Constraint Violations Research Articles

Clustering-based evolutionary algorithm for constrained multimodal multi-objective optimization

Handling constrained multimodal multi-objective optimization problems (CMMOPs) is a tremendous challenge as it involves the discovery of multiple equivalent constrained Pareto sets (CPSs) with the identical constrained Pareto front (CPF). However, the existing constrained multi-objective evolutionary algorithms are rarely suitable for solving CMMOPs due to the fact that they focus solely on locating CPF and do not intend to search for multiple equivalent CPSs. To address this issue, this paper proposes a framework of clustering-based constrained multimodal multi-objective evolutionary algorithm, termed FCCMMEA. In the proposed FCCMMEA, we adopt a clustering method to separate the population into multiple subpopulations for locating diverse CPSs and maintaining population diversity. Subsequently, each subpopulation evolves independently to produce offspring by an evolutionary algorithm. To balance the convergence and feasibility, we develop a quality evaluation metric in the classification strategy that considers the local convergence quality and constraint violation values, and it divides the populations into superior and inferior populations according to the quality evaluation of individuals. Furthermore, we also employ a diversity maintenance methodology in environmental selection to maintain the diverse population. The proposed FCCMMEA algorithm is compared with seven state-of-the-art competing algorithms on a standard CMMOP test suite, and the experimental results validate that the proposed FCCMMEA enables to find multiple CPSs and is suitable for handling CMMOPs. Also, the proposed FCCMMEA won the first place in the 2023 IEEE Congress on Evolutionary Computation competition on CMMOPs.

Interior-point policy optimization based multi-agent deep reinforcement learning method for secure home energy management under various uncertainties

Improving the efficiency of home energy management (HEM) is of great significance in reducing resource waste and prompting renewable energy consumption. With the development of advanced HEM systems and internet-of-things technology, more residents are willing to participate in the electricity market through a demand response mechanism, which can not only reduce the electricity bill but also stabilize the operation of the main grid through peak shaving and valley filling. However, the uncertainties from household appliance parameters, user behaviors, penetrated renewable energy, and electricity prices render the HEM problem a non-trivial task. Although previous deep reinforcement learning (DRL) methods have no requirement for system dynamics due to their model-free and data-driven merits, the unrestricted action space may violate the physical constraints of various devices, and few works have concentrated on this area before. To solve the above challenges, this paper proposes a novel interior-point policy optimization-based multi-agent DRL algorithm to optimize the home energy scheduling procedure while guaranteeing safety during its operation. Besides, a time-series prediction model based on a non-stationary Transformer neural network is proposed to predict the future trend of solar generation and electricity price, which can provide the agents with abundant information to make better decisions. The superior performance of our proposed predictive-control coupled method is demonstrated through extensive numerical experiments, which achieves more precise prediction results, near-zero constraint violations, and better trade-offs between cost and safety than several benchmark methods.

Hierarchical Bayesian spectral regression with shape constraints for multi-group data

We propose a hierarchical Bayesian (HB) model for multi-group analysis with group–specific, flexible regression functions. The lower–level (within group) and upper–level (between groups) regression functions have hierarchical Gaussian process priors. HB smoothing priors are developed for the spectral coefficients. The HB priors smooth the estimated functions within and between groups. The HB model is particularly useful when data within groups are sparse because it shares information across groups, and provides more accurate estimates than fitting separate nonparametric models to each group. The proposed model also allows shape constraints, such as monotone, U and S–shaped, and multi-modal constraints. When appropriate, shape constraints improve estimation by recognizing violations of the shape constraints as noise. The model is illustrated by two examples: monotone growth curves for children, and happiness as a convex, U-shaped function of age in multiple countries. Various basis functions could also be used, and the paper also implements versions with B-splines and orthogonal polynomials.

An incremental algorithm for repairing denial constraint violations

Data repairing algorithms are extensively studied for improving data quality. Denial constraints (DCs) are commonly employed to state quality specifications that data should satisfy and hence facilitate data repairing since DCs are general enough to subsume many other dependencies. Data in practice are usually frequently updated, which motivates the quest for efficient incremental repairing techniques in response to data updates. In this paper, we present the first incremental algorithm for repairing DC violations. Specifically, given a relational instance I consistent with a set Σ of DCs, and a set △I of tuple insertions to I, our aim is to find a set △I′ of tuple insertions such that Σ is satisfied on I+△I′. We first formalize and prove the complexity of the problem of incremental data repairing with DCs. We then present techniques that combine auxiliary indexing structures to efficiently identify DC violations incurred by △Iw.r.t.Σ, and further develop an efficient repairing algorithm to compute △I′ by resolving DC violations. Finally, using both real-life and synthetic datasets, we conduct extensive experiments to demonstrate the effectiveness and efficiency of our approach.

Tracking control via time-varying feedback for an uncertain robotic system with both output constraint and dead-zone input

This paper is devoted to the tracking control for an uncertain robotic system with both output constraint and dead-zone input. Remarkably, the distinctive characters of the system are reflected by system uncertainties and output constraint. First, more serious uncertainties are involved since unknown nonlinear dynamic matrices, external disturbance and the dead-zone input (see unknown slopes and break points therein) are simultaneously considered, but those of the related literature are not. Second, weaker conditions on the output constraint are allowed since the constraint functions considered are only first but not more order continuously differentiable while any their time derivatives are not necessarily available for feedback. This leads to the incapability of the traditional control schemes on this topic. To solve the control problem, a novel control framework is proposed based on time-varying feedback which overcomes the serious system uncertainties while relaxes the conditions on output constraints. Specifically, a state transformation with a time-varying gain is first introduced to derive a new system. Then, by using the traditional backstepping method with the introduction of the time-varying gain in the estimations of some uncertain terms, a time-varying feedback controller is explicitly designed, which ensures that all the states of the resulting closed-loop system are bounded while system output asymptotically tracks the reference signal without any violation of the output constraint. Finally, simulation results for two practical examples are provided to validate the effectiveness of the proposed theoretical results, and moreover, a comparison with PID method is given to show the superiority of the proposed method on tracking accuracy and robustness.

Two-stage coevolutionary constrained multi-objective optimization algorithm for solving optimal power flow problems with wind power and FACTS devices

As a large amount of wind energy is integrated into the grid, the randomness it brings poses a challenge to modern power systems. The application of Flexible AC Transmission Systems (FACTS) in the grid is becoming more and more common, and it is necessary to consider how to choose suitable equipment in the appropriate locations. In this paper, a multi-objective optimal power flow (MOOPF) model with wind farms and FACTS devices is established. The Weibull probability density function is used to establish the wind speed model, and the cost problem brought by wind power is considered. The locations and ratings of thyristor-controlled series compensators, thyristor-controlled phase shifters, and static VAR compensators are added to the system as control variables. In addition, the constraints on the prohibited operating areas of thermal power generators and the valve point effect are also considered. Coevolutionary constrained multi-objective optimization algorithm (CCMO) is an advanced technology, and this paper improves it and names it two-stage coevolutionary constrained multi-objective optimization algorithm (TSCCMO). The proposed algorithm uses the constraint violation value as an additional objective function in the sub-population environmental selection process, and integrates a neighborhood selection strategy into the mating selection process. The population evolution process is divided into two stages, in the first stage the two populations cooperate weakly, and in the second stage the two populations will have strong cooperation. TSCCMO is used to solve this complex constrained MOOPF problem, and its results are compared and analyzed with CCMO, NSGA–II–CDP, C3M, and PPS. The comprehensive performance of TSCCMO is the best among the 6 cases.

A trust-region scheme for constrained multi-objective optimization problems with superlinear convergence property

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable l ∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front.

Incentivizing energy and carbon rights transactions among network-constrained energy hubs: Cooperative game with externalities

Joint energy and carbon rights transactions for multiple energy hubs could boost the utilization of renewable distributed energy resources and reduce carbon emissions in energy sectors. The joint transaction mechanism based on the cooperative game is proposed, in which cooperative energy hubs form a grand coalition to share diverse forms of energy and carbon rights in order to maximize their total benefit. Furthermore, the grand coalition-based transaction mechanism is augmented with network constraints to account for the influence of network constraints on the trading behaviors of energy hubs, which is mathematically represented as a cooperative game with externalities. In addition, mathematical proof is provided to demonstrate the stability of the formed network-constrained grand coalition. To determine the trading behaviors and allocate payoff among energy hubs while satisfying both network constraints and coalition stability, a scalable two-stage optimization structure is provided, with the first stage ensuring coalition stability and the second preventing network constraint violations. A solution technique combined with Karush-Kuhn-Tucker conditions and Benders decomposition is proposed to solve the two-stage optimization problem. The effectiveness and scalability of the proposed joint transaction mechanism and the solution technique are supported by numerical results for the 4-EH and 33-EH systems. The introduction of the carbon market leads to a 20.6 % reduction in carbon emissions and a 10.5 % increase in total payoff by facilitating peer-to-peer trading of both energy and carbon rights.

Equality‐embedded augmented Lagrangian neural network for DC optimal power flow

AbstractDirect current optimal power flow (DC‐OPF) problems need to be solved more frequently to maintain safety and economic power system operation. Traditional solvers take too much time to get optimal results. To overcome it, a new self‐supervised augmented Lagrangian neural network (ALNN) is proposed to solve DC‐OPF problem. The proposed ALNN consists of two neural networks: the control net and the penalty net. The control net predicts active power of generators; the penalty net updates the Lagrangian multipliers. The equality constraints are embedded into the control net to guarantee no equality violations. The generalized reduced gradient method is used to reduce theviolations of inequality constraint. The effectiveness of the proposed model is demonstrated on IEEE 118‐bus. The results show that with the help of equality embedding, the equality constraints are always satisfied, which in turn improves the feasibility of ALNN. Compared to the state‐of‐art models, the proposed model has higher feasibility and less constraint violations without comprising optimality. What is more, most of the inactive constraints can be found during the training process and then they are used to speed up the post‐processing part.

Distributed Frank-Wolfe Solver for Stochastic Optimization With Coupled Inequality Constraints.

Distributed stochastic optimization (DSO) with local set constraints and coupled inequality constraints over a multiagent network is considered in this article. Usually, such problems are tackled by projected primal-dual methods, which require expensive projection operations when set constraints are complicated. In this context, this article focuses on the Frank-Wolfe (FW) framework, which provides computational simplicity by avoiding expensive projection operations, for solving DSO with local set and coupled inequality constraints. By combining recursive momentum and weighted averaging, this article proposes a distributed stochastic FW primal-dual algorithm (DSFWPD), which is the first stochastic FW solver for DSO problems with coupled constraints. The proposed algorithm achieves zero constraint violation on average with a sublinear decay of the optimality gap over a directed and time-varying network. The efficacy of DSFWPD is demonstrated by several numerical experiments.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Balancing exploration and exploitation in dynamic constrained multimodal multi-objective co-evolutionary algorithm

Constrained multimodal multi-objective optimization (CMMOPs) involves multiple equivalent constrained Pareto optimal sets (CPSs) matching the same constrained Pareto front (CPF). An essential challenge in solving CMMOPs is how to balance exploration and exploitation in searching for the CPSs. To tackle this issue, a dynamic constrained co-evolutionary multimodal multi-objective algorithm termed DCMMEA is developed in this paper. DCMMEA involves a constraint-relaxed population for handling constraints and a convergence-relaxed population for improving convergence quality. Subsequently, a constraint-relaxed epsilon strategy that considers the constraint violation degree between individuals is designed and applied dynamically in the constraint-relaxed population to develop equivalent CPSs. Similarly, a dynamic convergence-relaxed epsilon strategy that considers the differences between objective values is developed and used dynamically in the convergence-relaxed population. It explores CPSs with high convergence quality and transfers the convergence knowledge to the constraint-relaxed population. Additionally, the constraint- relaxed population size is dynamically increased and the convergence-relaxed population size is dynamically decreased to balance the exploration and exploitation procedures. Experiments are performed on standard CMMOP test suites and validate that DCMMEA obtains superior performance on solving CMMOPs in comparison to state-of-the-art algorithms. Also, DCMMEA is implemented on standard CMOPs and demonstrated good performance in handling CMOPs.

Stochastic Optimal Operation of SOP-Assisted Active Distribution Networks with High Penetration of Renewable Energy Sources

This paper introduces a mixed-integer convex model for optimizing the scheduling of soft open points (SOPs) integrated with energy storage (ES) in active distribution networks (ADNs) with high proportions of photovoltaic sources, designed to ensure zero risk of constraint violations. A stochastic optimization model for ADNs is proposed to maximize the benefits of SOPs while simultaneously minimizing system power losses, SOP power losses, voltage deviations, PV power curtailment, battery energy storage system (BESS) operation cost, and utility power purchase. Uncertainties in PV generation and load demand are considered by Monte Carlo simulation and k-means technologies. Finally, simulation cases from a 21-bus distribution network show that the curtailment of PV sources is minimized and the power fluctuations of the BESS are reduced in comparison to the case without SOP. Constraints in the nodal voltages, power outputs, energy balance, and power flow are all satisfied.

Simulation study on four-wheeled mobile robot mechanisms using various performance criteria

In this paper, the performance criteria for various four-wheeled mobile robots that are crucial for assessing a robot’s fitness for mobility to successfully complete missions are introduced. The seven proposed performance indices, the root mean squared acceleration (RMSA), posture variance index (PVI), static stability margin (SSM), force angle stability margin (FASM), energy stability margin (ESM), friction requirement (μr), and velocity constraint violation (VCV), address the fluctuation, rollover, and slippage problems in four-wheeled mobile robots. The simulations considered a square bump-shaped obstacle, and the dimensions of the robot were based on nine simulation cases in a 3D environment. Additionally, a methodology for evaluating these seven criteria is outlined. To streamline the simulation process, Taguchi’s catalog of orthogonal arrays (OAs) was used for the experimental design, specifically L9 OA with four factors and three levels was used. Analysis of means (ANOM) was applied to assess the influence of each design factor on the seven criteria, leveraging the OA orthogonality. Finally, the sensitivity analysis and potential for evaluating general mobile robots in the future are discussed.

Comparison of different control methods on the thermally activated building system (TABS) with large energy flexibility

Thermally Activated Building Systems (TABS) has great energy flexibility potential for the effective demand response, but the inherent large thermal inertia creates challenges for the control. Model Predictive Control (MPC) can improve the control efficiency while achieving certain objectives. However, the modeling mechanism of the TABS thermal behavior can lead to the difference in the controller performances. In this study, the white-box model, grey-box model, and black-box model based MPCs (referred to as W-MPC, G-MPC, and B-MPC) are developed and analyzed in depth for a case TABS with high heat flexibility potential. The performances of MPC strategies are investigated together with the baseline Rule Based Control (RBC) strategy under normal conditions as well as a variety of uncertainty events. In general, MPC strategies show better performance compared to the RBC. The prediction-based control can effectively maintain the indoor temperature within the constraints considering the uncertain disturbances and the gradual outdoor climate change. Moreover, MPC strategies help to increase the cost savings due to the effective load shifting by 30%–50%, and enhance the flexible energy utilization by 14%–29%. In terms of the comparison among the different MPC strategies, W-MPC shows better performance in the room temperature control, which reduces the violation of the indoor temperature constraint by 30% and 15% compared to G-MPC and B-MPC, respectively. G-MPC shows slight superiority concerning the economy and flexible energy usage. The normalized cost saving of G-MPC is approximately 3% and 8% lower compared to the W-MPC and B-MPC, respectively, while the utilization efficiencies of the flexible energy are approximately 6% and 12% higher.

Optimizing the management of multiple water resources in irrigation area under uncertainty: A novel scenario-based multi-objective fuzzy-credibility constrained programming model

Effective water resources management is vital for sustainable development, healthy ecosystems, stable socio-economic, and human well-being. However, managing water resources faces challenges due to the involvement of multiple stakeholders and uncertainties in various hydrologic fluxes. This complexity makes it rare for research to simultaneously address the hidden uncertainties in both objectives and constraints. Here, we developed a scenario-based multi-objective fuzzy-credibility constrained programming approach and applied it to the water resource management system (SMOFCP-WRMS) of the Zhaokou Yellow River Diversion Irrigation Area Phase II Project (ZKID-II). This method handles uncertainties represented by scenarios and fuzzy sets, while also resolving fuzzy uncertainty parameters within the multiple objectives and constraints of the model. We solve the SMOFCP-RWMS model by integrating the Nondominated sorting genetic algorithm III (NSGA-III) and compromise programming (CP) method. The results show that: (1) An increase in constraints violation risks (credibility level from 0.5 to 1.0) results in a decrease in water resources allocation and pollutant discharge by 25.95 × 106 m3 and 207.63 tonne, respectively, accompanied by a decline in net economic income by 68.04 × 106 CNY; (2) From extraordinary dry year to normal year (design frequencies from 95 % to 50 %) leads to a reduction in water shortage by 167.07 × 106 m3. Incorporating ‘credibility levels’ and ‘design frequencies’ would be beneficial for addressing uncertainties, including fuzzy information and discrete possibilities for the future; (3) Regarding the multi-objective model solution, the combined NSGA-III and CP approach demonstrates an average increase of 1.71 % in net economic benefits and 5.91 % in total pollution discharge, along with a 6.77 % reduction in the water deficit ration compared to the traditional CP method. Although the ecological benefits decrease slightly in the compromise-optimal solutions using the combined NSGA-III and CP method, the economic and social benefits are improved compared to those from the combined NSGA-II and CP method. This study provides valuable decision-making guidance for water resources managers in irrigated areas, aiding them in balancing economic, social, and ecological benefits, and enabling the section of an optimal water resources management scheme based on acceptable risk levels under various uncertain conditions.

Real-time automatic control of multi-energy system for smart district community: A coupling ensemble prediction model and safe deep reinforcement learning

Energy system autonomous control is influenced by day-ahead forecasting, despite being carried out independently in the literature. This paper develops an energy management modular platform that integrates multi-variable timeseries prediction and autonomous energy infrastructure scheduling in real-time. Firstly, an ensemble prediction model is developed for the day-ahead multi-energy and renewable power prediction, which is implemented by coupling variants of CNN, GRU, and BiLSTM models into a global model using an ensemble approach. Secondly, a deep reinforcement learning (DRL) with a soft actor critic (SAC) algorithm that include safety-guided network to make the policy network constraint-aware is proposed. A multi-energy system with renewable energy and carbon capture technology is then anticipated as the energy infrastructure for achieving a carbon neutral community and evaluating our proposed model. The proposed models are trained and tested on a real-world dataset from Arizona, USA. The ensemble prediction model achieved the least root mean squared error (RMSE). On the other hand, the improved DRL method exhibits superior performance in reducing energy cost, minimum constraint violation, and fast deployment compared to state-of-the-art DRL methods. Finally, the two models are coupled and carry out generalization performance on the prediction and energy management scheme, including the sensitivity analysis on carbon capture price, in the case studies.

Intrafraction organ movement in adaptive MR-guided radiotherapy of abdominal lesions – dosimetric impact and how to detect its extent in advance

IntroductionMagnetic resonance guided radiotherapy (MRgRT) allows daily adaptation of treatment plans to compensate for positional changes of target volumes and organs at risk (OARs). However, current adaptation times are relatively long and organ movement occurring during the adaptation process might offset the benefit gained by adaptation. The aim of this study was to evaluate the dosimetric impact of these intrafractional changes. Additionally, a method to predict the extent of organ movement before the first treatment was evaluated in order to have the possibility to compensate for them, for example by adding additional margins to OARs.Materials & methodsTwenty patients receiving adaptive MRgRT for treatment of abdominal lesions were retrospectively analyzed. Magnetic resonance (MR) images acquired at the start of adaptation and immediately before irradiation were used to calculate adapted and pre-irradiation dose in OARs directly next to the planning target volume. The extent of organ movement was determined on MR images acquired during simulation sessions and adaptive treatments, and their agreement was evaluated. Correlation between the magnitude of organ movement during simulation and the duration of simulation session was analyzed in order to assess whether organ movement might be relevant even if the adaptation process could be accelerated in the future.ResultsA significant increase in dose constraint violations was observed from adapted (6.9%) to pre-irradiation (30.2%) dose distributions. Overall, OAR dose increased significantly by 4.3% due to intrafractional organ movement. Median changes in organ position of 7.5 mm (range 1.5–10.5 mm) were detected within a median time of 17.1 min (range 1.6–28.7 min). Good agreement was found between the range of organ movement during simulation and adaptation (66.8%), especially if simulation sessions were longer and multiple MR images were acquired. No correlation was determined between duration of simulation sessions and magnitude of organ movement.ConclusionIntrafractional organ movement can impact dose distributions and lead to violations of OAR tolerance doses, which impairs the benefit of daily on-table plan adaptation. By application of simulation images, the extent of intrafractional organ movement can be predicted, which possibly allows to compensate for them.

Hybrid calibration method for a single camera stereo digital image correlation system

In single camera stereo digital image correlation systems, the existing calibration methods have problems with poor accuracy and violation of theoretical constraints, so we have proposed a hybrid calibration method. In this study, we first explain the principles of the existing single camera stereo measurement calibration methods. Then, on the basis of the classical camera calibration method combined with the characteristics of planar mirror reflection imaging, a hybrid calibration method is proposed that not only satisfies the constraints of the same intrinsic parameters but also has higher accuracy. Next, we complete the mathematical model of the hybrid calibration method and explain the specific calibration process. Finally, the experimental results of point distance reconstruction and static displacement measurement show that, compared with the existing calibration methods, the hybrid calibration method has lower error and higher reconstruction accuracy.

Privacy-preserving multi-level co-regulation of VPPs via hierarchical safe deep reinforcement learning

Large amounts of distributed energy sources have brought challenges in terms of the safe and stable operation of the power grid. As a key technology between user-side energy resources and the distribution network (DN), how to realize the online coordinated scheduling of VPP and DN as well as the real-time response strategy of distributed equipment (DE) within VPP is the focus of this study. Thus, the hierarchical deep reinforcement learning (DRL) Hierarchical-TD3 algorithm is designed based on the unified modeling of adjustable space to achieve the real-time economic scheduling of VPPs. The upper layer DN considers the network security constraints and solves the economic scheduling model of VPPs based on the single-agent TD3 algorithm. Based on the scheduling instructions from the upper layer, the lower layer VPPs consider the requirements of privacy protection and control autonomy and realize real-time response of the DE within VPP via multi-agent MATD3 algorithm. Numerical results in the modified 33-nodes system show that the proposed Hierarchical-TD3 algorithm can achieve privacy protection and the coordinated scheduling of VPP and DE to reduce the operating cost. It differs from the optimal value by only 1.46% but can achieve online decision-making on the millisecond scale. Compared with the traditional centralized and decentralized DRL algorithms, the total cost is reduced by 10.15% and 5.52% respectively. Compared with the traditional soft-constraint method, there is no constraint violation during the training and testing phases. Finally, the actual 116-nodes testing system validates the scalability of the proposed Hierarchical-TD3 algorithm.