Feasibility Constraints Research Articles

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

Identifying climate model structural inconsistencies allows for tight constraint of aerosol radiative forcing

Abstract. Aerosol radiative forcing uncertainty affects estimates of climate sensitivity and limits model skill in terms of making climate projections. Efforts to improve the representations of physical processes in climate models, including extensive comparisons with observations, have not significantly constrained the range of possible aerosol forcing values. A far stronger constraint, in particular for the lower (most-negative) bound, can be achieved using global mean energy balance arguments based on observed changes in historical temperature. Here, we show that structural deficiencies in a climate model, revealed as inconsistencies among observationally constrained cloud properties in the model, limit the effectiveness of observational constraint of the uncertain physical processes. We sample the uncertainty in 37 model parameters related to aerosols, clouds, and radiation in a perturbed parameter ensemble of the UK Earth System Model and evaluate 1 million model variants (different parameter settings from Gaussian process emulators) against satellite-derived observations over several cloudy regions. Our analysis of a very large set of model variants exposes model internal inconsistencies that would not be apparent in a small set of model simulations, of an order that may be evaluated during model-tuning efforts. Incorporating observations associated with these inconsistencies weakens any forcing constraint because they require a wider range of parameter values to accommodate conflicting information. We show that, by neglecting variables associated with these inconsistencies, it is possible to reduce the parametric uncertainty in global mean aerosol forcing by more than 50 %, constraining it to a range (around −1.3 to −0.1 W m−2) in close agreement with energy balance constraints. Our estimated aerosol forcing range is the maximum feasible constraint using our structurally imperfect model and the chosen observations. Structural model developments targeted at the identified inconsistencies would enable a larger set of observations to be used for constraint, which would then very likely narrow the uncertainty further and possibly alter the central estimate. Such an approach provides a rigorous pathway to improved model realism and reduced uncertainty that has so far not been achieved through the normal model development approach.

Fully Distributed Algorithm for Resource Allocation Over Unbalanced Directed Networks Without Global Lipschitz Condition

This note investigates the distributed optimal resource allocation problem of multi-agent systems over unbalanced directed networks under the relaxed condition that the gradients of local cost functions are locally Lipschitz. The objective is to cooperatively drive the decision variables of the agents to the optimal solution, which minimizes the sum of the local cost functions, while ensuring that the network resource constraints and local feasibility constraints are satisfied. A novel distributed algorithm is developed over unbalanced directed network topologies based on the topology balancing technique and adaptive control approach. The developed algorithm is fully distributed in the sense that it depends on neither the global Lipschitz continuity of the gradients nor prior global information about the network connectivity. By regarding the proposed algorithm as a perturbed system, its input-to-state stability with a vanishing perturbation is first established, and asymptotic convergence of the decision variables toward the optimal solution is then proved. The effectiveness of the proposed fully distributed algorithm is illustrated with two examples.

Differential Flatness-Based Real-Time Trajectory Planning for Multihelicopter Cooperative Transportation in Crowded Environments

Trajectory planning for a multihelicopter transportation system requires optimizing numerous variables while considering obstacle avoidance, formation shape change, multibody dynamics and other feasibility constraints, making it challenging to achieve real-time effectiveness and convergence. To overcome this issue, a real-time trajectory planning method based on differential flatness and a minimum control effort (MINCO) trajectory expression is proposed. This method enables the implicit consideration of dynamic constraints and formation shape change requirements, and it handles obstacle avoidance and feasibility constraints linearly, reducing the complexity of planning. Specifically, the flatness characteristics and related assumptions of the system are given in detail by considering two cases where the load is modeled as a mass point or a rigid body. The obstacle avoidance trajectory planning problem is transformed into an unconstrained optimization problem based on MINCO and its spatial–temporal deformation. This optimization aims to minimize the trajectory energy and total time consumption while considering cost functions related to load obstacle avoidance, load state feasibility, helicopter obstacle avoidance, swarm avoidance between helicopters, cable obstacle avoidance, and cable force feasibility constraints. Finally, simulations are conducted in both cases where the load is modeled as a mass point and a rigid body to verify the feasibility of the proposed method. Overall, the proposed method has the potential to solve the problem of trajectory planning with obstacle avoidance in a multihelicopter transportation system in real time with improved efficiency and effectiveness.

Multi-source motion constrained model predictive control for tractor-trailer trucks with coupled dynamics

This paper proposes a constrained model predictive control (MPC) for tractor-trailer trucks with the complicated physical characteristics, where motion constraints can be considered to govern the vehicle maneuver. Firstly, a targeted theoretical derivation method is developed to establish a more accurate nonlinear model for articulated vehicles, with expressly considering the articulation coupling effects. As an essential basis, the kinematic coupling behavior is further investigated. Secondly, multi-source motion constraints are introduced in particular with the analysis of nonholonomic constraints on the underactuated trailer: (i) keeping trucks traveling in the feasible domain away from collision; (ii) maintaining the vehicle states in a stable field through the steady-state response and side-slip thresholds. Thirdly, a constrained MPC controller is constructed for the automatic tracking operation, wherein vehicle demands of position security and yaw stability will be taken into reasonable consideration. For this purpose, vehicle states information can be fully utilized in a parallel approach to optimize quadratic programming (QP) in MPC: model prediction and updated constraints. In the end, the contrasted-simulation analysis is carried out to verify the accuracy of derived model and effectiveness of the designed controller, along with the feasibility of the additive multi-source constraints.

End-to-End Learning for Optimization via Constraint-Enforcing Approximators

In many real-world applications, predictive methods are used to provide inputs for downstream optimization problems. It has been shown that using the downstream task-based objective to learn the intermediate predictive model is often better than using only intermediate task objectives, such as prediction error. The learning task in the former approach is referred to as end-to-end learning. The difficulty in end-to-end learning lies in differentiating through the optimization problem. Therefore, we propose a neural network architecture that can learn to approximately solve these optimization problems, particularly ensuring its output satisfies the feasibility constraints via alternate projections. We show these projections converge at a geometric rate to the exact projection. Our approach is more computationally efficient than existing methods as we do not need to solve the original optimization problem at each iteration. Furthermore, our approach can be applied to a wider range of optimization problems. We apply this to a shortest path problem for which the first stage forecasting problem is a computer vision task of predicting edge costs from terrain maps, a capacitated multi-product newsvendor problem, and a maximum matching problem. We show that this method out-performs existing approaches in terms of final task-based loss and training time.

Assessing feasibility of design constraints for mills in planning and scheduling of cold rolling: A case of steel industry

Assessing feasibility of design constraints for mills in planning and scheduling of cold rolling: A case of steel industry

Is Approximation of an Ideal Defensible?

What role does our knowledge about the ideal society play in guiding policymaking in the real world? One intuitive answer is to approximate. Namely, we have a duty to approximate the ideal within the relevant constraints of feasibility. However, political philosophers seem to have what might be called ‘approximatophobia'. Many philosophers, including idealists such as David Estlund, warn against approximation. Their criticism is chiefly motivated by ‘the problem of second best’, which points out that your second-best option may not be closest to your best option. This paper aims to dispel ‘approximatophobia'. The difficulty posed by the problem of second best is often overstated. More positively, I present a novel defence of approximation, arguing that approximation of an ideal can be a reasonably reliable default strategy of action guidance in the real world. Difficulties that may afflict the project of approximation can be mitigated by sophistication of the project of approximation. After showing that critics of approximation overstep their mark in issuing the strong or moderate warning against approximation, I propose an account of sophisticated approximation. It seeks a series of reforms that make existing social institutions closer to the ideal based on careful selection of frame of analysis. Three virtuous correlations are identified as indicators for successful project of approximation, linking descriptive similarity to desirability, feasibility and knowledge of the ideal. I also explain a two-staged strategy of sophisticating the way you approximate the ideal, with an expected positive feedback effect.

A new solution approach for non-convex combined heat and power economic dispatch problem considering power loss

The combined heat and power economic dispatch (CHPED) problem is a non-convex multivariate global optimization problem. The objective of the problem is to reduce total production costs while imposing a variety of constraints and meeting the demand for power and heat. Three recently presented metaheuristic approaches, Slime Mould Algorithm (SMA), COOT algorithm and Marine Predators Algorithm (MPA), are applied for solving CHPED problem. Studies dealing with the CHPED problem in the literature often do not consider valve points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, all at once. Furthermore, power losses are neglected especially in large-scale problems. In this study, the CHPED problem is solved by considering all operational constraints including active power transmission losses. Three separate case studies with dimensions of 11 units, 48 units, and 96 units were used in the tests under various limitations. The experimental results revealed that MPA outperformed not only SMA, and COOT but also the algorithms proposed previously in the literature.

Physics-assisted reduced-order modeling for identifying dominant features of transonic buffet

Transonic buffet is a flow instability phenomenon that arises from the interaction between the shock wave and the separated boundary layer. This flow phenomenon is considered to be highly detrimental during flight and poses a significant risk to the structural strength and fatigue life of aircraft. Up to now, there has been a lack of an accurate, efficient, and intuitive metric to predict buffet and impose a feasible constraint on aerodynamic design. In this paper, a Physics-Assisted Variational Autoencoder is proposed to identify dominant features of transonic buffet, which combines unsupervised reduced-order modeling with additional physical information embedded via a buffet classifier. Specifically, four models with various weights adjusting the contribution of the classifier are trained so as to investigate the impact of buffet information on the latent space. Statistical results reveal that the buffet state can be determined exactly with just one latent space when a proper weight of classifier is chosen. The dominant latent space further reveals a strong relevance with the key flow features located in the boundary layers downstream of shock. Based on this identification, the displacement thickness at 80% chordwise location is proposed as a metric for buffet prediction. This metric achieves an accuracy of 98.5% in buffet state classification, which is more reliable than the existing separation metric used in design. The proposed method integrates the benefits of feature extraction, flow reconstruction, and buffet prediction into a unified framework, demonstrating its potential in low-dimensional representations of high-dimensional flow data and interpreting the “black box” neural network.

Minimum conflict consensus models for group decision-making based on social network analysis considering non-cooperative behaviors

Decision makers (DMs) may exhibit non-cooperative behaviors such as deviating from recommendations or making only minor modifications in consensus-based group decision-making (GDM) problems. These non-cooperative behaviors will lead to high intra-group conflicts and low consensus efficiency. This paper designs a budget-constrained consensus framework with minimum group conflict based on social network analysis to address non-cooperative behaviors. First, the conflict degrees among DMs are quantified by opinion discrepancies and asymmetric 2-tuple linguistic trust values. Then, DMs’ weights are derived by considering degree centrality and node strength indices in the constructed conflict network. To obtain a feasible budget constraint for the consensus, the non-linear optimization models considering non-cooperative behaviors are proposed. Furthermore, two kinds of minimum conflict consensus models are established to deal with general and completely non-cooperative DMs, respectively. The existence of the optimal solutions of these consensus models and the convergence of the consensus reaching process are proved. Finally, the proposed consensus models are illustrated by an example of the negotiation of the sewage discharge standards. Compared with the consensus models based on minimum cost or adjustment, the proposed consensus models could achieve higher consensus and lower group conflict.

Barriers to powering past coal: Implications for a just energy transition in South Africa

The feasibility of South Africa's just energy transition, as dictated by the speed of phasing out coal and scaling up renewables, will rest on a range of techno-economic, socio-political, and socio-technical factors. Interactions between these dimensions of the transition carry significant implications for energy justice. In response, this paper proposes the Just Transition Feasibility Framework (JTFF) to better evaluate how feasibility constraints may impact South Africa's energy transition ambitions, and its more recent commitments to energy justice. Drawing on qualitative findings from interviews with South African energy experts, the study provides critical insights on the national- and community-scale implications of current energy policies. The analysis highlights socio-political constraints related to the Renewable Independent Power Producer Programme (REI4P) which aggravate energy vulnerabilities and misrecognition of places. In addition to strategically tackling a range of techno-economic and socio-technical constraints which are seen to exacerbate distributive injustice, the South African government should extend the 50 km radius scheme of the REI4P to a wider and more inclusive regional basis. Foremost, policy interventions must seek to realign South Africa's Minerals Energy Complex towards a just transition pathway committed to renewable electrification, community empowerment, and sustainable socio-economic structures.

Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

We study combinatorial auctions with interdependent valuations, where each agent i has a private signal si that captures her private information and the valuation function of every agent depends on the entire signal profile, [Formula: see text]. The literature in economics shows that the interdependent model gives rise to strong impossibility results and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single-item auctions or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed single crossing (or variants thereof). We consider the class of submodular over signals (SOS) valuations (without imposing any single crossing-type assumption) and provide the first welfare approximation guarantees for multidimensional combinatorial auctions achieved by universally ex post incentive-compatible, individually rational mechanisms. Our main results are (i) four approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; (ii) four approximation for any combinatorial auction with multidimensional signals and separable-SOS valuations; and (iii) (k + 3) and (2 log(k) + 4) approximation for any combinatorial auction with single-dimensional signals, with k-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, d-approximate SOS, while losing a factor that depends on d. Funding: A. Eden was partially supported by NSF Award IIS-2007887, the European Research Council (ERC) under the European Union's Seventh Framework Programme [FP7/2007-2013]/ERC Grant Agreement 337122, by the Israel Science Foundation [Grant 317/17], and by an Amazon research award. M. Feldman received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program [Grant Agreement 866132], by the Israel Science Foundation [Grant 317/17], by an Amazon research award, and by the NSF-BSF [Grant 2020788]. The work of K. Goldner was supported partially by NSF awards DMS-1903037 and CNS-2228610 and a Shibulal Family Career Development Professorship. A. R. Karlin was supported by the NSF-CCF [Grant 1813135].

Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization

This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. The goal of the network is to minimize the network-wide loss accumulated over time. Two distributed online algorithms with full-information and bandit feedback are proposed. Both dynamic and static network regret bounds are analyzed for the proposed algorithms, and network cumulative constraint violation is used to measure constraint violation, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. In particular, we show that the proposed algorithms achieve $\mathcal{O}(T^{\max\{\kappa,1-\kappa\}})$ static network regret and $\mathcal{O}(T^{1-\kappa/2})$ network cumulative constraint violation, where $T$ is the time horizon and $\kappa\in(0,1)$ is a user-defined trade-off parameter. Moreover, if the loss functions are strongly convex, then the static network regret bound can be reduced to $\mathcal{O}(T^{\kappa})$. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

The Feasibility of Animal-Based Indicators of Consciousness and Unconsciousness for Stunning in Sheep: A Systematic Review.

According to EU legislation, animal-based indicators (ABMs) are used to evaluate the efficacy of stunning methods to ensure that animals do not regain consciousness. EFSA has provided a list of ABMs for electrical and mechanical stunning in sheep; however, there is still a lack of information on their feasibility. We aimed to identify and evaluate the feasibility constraints of ABMs commonly applied in slaughterhouses to assess proper stunning in sheep. For this systematic review, we searched the Scopus and Web of Science databases from 2000 to 8 August 2022, including full peer-reviewed papers written in English on the welfare of sheep at the stunning and restraint phases. We excluded studies using a gas stunning method or without prior stunning, as well as manuscripts in which indicators were applied after sticking. Of 1289 records identified, only 8 papers were eligible for the critical evaluation of physical aspects that affect the feasibility of ABMs. These aspects were defined as a given definition of the feasibility of ABMs, and information was summarized and critically evaluated. The results highlighted a lack of information on the feasibility of ABMs which should be considered in the various conditions of commercial slaughterhouses.

Designing Human-centered AI for Mental Health: Developing Clinically Relevant Applications for Online CBT Treatment

Recent advances in AI and machine learning (ML) promise significant transformations in the future delivery of healthcare. Despite a surge in research and development, few works have moved beyond demonstrations of technical feasibility and algorithmic performance. However, to realize many of the ambitious visions for how AI can contribute to clinical impact requires the closer design and study of AI tools or interventions within specific health and care contexts. This article outlines our collaborative, human-centered approach to developing an AI application that predicts treatment outcomes for patients who are receiving human-supported, internet-delivered Cognitive Behavioral Therapy (iCBT) for symptoms of depression and anxiety. Intersecting the fields of HCI, AI, and healthcare, we describe how we addressed the specific challenges of (1) identifying clinically relevant AI applications ; and (2) designing AI applications for sensitive use contexts like mental health. Aiming to better assist the work practices of iCBT supporters, we share how learnings from an interview study with 15 iCBT supporters surfaced their practices and information needs and revealed new opportunities for the use of AI. Combined with insights from the clinical literature and technical feasibility constraints, this led to the development of two clinical outcome prediction models. To clarify their potential utility for use in practice, we conducted 13 design sessions with iCBT supporters that utilized interface mock-ups to concretize the AI output and derive additional design requirements. Our findings demonstrate how design choices can impact interpretations of the AI predictions as well as supporter motivation and sense of agency. We detail how this analysis and the design principles derived from it enabled the integration of the prediction models into a production interface. Reporting on identified risks of over-reliance on AI outputs and needs for balanced information assessment and preservation of a focus on individualized care, we discuss and reflect on what constitutes a responsible, human-centered approach to AI design in this healthcare context.

On Fair Division under Heterogeneous Matroid Constraints

We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints or allow free disposal of items. An open problem is the existence of EF1 complete allocations among agents who differ both in their valuations and in their feasibility constraints. In this work, we make progress on this problem by providing positive and negative results for several matroid and valuation types. Among other results, we devise polynomial-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous (non-identical) binary valuations and partition matroids with heterogeneous capacities; (ii) two agents with heterogeneous additive valuations and partition matroids with heterogeneous capacities; and (iii) three agents with heterogeneous binary valuations and identical base-orderable matroid constraints.

Energy-efficient lane-change motion planning for personalized autonomous driving

With the aim of realizing energy-efficient, personalized, and safe mobility, a novel lane-changing motion planning strategy for personalized energy-efficient autonomous driving is proposed in this research. The key technologies consist of trajectory planning and trajectory tracking. Taking the quintic polynomials as the general trajectory cluster generator, the overall trajectory planning is converted into a constrained optimization problem using the lane-changing duration. The feasible and safe lane-changing trajectories can be extracted from the general trajectory cluster by introducing a stable handling envelope and a safe lane-changing area considering the constraints of vehicle dynamics limitation and surrounding traffic vehicles. A driving style identification module is developed based on multi-class Gaussian process classification utilizing real driving data to determine the trajectories that can characterize personalized features. Reflecting the constraints of feasibility, safety, and personalization on the boundaries of lane-changing duration, an energy-optimal lane-changing trajectory representing a specific driving style can be found and regarded as a reference. To precisely and rapidly control the vehicle to track the reference trajectory, a real-time nonlinear model predictive controller is designed and solved utilizing the parallel method. The algorithms proposed above are integrated and Driver-in-the-Loop experimental verifications are conducted. Experiment results demonstrated that the proposed strategy is able to realize lane change with an energy saving rate of 2.87% to 5.73% compared with human drivers’ maneuver. Comparative simulation with a typical automatic lane-change model also shows the effectiveness of the proposed approach, which is capable of not only accomplishing the energy-efficient lane change but also satisfying human driver’s personalized driving preferences.

Constrained expectation-maximisation for inference of social graphs explaining online user–user interactions

Current network inference algorithms fail to generate graphs with edges that can explain whole sequences of node interactions in a given dataset or trace. To quantify how well an inferred graph can explain a trace, we introduce feasibility, a novel quality criterion, and suggest that it is linked to the result’s accuracy. In addition, we propose CEM-*, a network inference method that guarantees 100% feasibility given online social media traces, which are a non-trivial extension of the Expectation-Maximization algorithm developed by Newman (Nature Phys 14:67–75, 2018). We propose a set of linear optimization updates that incorporate a set of auxiliary variables and a set of feasibility constraints; the latter takes into consideration all the hidden paths that are possible between users based on their timestamps of interaction and guides the inference toward feasibility. We provide two CEM-* variations, that assume either an Erdős–Rényi (ER) or a Stochastic Block Model (SBM) prior for the underlying graph’s unknown distribution. Extensive experiments on one synthetic and one real-world Twitter dataset show that for both priors CEM-* can generate a posterior distribution of graphs that explains the whole trace while being closer to the ground truth. As an additional benefit, the use of the SBM prior infers and clusters users simultaneously during optimization. CEM-* outperforms baseline and state-of-the-art methods in terms of feasibility, run-time, and precision of the inferred graph and communities. Finally, we propose a heuristic to adapt the inference to lower feasibility requirements and show how it can affect the precision of the result.

Model predictive control for path tracking in cable driven parallel robots with flexible cables: collocated vs. noncollocated control

This paper proposes a novel control scheme for precise path tracking control in cable driven parallel robots (CDPRs) with axially-flexible cables, with particular focus to the challenging case of cable suspended parallel robots (CSPRs). To handle model nonlinearities while ensuring small computational effort, a controller made by two sequential control actions is developed. The first term is a position-dependent, model predictive control (MPC) with embedded integrator to compute the optimal cable tensions ensuring accurate path tracking and fulfilling the feasibility constraints; bounds on the feasible tensions are also included. The second control term transforms the optimal tensions into the commanded motor torques, and hence currents, that are evaluated through the kinetostatic model of the electric motors used for winding and unwinding the cables. Control design is performed through the robot dynamics model, formulated with the assumption of rigid cables. Moreover, the proposed control strategy is presented in two different architectures, collocated control and noncollocated control. Flexibility is handled by penalizing large tension variations in the cost function adopted in the controller design, plus some hard constraints on the maximum tension derivatives. These features, together with the embedding of the integrator within the MPC formulation, ensure smooth control tensions that allow handling the axial flexibility of the cables, although it is not explicitly considered in the controller design.To assess the performances of the proposed control algorithm, a kinematically-determined robot with a suspended, lumped end-effector is simulated by also adopting very flexible cables. Additionally, a simplified dynamic model of the electrical dynamics and the sensor quantization are included to provide a realistic representation of the real environments. The results, together with the fair comparison with a benchmark, corroborate the effectiveness of the proposed approach, its robustness, and its feasibility in real-time controllers due to the wise reduction of the computational effort.