Constraints Of Problem Research Articles

Solvi: A visual constraint modeling tool

Discrete constraint problems surface often in everyday life. Teachers might group students with complex considerations and hospital administrators need to produce staff rosters. Constraint programming (CP) provides techniques to efficiently find solutions. However, there remains a key challenge: these techniques are still largely inaccessible because expressing constraint problems requires sophisticated programming and logic skills. In this work we contribute a language and tool that leverage knowledge of how non-experts conceptualize problems to facilitate the expression of constraint models. Additionally, we report the results of a study surveying the advantages and remaining challenges towards making CP accessible to the wider public.

Combined non-convex second-order total variation with overlapping group sparsity for full waveform inversion

Full waveform inversion (FWI) can provide an accurate velocity model by matching observed and simulated seismograms. Mathematically, FWI is a highly ill-posed inverse problem that the observed data are independent of the model and cannot be inverted accurately. For a stable and reasonable inversion, proper regularization methods have to be taken into account. We propose a novel composite regularization for frequency-domain FWI problem, which uses a non-convex second-order total variation (TV) term and an overlapping group sparse TV (OGS-TV) regularization term. Compared with the conventional TV regularization, our method has better accuracy and robustness, and could effectively make use of the sparsity in the velocity model. Furthermore, the alternating direction multiplier algorithm with the adaptive selection of the penalty parameters is developed to solve this composite constraint problem, which can improve the stability of the FWI process. To illustrate the superior method both visually and quantitatively, we experimentally compare the proposed method with the conventional TV regularized FWI and the second-order total generalized variation regularized FWI and overlapping group sparsity regularized FWI on the well-known geological models.

Node depth Representation-based Evolutionary Multitasking Optimization for Maximizing the Network Lifetime of Wireless Sensor Networks

Wireless Sensor Networks (WSNs) face challenges related to limited energy resources in sensor nodes, making network lifetime and energy consumption critical considerations. In this paper, we introduce a novel approach to extend network lifetime and reduce energy consumption in WSNs by optimizing network architecture selection. We explore various architecture options, including single-layer and multi-layer networks, to determine the most suitable configuration. Several studies have applied knowledge transfer in evolutionary multitasking optimization to maximize network lifetime, achieving state-of-the-art results for the problem. However, they still have some drawbacks, such as redundant representations, i.e., many genotypes represent the same phenotype, and invalid solution generation. To address these limitations, we propose a new evolutionary multitasking algorithm incorporating efficient encoding to represent tree-structure solutions (network architectures) to the problem. Additionally, we tailor new genetic operators, such as recombination and mutation, to meet the specific requirements of our proposed evolutionary multitasking algorithm. The standout feature of our proposal lies in its ability to consistently generate valid solutions for the problem, which significantly reduces redundancy within the genotype search space and effectively satisfies the problem constraints. Additionally, our multitask evolutionary algorithm facilitates the exploration of various network architectures, harnessing knowledge transfer to enhance optimal performance and reduce computation time compared to single-task methods. We conduct comprehensive experiments on diverse datasets and use statistical tests, e.g., the Wilcoxon signed rank test, to verify the performance of our proposed algorithms. The empirical results demonstrate that our proposed algorithm outperforms existing methods and achieves state-of-the-art results in terms of solution quality, convergence rate, and running time across a wide range of data instances. Specifically, our algorithm provides 49.54% better solution quality on average across all data types compared to the previous state-of-the-art method.

On inequality constraints in well-known optimisation problems: properties and applications

This work studies transportation, assignment, transshipment, shortest path, and dynamic lot sizing problems. Particularly, it shows how to modify their formulations to handle excess supply and node elimination. The paper proceeds by using the conservation of flow to derive the original constraints of these problems. Thereafter, a general form of the conservation of flow is used to reformulate these problems. The results are problems with inequality constraints. This paper shows that solving each of these new formulations returns the same optimal solution as its original form. It also shows how problems with inequality constraints can handle excess supply and node elimination. Along the way, some additional properties of these alternative formulations are explored.

Shifting and state transformations-based adaptive tracking control for deferred full state-constrained uncertain nonlinear systems

This paper concerns the tracking control problem of a class of uncertain nonlinear systems subject to deferred time-varying state constraints and external disturbances. The states of the system are free in the initial phase and are restricted by some time-varying constraints after a particular time. A class of novel shifting functions are defined, which make any initial states that beyond the constraint region move to the desired position (such as zero). Thereafter, a new state transformation is implemented for the shifted state, which transforms the state constraint problem into the boundedness of a new variable. Compared with the existing BLF method, this approach avoids feasibility test for virtual control variables. Adaptive backstepping control and dynamic surface control are used in system controller design and stability analysis, and the ideal tracking performance is achieved. Finally, simulation example and comparative studies are carried out to illustrate the effectiveness and outstanding characteristics of the proposed approach. Simulation results show that the proposed control scheme broadens the scope of application, shortens running time and improves control efficiency compared with the existing control strategies.

Complexity and algorithm of setting optimal location for data sink in real-time NOMA-based IIoTs

Real-time performance is one of the most vital metrics in Non-Orthogonal Multiple Access (NOMA) based Industrial Internet of Things (IIoTs) applications. Since the relative geographic relationship between data sink and wireless sensors affects the transmission parallelism and thus the real-time performance, setting a reasonable location for the data sink is thus a feasible way to high real-time performance for applications where the locations of wireless sensors are fixed. In this paper, we consider how to find an optimal location for the data sink to minimize average access delay. We first formulate the problem and prove it to be NP-Complete by presenting an original reduction proof from classic set partition problem. Second, by tightening the NOMA decoding constraint of the original problem, a heuristic algorithm, which is designed based on Apollonian Circle Theorem and Dilworth Theorem, obtains a feasible location for the data sink. Simulation results reveal that the real-time performance loss of the heuristic algorithm is no more than 50% of the best one. Compared with the classic TDMA scheme, the real-time performance increases by more than 60% for some typical settings, and it can even reach 70% for the linear network topology, owing to the full exploitation of NOMA parallelism.

Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors.

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.

A reverse chain search algorithm for the resource constraint in deep space detectors

Deep space exploration activities can effectively promote the development and application of space technology, which holds significant scientific and strategic value. Detectors operating in deep space are of long mission periods and substantial distance from Earth, posing challenges in timely resource replenishment. Moreover, scheduled missions may face external uncertainties, hindering their smooth execution. Therefore, resource constraint processing strategies that possess dynamic adjustment capabilities play a crucial role in ensuring the successful execution of deep space detectors. Existing methods mainly focus on studying fixed mission sequences, and the efficiency of planning methods is not high. Specifically, the single uncertainty is only considered, and there is a lack of detection and processing mechanisms, rendering the requirements of deep space detectors inadequate. In this paper, we propose a reverse chain search algorithm, aiming to efficiently plan missions subject to resource constraints and let the mission sequence to possess a certain degree of dynamic repair capability. The results have demonstrated that the resource allocated to each mission is within the resource value range. Compared with the classic algorithm, the proposed algorithm has fewer iterations and whose maximum flow value is accurate. Meanwhile, the potential resource constraints problem during execution can be alerted with the detection and warning system. The missions that were warned are repaired by a dynamic resource repair system, and the proposed algorithm is of higher efficiency and a certain ability to resist external uncertainties. Overall, this paper lays a solid foundation for the processing of resource constraints for deep space detectors.

A Novel Asynchronous Sliding Mode Design for Switched Systems under Input–Output Finite-Time Stability

In this work, the input–output finite-time stability (IO-FTS) of a class of continuous-time switched systems characterized by uncertainties and subjected to external disturbances is studied under asynchronous switching by means of the sliding mode control (SMC) method. The IO-FTS poses a finite-time constraint problem, which involves addressing two main issues: firstly, ensuring that the state trajectory of the switched system reaches the given sliding mode surface within the specified time, and secondly, achieving IO-FTS for the closed-loop switched system during asynchronous switching. To address these issues, we apply a partitioning strategy and construct asynchronous sliding mode controllers with adjustable parameters to ensure the reachability of the system’s state trajectory within a finite time. Subsequently, we employ a multiple Lyapunov function (MLF) approach to provide sufficient conditions that ensure IO-FTS during the whole phase [0,T] for the resulting switched system. Additionally, we analyze the asynchronous characteristics concerning the reachability phase of the designed sliding surface, considering the system’s switching properties. Finally, we demonstrate the efficacy of the proposed approach with a numerical example.

Bayesian and Classical Semi-parametric Estimation of the Balanced Longitudinal Data Model

The primary objective of this study is to employ semi-parametric regression techniques in the balanced longitudinal data model. Where the parametric regression models are plagued by the problem of strict constraints, while non-parametric regression models, despite their flexibility, suffer from the problem of the curse of dimensionality. Consequently, semi-parametric regression presents a suitable solution to address the problems in parametric and non-parametric regression methods. The advantage of this model is that it contains all the positive properties included in the previous two models such as containing strict restrictions in its parametric component, complete flexibility in its non-parametric component, and clarity of the interaction between its parametric and non-parametric components. According to the above, two methods were used to estimate a semi-parametric balanced longitudinal data model. The first is the Bayesian estimating method; the second is the Speckman method, which estimated the unknown nonparametric smoothing function by employing the kernel smoothing Nadaraya & Watson method. The Aim was to make a comparison between the Bayesian estimation method and the classical estimation method. Based on simulation experiments conducted on three different sample sizes (50, 100, and 200), it was concluded that the Bayes method is best at the variance levels (1,5). In contrast, the Profile least square method is best at the variance level (10).

Weighted tardiness minimisation for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimisation. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times, and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component – vital to guarantee the non-violation of the problem's constraints – which optimally allocates resources with respect to tardiness minimisation. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure are revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight due dates, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights.

Integral BLF-Based Adaptive Neural Constrained Regulation for Switched Systems With Unknown Bounds on Control Gain.

In this article, an integral barrier Lyapunov-function (IBLF)-based adaptive tracking controller is proposed for a class of switched nonlinear systems under the arbitrary switching rule, in which the unknown terms are approximated by radial basis function neural networks (RBFNNs). The IBLF method is used to solve the problem of state constraint. This method constrains states directly and avoids the verification of feasibility conditions. In addition, a completely unknown control gain is considered, which makes it impossible to directly apply previous existing methods. To offset the effect of the unknown control gain, the lower bound of the control gain is added into the barrier Lyapunov function, and a regulating term is introduced into the controller. The proposed control strategy realizes three control objectives: 1) all the signals in the resulting system are bounded; 2) the system output tracks the reference signal to a arbitrarily small compact set; and 3) all the constraint conditions for system states are not violated. Finally, a simulation example is used to show the effectiveness of the proposed method.

Explicit Linear Model of Bus Impedance With Unknown Branch Status

This letter presents an accurate and explicit linear model of bus impedance for a power network with unknown branch status. Firstly, an equivalent network of the power network is constructed, and the relationship between bus voltage and bus impedance is established. Then, the linear expression of bus impedance with unknown branch status is built. This model can be easily included as constraints in various optimization problems with network topology adjustment involving short circuit calculation.

An efficiency-based interactive dynamic technique with interval-valued hesitant fuzzy constraint cone for rescue route planning

This paper develops an efficiency-based interactive dynamic technique to design the post-disaster rescue route by combining the data envelopment analysis (DEA), traveling salesman problem (TSP) and interval-valued hesitant fuzzy constraint cone (IVHFCC). The traditional DEA potentially presumes that the weights of the input (output) criteria are unrestricted, resulting in its inapplicability to some complex decision problems. To restrict the weights of input (output) criteria legitimately, this paper constructs an IVHFCC based on expert’s subjective preferences in the form of interval-valued hesitant fuzzy sets. This paper defines the additive consistent normal interval-valued hesitant fuzzy preference relation (NIVHFPR) and analyses its desirable properties. Based on these properties, three linear programming models are proposed to repair the incomplete NIVHFPR, judge the additive consistency of the repaired NIVHFPR and generate the additive consistent NIVHFPR. By incorporating the TSP, DEA and the constructed IVHFCC, an efficiency-based interactive dynamic model is originally proposed to generate the optimal rescue route for the rescue team. Some desirable properties of this efficiency-based interactive dynamic model are analyzed. The validity of this model is demonstrated with a real post-disaster rescue route planning problem of Wenchuan earthquake. Some comparative analyses are provided to show the superiorities of the proposed technique.

Route optimization via improved ant colony algorithm with graph network

<p>Route optimization problem using vehicle routing problem (VRP) and time window constraint is explained as finding paths for a finite count of vehicles to provide service to a huge number of customers and hence, optimizing the path in a given duration of the time window. The vehicles in the loop have restricted intake of capacity. This path initiates from the depot, delivers the goods, and stops at the depot. Each customer is to serve exactly once. If the arrival of the vehicle is before the time window “opens” or when the time window “closes,” there will be waiting for cost and late cost. The challenge involved over here is to scheduling visits to customers who are only available during specific time windows. Ant colony optimization (ACO) algorithm is a meta-heuristic algorithm stimulated by the growing behaviour of real ants. In this paper, we combine the ACO algorithm with graph network henceforth increasing the number of vehicles in a particular depot for increasing the efficiency for timely delivery of the goods in a particular time width. This problem is solved by, an efficient technique known as the ACO+graph algorithm.</p>

Longitudinal and lateral stability control for autonomous vehicles in curved road scenarios with road undulation

PurposeThis research aims to present a novel cooperative control architecture designed specifically for roads with variations in height and curvature. The primary objective is to enhance the longitudinal and lateral tracking accuracy of the vehicle.Design/methodology/approachIn addressing the challenges posed by time-varying road information and vehicle dynamics parameters, a combination of model predictive control (MPC) and active disturbance rejection control (ADRC) is employed in this study. A coupled controller based on the authors’ model was developed by utilizing the capabilities of MPC and ADRC. Emphasis is placed on the ramifications of road undulations and changes in curvature concerning control effectiveness. Recognizing these factors as disturbances, measures are taken to offset their influences within the system. Load transfer due to variations in road parameters has been considered and integrated into the design of the authors’ synergistic architecture.FindingsThe framework's efficacy is validated through hardware-in-the-loop simulation. Experimental results show that the integrated controller is more robust than conventional MPC and PID controllers. Consequently, the integrated controller improves the vehicle's driving stability and safety.Originality/valueThe proposed coupled control strategy notably enhances vehicle stability and reduces slip concerns. A tailored model is introduced integrating a control strategy based on MPC and ADRC which takes into account vertical and longitudinal force variations and allowing it to effectively cope with complex scenarios and multifaceted constraints problems.

Discrete optimal designs for distributed energy systems with nonconvex multiphase optimal power flow

The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. There is a significant lack of studies on how DES designs, especially those with electrified heating systems, impact unbalanced low-voltage distribution networks to which most DES are connected. This is the first study to present an optimisation framework for obtaining discrete technology sizing and selection for grid-connected DES design, while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution networks. An algorithm is developed to solve the resulting Mixed-Integer Nonlinear Programming (MINLP) formulation. It employs a decomposition based on Mixed-Integer Linear Programming (MILP) and Nonlinear Programming (NLP) and uses integer cuts and complementarity reformulations to obtain discrete designs that are also feasible with respect to the network constraints. A heuristic modification to the original algorithm is also proposed to improve computational speed. Improved formulations for selecting feasible combinations of air source heat pumps (ASHPs) and hot water storage tanks are also presented. Two networks of varying size are used to test the optimisation methods. Designs with electrified heating (ASHPs and tanks) are compared to those with conventional gas boilers. The algorithms outperform one of the existing state-of-the-art commercial deterministic MINLP solvers, which fails to find any solutions in two instances within specified time limits. While feasible solutions were obtained for all cases, convergence was not achieved for all, especially for those involving the larger network. Where converged, the algorithm with the heuristic modification has achieved results up to 70% faster than the original algorithm. Results for case studies suggest that including ASHPs can support up to 16% higher renewable generation capacity compared to gas boilers, albeit with higher ASHP investment costs, as local generation and consumption minimises network violations associated with excess power export. The results also show the importance of including nonlinear power flow constraints in DES design problems. The optimisation framework and results can be used to inform stakeholders such as policymakers and network operators, to increase renewable energy capacity and aid the decarbonisation of domestic heating systems.

Application of data mining techniques for assessment of fracture load and energy in double cantilever beam solder joints

Predicting the exact values of fracture load and energy has a significant effect in preventing solder joint failure. In this research, various double cantilever beam (DCB) solder joints with different geometric constraints, including adherend thickness, adherend width, loading arm length, and solder thickness were tested under mode I crack propagation and at a strain rate of 0.03 . According to ANOVA test results, all the mentioned geometric factors influence the fracture load, but adherend width and solder thickness don't change the failure energy remarkably, considering the type I error is equal to 0.05. The failure load and energy forecasting using the random forest algorithm showed that the prediction accuracy is 92% and 81% respectively. Linear regression and lasso regression were also utilized to identify the solder joint's fracture behavior. The coefficient of determination in both methods is acceptable for solder joint fracture force prediction, but for fracture energy, it has decreased to about 70%. Finally, multi-objective optimization was done with the help of the NSGA-II method, and the Pareto front diagram drawn according to the problem's constraints to find the optimal values for fracture force and energy.

Fixed-time adaptive path-following control of autonomous surface vehicles with asymmetric output performance and feasibility constraints

This paper proposes a fixed-time adaptive path-following control scheme for autonomous surface vehicles (ASVs) to address accuracy and safety considerations in actual navigation practice. The proposed scheme is designed to effectively follow a reference path while satisfying output performance and feasibility constraints during navigation. For the output constraint problem, a modified version of the universal barrier Lyapunov function is used for the analysis of path-dependent constraint requirements. Additionally, a new type of path-dependent constraint function is proposed that depends on the path parameters rather than directly on the time variables. A new adaptive backstepping method is also devised to address the problem of fixed-time convergence, as well as the 'complexity explosion' in the controller design process, and the unknown dynamics of the model. The study shows that, under this control scheme, the ASV's position and heading errors can converge to a set near the equilibrium point at a fixed time convergence rate, while always satisfying the path-dependent constraints. Simulation and experimental studies further validate the effectiveness of the proposed scheme.

National-scale bi-directional EV fleet control for ancillary service provision

Deploying real-time control on large-scale fleets of electric vehicles (EVs) is becoming pivotal as the share of EVs over internal combustion engine vehicles increases. In this paper, we present a Vehicle-to-Grid (V2G) algorithm to simultaneously schedule thousands of EVs charging and discharging operations, that can be used to provide ancillary services. To achieve scalability, the monolithic problem is decomposed using the alternating direction method of multipliers (ADMM). Furthermore, we propose a method to handle bilinear constraints of the original problem inside the ADMM iterations, which changes the problem class from Mixed-Integer Quadratic Program (MIQP) to Quadratic Program (QP), allowing for a substantial computational speed up. We test the algorithm using real data from the largest carsharing company in Switzerland and show how our formulation can be used to retrieve flexibility boundaries for the EV fleet. Our work thus enables fleet operators to make informed bids on ancillary services provision, thereby facilitating the integration of electric vehicles.