a subcase of deterministic truthlikeness for quantitative theories (Sects. 4–6). In contrast, the epistemic notion of probabilistic truthlikeness (evaluated relative to given empirical evidence) creates genuinely new problems, especially for hypotheses about single case probabilities that are evaluated not by comparison to observed frequencies (as statistical probabilities), but by comparison to the truth values of single event statements (Sect. 6). By the method of meta-induction, competing theories about single case probabilities can be aggregated into a combined theory with optimal predictive success and epistemic truthlikeness (Sect. 7).

Probabilistic thermodynamic analysis of metabolic networks.

MotivationRandom sampling of metabolic fluxes can provide a comprehensive description of the capabilities of a metabolic network. However, current sampling approaches do not model thermodynamics explicitly, leading to inaccurate predictions of an organism’s potential or actual metabolic operations.ResultsWe present a probabilistic framework combining thermodynamic quantities with steady-state flux constraints to analyze the properties of a metabolic network. It includes methods for probabilistic metabolic optimization and for joint sampling of thermodynamic and flux spaces. Applied to a model of Escherichia coli, we use the methods to reveal known and novel mechanisms of substrate channeling, and to accurately predict reaction directions and metabolite concentrations. Interestingly, predicted flux distributions are multimodal, leading to discrete hypotheses on E.coli’s metabolic capabilities.Availability and implementationPython and MATLAB packages available at https://gitlab.com/csb.ethz/pta.Supplementary informationSupplementary data are available at Bioinformatics online.